| Seen Test (Topic: Italian Cuisine) | Unseen Test (Topic:Hunting) |
| ： A:I love chicken parmigiana as well, but I think my ultimate | ： W:That is true but we always have to watch out for excessive |
| favorite is beef lasagna...Extra cheese please! W: Chicken with sauce and mozzarella.. Be still my heart! A:Truthfully,anythingwith cheese is the best (Ours)ilove pizza too ！it'sa traditional italian dish | hunting. It has caused some species to be endangered. A:Yes Iagree.Idon't believe in the useless hunting that poachers do. Its so cruel. (Ours) iagree,poaching has been defined as the illegal hunting or |
| consisting of yeasted flatbread typically topped with tomato sauce and cheese (TMN) ilove cheese ! (E2E BERT+KL)i like mine topped with vegetables, meats, and condiments . (Human) especially cheddar cheese !it’s the second most | capturing of wild animals . (TMN)i thinks so,i’m not sure if you 're talking about poaching,but i know that poodles are the second most intelligent breed behind the poodle . (E2EBERT+KL)iagree.i think it’sa great way to catch fish . (Human) agreed,i remember reading one time that unless you |
+
+# 6 CONCLUSION
+
+This work investigated the issue of knowledge selection in multi-turn knowledge-grounded dialogue, and proposed a sequential latent variable model, for the first time, named sequential knowledge transformer (SKT). Our method achieved the new state-of-the-art performance on the Wizard of Wikipedia benchmark (Dinan et al., 2019) and a knowledge-annotated version of Holl-E dataset (Moghe et al., 2018). There are several promising future directions beyond this work. First, we can explore other inference models such as sequential Monte Carlo methods using filtering variational objectives (Maddison et al., 2017a). Second, we can study the interpretability of knowledge selection such as measuring the uncertainty of attention (Heo et al., 2018).
+
+# ACKNOWLEDGMENTS
+
+We thank Hyunwoo Kim, Chris Dongjoo Kim, Soochan Lee, Junsoo Ha and the anonymous reviewers for their helpful comments. This work was supported by SK T-Brain corporation and Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (No.2019-0-01082, SW StarLab). Gunhee Kim is the corresponding author.
+
+# REFERENCES
+
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+
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+
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+
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+Nikita Moghe, Siddhartha Arora, Suman Banerjee, and Mitesh M Khapra. Towards Exploiting Background Knowledge for Building Conversation Systems. In EMNLP, 2018.
+Prasanna Parthasarathi and Joelle Pineau. Extending Neural Generative Conversational Model using External Knowledge Sources. In EMNLP, 2018.
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+Lianhui Qin, Michel Galley, Chris Brockett, Xiaodong Liu, Xiang Gao, Bill Dolan, Yejin Choi, and Jianfeng Gao. Conversing by Reading: Contentful Neural Conversation with On-Demand Machine Reading. In ACL, 2019.
+Shiv Shankar and Sunita Sarawagi. Posterior Attention Models for Sequence to Sequence Learning. In ICLR, 2019.
+Zhihong Shao, Minlie Huang, Jiangtao Wen, Wenfei Xu, and Xiaoyan Zhu. Long and Diverse Text Generation with Planning-based Hierarchical Variational Model. In EMNLP, 2019.
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+Tsung-Hsien Wen, Yishu Miao, Phil Blunsom, and Steve Young. Latent intention dialogue models. In ICML, 2017.
+Yingce Xia, Fei Tian, Lijun Wu, Jianxin Lin, Tao Qin, Nenghai Yu, and Tie-Yan Liu. Deliberation Networks: Sequence Generation Beyond One-Pass Decoding. In NIPS, 2017.
+Zichao Yang, Zhiting Hu, Yuntian Deng, Chris Dyer, and Alex Smola. Neural Machine Translation with Recurrent Attention Modeling. In EACL, 2017.
+Semih Yavuz, Abhinav Rastogi, Guan-Lin Chao, and Hakkani-Tur Dilek. DeepCopy: Grounded Response Generation with Hierarchical Pointer Networks. In SIGDIAL, 2019.
+Saizheng Zhang, Emily Dinan, Jack Urbanek, Arthur Szlam, Douwe Kiela, and Jason Weston. Personalizing Dialogue Agents: I Have a Dog, Do You Have Pets Too? In ACL, 2018.
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+
+Wei Zhao, Liang Wang, Kewei Shen, Ruoyu Jia, and Jingming Liu. Improving Grammatical Error Correction via Pre-Training a Copy-Augmented Architecture with Unlabeled Data. In NAACLHLT, 2019a.
+
+Xueliang Zhao, Chongyang Tao, Wei Wu, Can Xu, Dongyan Zhao, and Rui Yan. A DocumentGrounded Matching Network for Response Selection in Retrieval-based Chatbots. In IJCAI, 2019b.
+
+Kangyan Zhou, Shrimai Prabhumoye, and Alan W Black. A Dataset for Document Grounded Conversations. In EMNLP, 2018.
+
+# A DERIVATION OF CONDITIONAL PROBABILITY
+
+In Section 3, we re-write the conditional probability of wizard’s response $\mathbf { y } ^ { t }$ given dialogue context $\mathbf { x } ^ { \leq t }$ and $\mathbf { y } ^ { < t }$ from Eq. (2) to Eq. (4). We can simply derive it as follows:
+
+p(y|x) (13)
+
+$$
+\begin{array} { l } { { = } \displaystyle \prod _ { t } \displaystyle \sum _ { \mathbf { k } ^ { \prime } } p _ { \theta } ( \mathbf { y } ^ { t } | \mathbf { x } ^ { \leq t } , \mathbf { y } ^ { < t } , \mathbf { k } ^ { \leq t } ) \pi _ { \theta } ( \mathbf { k } ^ { t } ) \quad \mathrm { ( b y ~ E q . ~ ( 2 ) ) } } \\ { { = \displaystyle \prod _ { i = 1 } ^ { t - 1 } \sum _ { \mathbf { k } ^ { \prime } } p _ { \theta } ( \mathbf { y } ^ { i } | \mathbf { x } ^ { \leq i } , \mathbf { y } ^ { < i } ) { \displaystyle p _ { \theta } ( \mathbf { k } ^ { i } ) } \Big ( \displaystyle \sum _ { \mathbf { k } ^ { t } } p _ { \theta } ( \mathbf { y } ^ { t } | \mathbf { x } ^ { \leq t } , \mathbf { y } ^ { < t } , \mathbf { k } ^ { \leq t } ) \pi _ { \theta } ( \mathbf { k } ^ { t } ) \Big ) \quad \mathrm { ( b y ~ B a y e s ' ~ n l e ) } } } \\ { { \approx \displaystyle \prod _ { i = 1 } ^ { t - 1 } \displaystyle \sum _ { \mathbf { k } ^ { i } } p _ { \theta } ( \mathbf { y } ^ { i } | \mathbf { x } ^ { \leq i } , \mathbf { y } ^ { < i } ) { q _ { \theta } ( \mathbf { k } ^ { i } ) } \Big ( \displaystyle \sum _ { \mathbf { k } ^ { t } } p _ { \theta } ( \mathbf { y } ^ { t } | \mathbf { x } ^ { \leq t } , \mathbf { y } ^ { < t } , \mathbf { k } ^ { \leq t } ) \pi _ { \theta } ( \mathbf { k } ^ { t } ) \Big ) } } \\ { { = \displaystyle \prod _ { i = 1 } ^ { t - 1 } \displaystyle \sum _ { \mathbf { k } ^ { t } } q _ { \phi } ( \mathbf { k } ^ { i } ) \Big ( \displaystyle \sum _ { \mathbf { k } ^ { t } } p _ { \theta } ( \mathbf { y } ^ { t } | \mathbf { x } ^ { \leq t } , \mathbf { y } ^ { < t } , \mathbf { k } ^ { t } ) \pi _ { \theta } ( \mathbf { k } ^ { t } ) \Big ) \quad \mathrm { ( x \leq t ~ a n d ~ \mathbf { y } ^ { < t } ~ a r e ~ g i v e n ) } } } \\ { { \approx p ( \mathbf { y } ^ { t } | \mathbf { x } ^ { \leq t } , \mathbf { y } ^ { < t } ) , } } \end{array}
+$$
+
+where $q _ { \phi } ( \mathbf { k } ^ { i } )$ is an approximated posterior distribution and $p _ { \theta } ( \mathbf { k } ^ { i } )$ is a true posterior distribution.
+
+# B TRAINING DETAILS
+
+All the parameters except pretrained parts are initialized with Xavier method (Glorot & Bengio, 2010). We use Adam optimizer (Kingma & Ba, 2015) with $\beta _ { 1 } = 0 . 9 , \beta _ { 2 } = 0 . 9 9 9 , \epsilon = 1 e - 0 7$ . For the models without BERT, we set the learning rate to 0.001 and initialize the embedding matrix with fastText (Bojanowski et al., 2016) trained on the Common Crawl corpus. For the models with BERT, we set the learning rate to 0.00002 and initialize encoder weights with BERT-Base, Uncased pretrained weights. We apply label smoothing (Pereyra et al., 2017; Edunov et al., 2017; Vaswani et al., 2017) for both knowledge selection and response generation, and set 0.1 and 0.05 for each. We set the temperature of Gumbel-Softmax to $\tau = 0 . 1$ and the hyperparameter for the knowledge loss to $\lambda = 1 . 0$ . For efficiency, we batch the dialogues rather than individual turns. We train our model up to 5 epochs on two NVIDIA TITAN Xp GPU.
+
+# C KNOWLEDGE SELECTION ACCURACY OVER TURNS
+
+Table 6 compares the knowledge selection accuracy of different methods for each turn on the Wizard of Wikipedia. Thanks to the sequential latent variable, our model consistently outperforms other methods for all turns in knowledge selection accuracy. Notably, in all models, the accuracy significantly drops after the first turn, which is often easily predictable as a topic definition sentence. It shows the diversity nature in knowledge selection, as discussed in Section 2.
+
+# D QUANTITATIVE RESULTS ON SEMI-SUPERVISED SETTING
+
+Table 7 shows the results of our model with partial knowledge labels on the Wizard of Wikipedia. We attain better performance with more labeled knowledge data for training as expected. Furthermore, our model achieves competitive performance with less label. For instance, our model using only 1/4 labeled training data is comparable to E2E Transformer MemNet and even better in Test Unseen. As a result, our sequential latent knowledge selection model can be utilized in a semi-supervised method without severe drop in the performance.
+
+Table 6: Knowledge selection accuracy for each turn on the Wizard of Wikipedia (Dinan et al., 2019). The method with $[ { ^ * } ]$ uses no knowledge loss. TMN stands for E2E Transformer MemNet.
+
+| SeenTest(Topic:TtalanCuisine) ： |
| A: Ilove chicken parmigiana as well,but I think my ultimate favorite is beef lasagna... Extra cheese please! |
| W: Chicken with sauce and mozzarella.... Be still my heart! A:Truthfully,anything with cheese is the best |
| Task 1: Knowledge Selection | Task 2: Response Generation ilove pizza too ！it’s a traditional italian dish |
| Ours | Pizza is a traditional Italian dish consisting of a yeasted flatbread typically topped with tomato sauce and cheese and baked in an oven. (from“Pizza”Wikipedia page) | nconsisting of yeasted flatbread typically topped with tomato sauce and cheese |
| TMN | no_passages_used | i love cheese |
| E2E BERT +KL | It can also be topped with additional vegetables,meats,and condiments,and can condiments . be made without cheese. (from“Pizza”Wikipedia page) | i like mine topped with vegetables,meats,and |
| Human | It is the second-most popular cheese in the US (behind mozzarella), with an average annual consumption of 10 lb (4.5 kg) per capita. (from “Cheddar cheese”Wikipedia page) | especially cheddar cheese !it ’s the second most popular cheese in the use ! |
+
+W: That is true but we always have to watch out for excessive hunting. It has cause some species to be endangered.
+
+Figure 5: Examples of selected knowledge and generated responses by our model and baselines on the WoW Unseen Test set.
+
+| Task1: Knowledge Selection | Task 2:Response Generation |
| Ours | Poaching has traditionally been defined as the illegal hunting or capturing of wild animals,usually associated with land use rights. (from“Poaching”Wikipedia page) | i agree,poaching has been defined as the illegal hunting or capturing of wild animals . |
| TMN | no_passages_used | i thinks so,i'm not sure if you ’re talking about poaching , but i know that poodles are the second most intelligent breed behind the poodle . |
| E2E BERT +KL | Hunting can also be a means of pest control. iagree .i think it ’s a great way to catch fish . (from“Poaching”Wikipedia page) | |
| Human | It is also not considered hunting to pursue animals without intent to kill them,as in wildlife photography, birdwatching,or scientific research (from“Hunting”Wikipedia page) | agreed,i remember reading one time that unless you plan to kill the animals its not considered hunting. |
\ No newline at end of file
diff --git a/parse/train/Hke0K1HKwr/Hke0K1HKwr_content_list.json b/parse/train/Hke0K1HKwr/Hke0K1HKwr_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..39140dacf48fa0503decc1d4c769b7ef2d8488bb
--- /dev/null
+++ b/parse/train/Hke0K1HKwr/Hke0K1HKwr_content_list.json
@@ -0,0 +1,1341 @@
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+ "type": "text",
+ "text": "SEQUENTIAL LATENT KNOWLEDGE SELECTION FOR KNOWLEDGE-GROUNDED DIALOGUE ",
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+ "text": "Byeongchang Kim Jaewoo Ahn Gunhee Kim \nDepartment of Computer Science and Engineering \nSeoul National University, Seoul, Korea \n{byeongchang.kim,jaewoo.ahn}@vision.snu.ac.kr gunhee@snu.ac.kr \nhttp://vision.snu.ac.kr/projects/skt ",
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+ "text": "ABSTRACT ",
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+ "text": "Knowledge-grounded dialogue is a task of generating an informative response based on both discourse context and external knowledge. As we focus on better modeling the knowledge selection in the multi-turn knowledge-grounded dialogue, we propose a sequential latent variable model as the first approach to this matter. The model named sequential knowledge transformer (SKT) can keep track of the prior and posterior distribution over knowledge; as a result, it can not only reduce the ambiguity caused from the diversity in knowledge selection of conversation but also better leverage the response information for proper choice of knowledge. Our experimental results show that the proposed model improves the knowledge selection accuracy and subsequently the performance of utterance generation. We achieve the new state-of-the-art performance on Wizard of Wikipedia (Dinan et al., 2019) as one of the most large-scale and challenging benchmarks. We further validate the effectiveness of our model over existing conversation methods in another knowledge-based dialogue Holl-E dataset (Moghe et al., 2018). ",
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+ "type": "text",
+ "text": "1 INTRODUCTION ",
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+ "text": "Knowledge-grounded dialogue is a task of generating an informative response based on both discourse context and selected external knowledge (Ghazvininejad et al., 2018). For example, it is more descriptive and engaging to respond “I’ve always been more of a fan of the American football team from Pittsburgh, the Steelers!” than “Nice, I like football too.” (Dinan & Weston, 2019). As it has been one of the key milestone tasks in conversational research (Zhang et al., 2018), a majority of previous works have studied how to effectively combine given knowledge and dialogue context to generate an utterance (Zhang et al., 2018; Li et al., 2019b; Parthasarathi & Pineau, 2018; Madotto et al., 2018; Gopalakrishnan et al., 2019). Recently, Dinan et al. (2019) proposed to tackle the knowledge-grounded dialogue by decomposing it into two sub-problems: first selecting knowledge from a large pool of candidates and generating a response based on the selected knowledge and context. ",
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+ "text": "In this work, we investigate the issue of knowledge selection in the multi-turn knowledge-grounded dialogue, since practically the selection of pertinent topics is critical to better engage humans in conversation, and technically the utterance generation becomes easier with a more powerful and consistent knowledge selector in the system. Especially, we focus on developing a sequential latent variable model for knowledge selection, which has not been discussed in previous research. We believe it brings several advantages for more engaging and accurate knowledge-based chit-chat. First, it can correctly deal with the diversity in knowledge selection of conversation. Since one can choose any knowledge to carry on the conversation, there can be one-to-many relations between dialogue context and knowledge selection. Such multimodality by nature makes the training of a dialogue system much more difficult in a data-driven way. However, if we can sequentially model the history of knowledge selection in previous turns, we can reduce the scope of probable knowledge candidates at current turn. Second, the sequential latent model can better leverage the response information, which makes knowledge selection even more accurate. It is naturally easy to select the knowledge in the pool once the response is known, because the response is generated based on the selected knowledge. Our sequential model can keep track of prior and posterior distribution over knowledge, which are sequentially updated considering the responses in previous turns, and thus we can better predict the knowledge by sampling from the posterior. Third, the latent model works even when the knowledge selection labels for previous dialogue are not available, which is common in practice. For example, if multiple people have discussion about given documents, knowledge selection of previous turns is done by others. The latent model can infer which knowledge others are likely to select and use. ",
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+ "img_path": "images/98998ccc880ad97e64bc2ddcbe2a9e0508d1408ea5583fd92e1c0fc8b0c9355f.jpg",
+ "image_caption": [
+ "Figure 1: An example of wizard’s tasks in knowledge-grounded conversation of Wizard of Wikipedia (Dinan et al., 2019). "
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+ "Table 1: Accuracy of knowledge selection with and without knowing the response. We test with GRU (Cho et al., 2014), Transformer (Vaswani et al., 2017) and BERT (Devlin et al., 2019) as the sentence encoder. For human evaluation, we randomly sample 20 dialogues and ask human annotators to select the most likely knowledge sentence from the pool. "
+ ],
+ "table_footnote": [],
+ "table_body": "| Seen Test (Topic: Italian Cuisine) | Unseen Test (Topic:Hunting) |
| ： A:I love chicken parmigiana as well, but I think my ultimate | ： W:That is true but we always have to watch out for excessive |
| favorite is beef lasagna...Extra cheese please! W: Chicken with sauce and mozzarella.. Be still my heart! A:Truthfully,anythingwith cheese is the best (Ours)ilove pizza too ！it'sa traditional italian dish | hunting. It has caused some species to be endangered. A:Yes Iagree.Idon't believe in the useless hunting that poachers do. Its so cruel. (Ours) iagree,poaching has been defined as the illegal hunting or |
| consisting of yeasted flatbread typically topped with tomato sauce and cheese (TMN) ilove cheese ! (E2E BERT+KL)i like mine topped with vegetables, meats, and condiments . (Human) especially cheddar cheese !it’s the second most | capturing of wild animals . (TMN)i thinks so,i’m not sure if you 're talking about poaching,but i know that poodles are the second most intelligent breed behind the poodle . (E2EBERT+KL)iagree.i think it’sa great way to catch fish . (Human) agreed,i remember reading one time that unless you |
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+ "text": "6 CONCLUSION ",
+ "text_level": 1,
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+ },
+ {
+ "type": "text",
+ "text": "This work investigated the issue of knowledge selection in multi-turn knowledge-grounded dialogue, and proposed a sequential latent variable model, for the first time, named sequential knowledge transformer (SKT). Our method achieved the new state-of-the-art performance on the Wizard of Wikipedia benchmark (Dinan et al., 2019) and a knowledge-annotated version of Holl-E dataset (Moghe et al., 2018). There are several promising future directions beyond this work. First, we can explore other inference models such as sequential Monte Carlo methods using filtering variational objectives (Maddison et al., 2017a). Second, we can study the interpretability of knowledge selection such as measuring the uncertainty of attention (Heo et al., 2018). ",
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+ "text": "ACKNOWLEDGMENTS ",
+ "text_level": 1,
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+ },
+ {
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+ "text": "We thank Hyunwoo Kim, Chris Dongjoo Kim, Soochan Lee, Junsoo Ha and the anonymous reviewers for their helpful comments. This work was supported by SK T-Brain corporation and Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (No.2019-0-01082, SW StarLab). Gunhee Kim is the corresponding author. ",
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+ "type": "text",
+ "text": "REFERENCES ",
+ "text_level": 1,
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+ 285,
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+ },
+ {
+ "type": "text",
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In AISTATS, 2010. \nKarthik Gopalakrishnan, Behnam Hedayatnia, Qinlang Chen, Anna Gottardi, Sanjeev Kwatra, Anu Venkatesh, Raefer Gabriel, Dilek Hakkani-Tur, and Amazon Alexa AI. Topical-Chat: Towards ¨ Knowledge-Grounded Open-Domain Conversations. In Interspeech, 2019. \nAnirudh Goyal Alias Parth Goyal, Alessandro Sordoni, Marc-Alexandre Cotˆ e, Nan Rosemary Ke, ´ and Yoshua Bengio. Z-Forcing: Training Stochastic Recurrent Networks. In NIPS, 2017. \nKelvin Guu, Tatsunori B Hashimoto, Yonatan Oren, and Percy Liang. Generating Sentences by Editing Prototypes. TACL, 6:437–450, 2018. \nYaru Hao, Li Dong, Furu Wei, and Ke Xu. Visualizing and Understanding the Effectiveness of BERT. In EMNLP, 2019. \nJay Heo, Hae Beom Lee, Saehoon Kim, Juho Lee, Kwang Joon Kim, Eunho Yang, and Sung Ju Hwang. Uncertainty-Aware Attention for Reliable Interpretation and Prediction. In NIPS, 2018. \nEric Jang, Shixiang Gu, and Ben Poole. Categorical Reparameterization with Gumbel-Softmax. 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Extending Neural Generative Conversational Model using External Knowledge Sources. In EMNLP, 2018. \nGabriel Pereyra, George Tucker, Jan Chorowski, Łukasz Kaiser, and Geoffrey Hinton. Regularizing Neural Networks by Penalizing Confident Output Distributions. In ICLR, 2017. \nLianhui Qin, Michel Galley, Chris Brockett, Xiaodong Liu, Xiang Gao, Bill Dolan, Yejin Choi, and Jianfeng Gao. Conversing by Reading: Contentful Neural Conversation with On-Demand Machine Reading. In ACL, 2019. \nShiv Shankar and Sunita Sarawagi. Posterior Attention Models for Sequence to Sequence Learning. In ICLR, 2019. \nZhihong Shao, Minlie Huang, Jiangtao Wen, Wenfei Xu, and Xiaoyan Zhu. Long and Diverse Text Generation with Planning-based Hierarchical Variational Model. In EMNLP, 2019. \nAshish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin. Attention is All You Need. In NIPS, 2017. \nWeiyue Wang, Derui Zhu, Tamer Alkhouli, Zixuan Gan, and Hermann Ney. Neural Hidden Markov Model for Machine Translation. In ACL, 2018. \nTsung-Hsien Wen, Yishu Miao, Phil Blunsom, and Steve Young. Latent intention dialogue models. In ICML, 2017. \nYingce Xia, Fei Tian, Lijun Wu, Jianxin Lin, Tao Qin, Nenghai Yu, and Tie-Yan Liu. Deliberation Networks: Sequence Generation Beyond One-Pass Decoding. In NIPS, 2017. \nZichao Yang, Zhiting Hu, Yuntian Deng, Chris Dyer, and Alex Smola. Neural Machine Translation with Recurrent Attention Modeling. In EACL, 2017. \nSemih Yavuz, Abhinav Rastogi, Guan-Lin Chao, and Hakkani-Tur Dilek. DeepCopy: Grounded Response Generation with Hierarchical Pointer Networks. In SIGDIAL, 2019. \nSaizheng Zhang, Emily Dinan, Jack Urbanek, Arthur Szlam, Douwe Kiela, and Jason Weston. Personalizing Dialogue Agents: I Have a Dog, Do You Have Pets Too? In ACL, 2018. \nTiancheng Zhao, Ran Zhao, and Maxine Eskenazi. Learning Discourse-level Diversity for Neural Dialog Models using Conditional Variational Autoencoders. In ACL, 2017. ",
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+ "text": "Wei Zhao, Liang Wang, Kewei Shen, Ruoyu Jia, and Jingming Liu. Improving Grammatical Error Correction via Pre-Training a Copy-Augmented Architecture with Unlabeled Data. In NAACLHLT, 2019a. ",
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+ "text": "Xueliang Zhao, Chongyang Tao, Wei Wu, Can Xu, Dongyan Zhao, and Rui Yan. A DocumentGrounded Matching Network for Response Selection in Retrieval-based Chatbots. In IJCAI, 2019b. ",
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+ "text": "Kangyan Zhou, Shrimai Prabhumoye, and Alan W Black. A Dataset for Document Grounded Conversations. In EMNLP, 2018. ",
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+ {
+ "type": "text",
+ "text": "A DERIVATION OF CONDITIONAL PROBABILITY ",
+ "text_level": 1,
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+ "text": "In Section 3, we re-write the conditional probability of wizard’s response $\\mathbf { y } ^ { t }$ given dialogue context $\\mathbf { x } ^ { \\leq t }$ and $\\mathbf { y } ^ { < t }$ from Eq. (2) to Eq. (4). We can simply derive it as follows: ",
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+ "text": "p(y|x) (13)",
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+ "img_path": "images/475cc006fbe8372de242615b267338bfa8a4424345bb40061d250a4bf334b539.jpg",
+ "text": "$$\n\\begin{array} { l } { { = } \\displaystyle \\prod _ { t } \\displaystyle \\sum _ { \\mathbf { k } ^ { \\prime } } p _ { \\theta } ( \\mathbf { y } ^ { t } | \\mathbf { x } ^ { \\leq t } , \\mathbf { y } ^ { < t } , \\mathbf { k } ^ { \\leq t } ) \\pi _ { \\theta } ( \\mathbf { k } ^ { t } ) \\quad \\mathrm { ( b y ~ E q . ~ ( 2 ) ) } } \\\\ { { = \\displaystyle \\prod _ { i = 1 } ^ { t - 1 } \\sum _ { \\mathbf { k } ^ { \\prime } } p _ { \\theta } ( \\mathbf { y } ^ { i } | \\mathbf { x } ^ { \\leq i } , \\mathbf { y } ^ { < i } ) { \\displaystyle p _ { \\theta } ( \\mathbf { k } ^ { i } ) } \\Big ( \\displaystyle \\sum _ { \\mathbf { k } ^ { t } } p _ { \\theta } ( \\mathbf { y } ^ { t } | \\mathbf { x } ^ { \\leq t } , \\mathbf { y } ^ { < t } , \\mathbf { k } ^ { \\leq t } ) \\pi _ { \\theta } ( \\mathbf { k } ^ { t } ) \\Big ) \\quad \\mathrm { ( b y ~ B a y e s ' ~ n l e ) } } } \\\\ { { \\approx \\displaystyle \\prod _ { i = 1 } ^ { t - 1 } \\displaystyle \\sum _ { \\mathbf { k } ^ { i } } p _ { \\theta } ( \\mathbf { y } ^ { i } | \\mathbf { x } ^ { \\leq i } , \\mathbf { y } ^ { < i } ) { q _ { \\theta } ( \\mathbf { k } ^ { i } ) } \\Big ( \\displaystyle \\sum _ { \\mathbf { k } ^ { t } } p _ { \\theta } ( \\mathbf { y } ^ { t } | \\mathbf { x } ^ { \\leq t } , \\mathbf { y } ^ { < t } , \\mathbf { k } ^ { \\leq t } ) \\pi _ { \\theta } ( \\mathbf { k } ^ { t } ) \\Big ) } } \\\\ { { = \\displaystyle \\prod _ { i = 1 } ^ { t - 1 } \\displaystyle \\sum _ { \\mathbf { k } ^ { t } } q _ { \\phi } ( \\mathbf { k } ^ { i } ) \\Big ( \\displaystyle \\sum _ { \\mathbf { k } ^ { t } } p _ { \\theta } ( \\mathbf { y } ^ { t } | \\mathbf { x } ^ { \\leq t } , \\mathbf { y } ^ { < t } , \\mathbf { k } ^ { t } ) \\pi _ { \\theta } ( \\mathbf { k } ^ { t } ) \\Big ) \\quad \\mathrm { ( x \\leq t ~ a n d ~ \\mathbf { y } ^ { < t } ~ a r e ~ g i v e n ) } } } \\\\ { { \\approx p ( \\mathbf { y } ^ { t } | \\mathbf { x } ^ { \\leq t } , \\mathbf { y } ^ { < t } ) , } } \\end{array}\n$$",
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+ "text": "where $q _ { \\phi } ( \\mathbf { k } ^ { i } )$ is an approximated posterior distribution and $p _ { \\theta } ( \\mathbf { k } ^ { i } )$ is a true posterior distribution. ",
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+ "type": "text",
+ "text": "B TRAINING DETAILS ",
+ "text_level": 1,
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+ "text": "All the parameters except pretrained parts are initialized with Xavier method (Glorot & Bengio, 2010). We use Adam optimizer (Kingma & Ba, 2015) with $\\beta _ { 1 } = 0 . 9 , \\beta _ { 2 } = 0 . 9 9 9 , \\epsilon = 1 e - 0 7$ . For the models without BERT, we set the learning rate to 0.001 and initialize the embedding matrix with fastText (Bojanowski et al., 2016) trained on the Common Crawl corpus. For the models with BERT, we set the learning rate to 0.00002 and initialize encoder weights with BERT-Base, Uncased pretrained weights. We apply label smoothing (Pereyra et al., 2017; Edunov et al., 2017; Vaswani et al., 2017) for both knowledge selection and response generation, and set 0.1 and 0.05 for each. We set the temperature of Gumbel-Softmax to $\\tau = 0 . 1$ and the hyperparameter for the knowledge loss to $\\lambda = 1 . 0$ . For efficiency, we batch the dialogues rather than individual turns. We train our model up to 5 epochs on two NVIDIA TITAN Xp GPU. ",
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+ "type": "text",
+ "text": "C KNOWLEDGE SELECTION ACCURACY OVER TURNS ",
+ "text_level": 1,
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+ "text": "Table 6 compares the knowledge selection accuracy of different methods for each turn on the Wizard of Wikipedia. Thanks to the sequential latent variable, our model consistently outperforms other methods for all turns in knowledge selection accuracy. Notably, in all models, the accuracy significantly drops after the first turn, which is often easily predictable as a topic definition sentence. It shows the diversity nature in knowledge selection, as discussed in Section 2. ",
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+ "text": "D QUANTITATIVE RESULTS ON SEMI-SUPERVISED SETTING ",
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+ "text": "Table 7 shows the results of our model with partial knowledge labels on the Wizard of Wikipedia. We attain better performance with more labeled knowledge data for training as expected. Furthermore, our model achieves competitive performance with less label. For instance, our model using only 1/4 labeled training data is comparable to E2E Transformer MemNet and even better in Test Unseen. As a result, our sequential latent knowledge selection model can be utilized in a semi-supervised method without severe drop in the performance. ",
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+ "img_path": "images/3f0084d6073b7816586b16cc7c13f29385ac591b9e146122271f449661e2184f.jpg",
+ "table_caption": [
+ "Table 6: Knowledge selection accuracy for each turn on the Wizard of Wikipedia (Dinan et al., 2019). The method with $[ { ^ * } ]$ uses no knowledge loss. TMN stands for E2E Transformer MemNet. "
+ ],
+ "table_footnote": [],
+ "table_body": "| SeenTest(Topic:TtalanCuisine) ： |
| A: Ilove chicken parmigiana as well,but I think my ultimate favorite is beef lasagna... Extra cheese please! |
| W: Chicken with sauce and mozzarella.... Be still my heart! A:Truthfully,anything with cheese is the best |
| Task 1: Knowledge Selection | Task 2: Response Generation ilove pizza too ！it’s a traditional italian dish |
| Ours | Pizza is a traditional Italian dish consisting of a yeasted flatbread typically topped with tomato sauce and cheese and baked in an oven. (from“Pizza”Wikipedia page) | nconsisting of yeasted flatbread typically topped with tomato sauce and cheese |
| TMN | no_passages_used | i love cheese |
| E2E BERT +KL | It can also be topped with additional vegetables,meats,and condiments,and can condiments . be made without cheese. (from“Pizza”Wikipedia page) | i like mine topped with vegetables,meats,and |
| Human | It is the second-most popular cheese in the US (behind mozzarella), with an average annual consumption of 10 lb (4.5 kg) per capita. (from “Cheddar cheese”Wikipedia page) | especially cheddar cheese !it ’s the second most popular cheese in the use ! |
",
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+ "text": "W: That is true but we always have to watch out for excessive hunting. It has cause some species to be endangered. ",
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+ "table_caption": [
+ "Figure 5: Examples of selected knowledge and generated responses by our model and baselines on the WoW Unseen Test set. "
+ ],
+ "table_footnote": [],
+ "table_body": "| Task1: Knowledge Selection | Task 2:Response Generation |
| Ours | Poaching has traditionally been defined as the illegal hunting or capturing of wild animals,usually associated with land use rights. (from“Poaching”Wikipedia page) | i agree,poaching has been defined as the illegal hunting or capturing of wild animals . |
| TMN | no_passages_used | i thinks so,i'm not sure if you ’re talking about poaching , but i know that poodles are the second most intelligent breed behind the poodle . |
| E2E BERT +KL | Hunting can also be a means of pest control. iagree .i think it ’s a great way to catch fish . (from“Poaching”Wikipedia page) | |
| Human | It is also not considered hunting to pursue animals without intent to kill them,as in wildlife photography, birdwatching,or scientific research (from“Hunting”Wikipedia page) | agreed,i remember reading one time that unless you plan to kill the animals its not considered hunting. |
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| ： A:I love chicken parmigiana as well, but I think my ultimate | ： W:That is true but we always have to watch out for excessive |
| favorite is beef lasagna...Extra cheese please! W: Chicken with sauce and mozzarella.. Be still my heart! A:Truthfully,anythingwith cheese is the best (Ours)ilove pizza too ！it'sa traditional italian dish | hunting. It has caused some species to be endangered. A:Yes Iagree.Idon't believe in the useless hunting that poachers do. Its so cruel. (Ours) iagree,poaching has been defined as the illegal hunting or |
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| favorite is beef lasagna...Extra cheese please! W: Chicken with sauce and mozzarella.. Be still my heart! A:Truthfully,anythingwith cheese is the best (Ours)ilove pizza too ！it'sa traditional italian dish | hunting. It has caused some species to be endangered. A:Yes Iagree.Idon't believe in the useless hunting that poachers do. Its so cruel. (Ours) iagree,poaching has been defined as the illegal hunting or |
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| E2E BERT +KL | Hunting can also be a means of pest control. iagree .i think it ’s a great way to catch fish . (from“Poaching”Wikipedia page) | |
| Human | It is also not considered hunting to pursue animals without intent to kill them,as in wildlife photography, birdwatching,or scientific research (from“Hunting”Wikipedia page) | agreed,i remember reading one time that unless you plan to kill the animals its not considered hunting. |
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| ： A:I love chicken parmigiana as well, but I think my ultimate | ： W:That is true but we always have to watch out for excessive |
| favorite is beef lasagna...Extra cheese please! W: Chicken with sauce and mozzarella.. Be still my heart! A:Truthfully,anythingwith cheese is the best (Ours)ilove pizza too ！it'sa traditional italian dish | hunting. It has caused some species to be endangered. A:Yes Iagree.Idon't believe in the useless hunting that poachers do. Its so cruel. (Ours) iagree,poaching has been defined as the illegal hunting or |
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| A: Ilove chicken parmigiana as well,but I think my ultimate favorite is beef lasagna... Extra cheese please! |
| W: Chicken with sauce and mozzarella.... Be still my heart! A:Truthfully,anything with cheese is the best |
| Task 1: Knowledge Selection | Task 2: Response Generation ilove pizza too ！it’s a traditional italian dish |
| Ours | Pizza is a traditional Italian dish consisting of a yeasted flatbread typically topped with tomato sauce and cheese and baked in an oven. (from“Pizza”Wikipedia page) | nconsisting of yeasted flatbread typically topped with tomato sauce and cheese |
| TMN | no_passages_used | i love cheese |
| E2E BERT +KL | It can also be topped with additional vegetables,meats,and condiments,and can condiments . be made without cheese. (from“Pizza”Wikipedia page) | i like mine topped with vegetables,meats,and |
| Human | It is the second-most popular cheese in the US (behind mozzarella), with an average annual consumption of 10 lb (4.5 kg) per capita. (from “Cheddar cheese”Wikipedia page) | especially cheddar cheese !it ’s the second most popular cheese in the use ! |
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| Ours | Poaching has traditionally been defined as the illegal hunting or capturing of wild animals,usually associated with land use rights. (from“Poaching”Wikipedia page) | i agree,poaching has been defined as the illegal hunting or capturing of wild animals . |
| TMN | no_passages_used | i thinks so,i'm not sure if you ’re talking about poaching , but i know that poodles are the second most intelligent breed behind the poodle . |
| E2E BERT +KL | Hunting can also be a means of pest control. iagree .i think it ’s a great way to catch fish . (from“Poaching”Wikipedia page) | |
| Human | It is also not considered hunting to pursue animals without intent to kill them,as in wildlife photography, birdwatching,or scientific research (from“Hunting”Wikipedia page) | agreed,i remember reading one time that unless you plan to kill the animals its not considered hunting. |
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+# MARGINALIZED AVERAGE ATTENTIONAL NETWORK FOR WEAKLY-SUPERVISED LEARNING
+
+Yuan Yuan12, Yueming Lyu3, Xi Shen4, Ivor W. Tsang3 & Dit-Yan Yeung1 1Hong Kong University of Science and Technology, 2Alibaba Group 3University of Technology Sydney, 4Ecole des Ponts ParisTech
+
+# ABSTRACT
+
+In weakly-supervised temporal action localization, previous works have failed to locate dense and integral regions for each entire action due to the overestimation of the most salient regions. To alleviate this issue, we propose a marginalized average attentional network (MAAN) to suppress the dominant response of the most salient regions in a principled manner. The MAAN employs a novel marginalized average aggregation (MAA) module and learns a set of latent discriminative probabilities in an end-to-end fashion. MAA samples multiple subsets from the video snippet features according to a set of latent discriminative probabilities and takes the expectation over all the averaged subset features. Theoretically, we prove that the MAA module with learned latent discriminative probabilities successfully reduces the difference in responses between the most salient regions and the others. Therefore, MAAN is able to generate better class activation sequences and identify dense and integral action regions in the videos. Moreover, we propose a fast algorithm to reduce the complexity of constructing MAA from ${ \dot { O ( 2 ^ { T } ) } }$ to $O ( T ^ { 2 } )$ Extensive experiments on two large-scale video datasets show that our MAAN achieves a superior performance on weakly-supervised temporal action localization.
+
+# 1 INTRODUCTION
+
+Weakly-supervised temporal action localization has been of interest to the community recently. The setting is to train a model with solely video-level class labels, and to predict both the class and the temporal boundary of each action instance at the test time. The major challenge in the weakly-supervised localization problem is to find the right way to express and infer the underlying location information with only the video-level class labels. Traditionally, this is achieved by explicitly sampling several possible instances with different locations and durations (Bilen & Vedaldi, 2016; Kantorov et al., 2016; Zhang et al., 2017). The instance-level classifiers would then be trained through multiple instances learning (Cinbis et al., 2017; Yuan et al., 2017a) or curriculum learning (Bengio et al., 2009). However, the length of actions and videos varies too much such that the number of instance proposals for each video varies a lot and it can also be huge. As a result, traditional methods based on instance proposals become infeasible in many cases.
+
+Recent research, however, has pivoted to acquire the location information by generating the class activation sequence (CAS) directly (Nguyen et al., 2018), which produces the classification score sequence of being each action for each snippet over time. The CAS along the 1D temporal dimension for a video is inspired by the class activation map (CAM) (Zhou et al., 2016a; 2014; Pinheiro & Collobert, 2015; Oquab et al., 2015) in weakly-supervised object detection. The CAM-based models have shown that despite being trained on image-level labels, convolutional neural networks (CNNs) have the remarkable ability to localize objects. Similar to object detection, the basic idea behind CAS-based methods for action localization in the training is to sample the non-overlapping snippets from a video, then to aggregate the snippet-level features into a video-level feature, and finally to yield a video-level class prediction. During testing, the model generates a CAS for each class that identifies the discriminative action regions, and then applies a threshold on the CAS to localize each action instance in terms of the start time and the end time.
+
+In CAS-based methods, the feature aggregator that aggregates multiple snippet-level features into a video-level feature is the critical building block of weakly-supervised neural networks. A model’s ability to capture the location information of an action is primarily determined by the design of the aggregators. While using the global average pooling over a full image or across the video snippets has shown great promise in identifying the discriminative regions (Zhou et al., 2016a; 2014; Pinheiro & Collobert, 2015; Oquab et al., 2015), treating each pixel or snippet equally loses the opportunity to benefit from several more essential parts. Some recent works (Nguyen et al., 2018; Zhu et al., 2017) have tried to learn attentional weights for different snippets to compute a weighted sum as the aggregated feature. However, they suffer from the weights being easily dominated by only a few most salient snippets.
+
+In general, models trained with only video-level class labels tend to be easily responsive to small and sparse discriminative regions from the snippets of interest. This deviates from the objective of the localization task that is to locate dense and integral regions for each entire action. To mitigate this gap and reduce the effect of the domination by the most salient regions, several heuristic tricks have been proposed to apply to existing models. For example, (Wei et al., 2017; Zhang et al., 2018b) attempt to heuristically erase the most salient regions predicted by the model which are currently being mined, and force the network to attend other salient regions in the remaining regions by forwarding the model several times. However, the heuristic multiple-run model is not end-to-end trainable. It is the ensemble of multiple-run mined regions but not the single model’s own ability that learns the entire action regions. “Hide-and-seek”(Singh & Lee, 2017) randomly masks out some regions of the input during training, enforcing the model to localize other salient regions when the most salient regions happen to be masked out. However, all the input regions are masked out with the same probability due to the uniform prior, and it is very likely that most of the time it is the background that is being masked out. A detailed discussion about related works can be found in Appendix D.
+
+To this end, we propose the marginalized average attentional network (MAAN) to alleviate the issue raised by the domination of the most salient region in an end-to-end fashion for weakly-supervised action localization. Specifically, MAAN suppresses the action prediction response of the most salient regions by employing marginalized average aggregation (MAA) and learning the latent discriminative probability in a principled manner. Unlike the previous attentional pooling aggregator which calculates the weighted sum with attention weights, MAA first samples a subset of features according to their latent discriminative probabilities, and then calculates the average of these sampled features. Finally, MAA takes the expectation (marginalization) of the average aggregated subset features over all the possible subsets to achieve the final aggregation. As a result, MAA not only alleviates the domination by the most salient regions, but also maintains the scale of the aggregated feature within a reasonable range. We theoretically prove that, with the MAA, the learned latent discriminative probability indeed reduces the difference of response between the most salient regions and the others. Therefore, MAAN can identify more dense and integral regions for each action. Moreover, since enumerating all the possible subsets is exponentially expensive, we further propose a fast iterative algorithm to reduce the complexity of the expectation calculation procedure and provide a theoretical analysis. Furthermore, MAAN is easy to train in an end-to-end fashion since all the components of the network are differentiable. Extensive experiments on two large-scale video datasets show that MAAN consistently outperforms the baseline models and achieves superior performance on weakly-supervised temporal action localization.
+
+In summary, our main contributions include: (1) a novel end-to-end trainable marginalized average attentional network (MAAN) with a marginalized average aggregation (MAA) module in the weaklysupervised setting; (2) theoretical analysis of the properties of MAA and an explanation of the reasons MAAN alleviates the issue raised by the domination of the most salient regions; (3) a fast iterative algorithm that can effectively reduce the computational complexity of MAA; and (4) a superior performance on two benchmark video datasets, THUMOS14 and ActivityNet1.3, on the weakly-supervised temporal action localization.
+
+# 2 MARGINALIZED AVERAGE ATTENTIONAL NETWORK
+
+In this section, we describe our proposed MAAN for weakly-supervised temporal action localization. We first derive the formulation of the feature aggregation module in MAAN as a MAA procedure in Sec. 2.1. Then, we study the properties of MAA in Sec. 2.2, and present our fast iterative computation algorithm for MAA construction in Sec. 2.3. Finally, we describe our network architecture that incorporates MAA, and introduce the corresponding inference process on weakly-supervised temporal action localization in Sec. 2.4.
+
+
+Figure 1: An illustration of the weighted sum aggregation and the marginalized average aggregation.
+
+# 2.1 MARGINALIZED AVERAGE AGGREGATION
+
+Let $\{ \mathbf { x } _ { 1 } , \mathbf { x } _ { 2 } , \cdot \cdot \cdot \mathbf { x } _ { T } \}$ denote the set of snippet-level features to be aggregated, where $\mathbf { x } _ { t } \in \mathbb { R } ^ { m }$ is the $m$ dimensional feature representation extracted from a video snippet centered at time $t$ , and $T$ is the total number of sampled video snippets. The conventional attentional weighted sum pooling aggregates the input snippet-level features into a video-level representation $\overline { { \mathbf { x } } }$ . Denote the set of attentional weights corresponding to the snippet-level features as $\{ \lambda _ { 1 } , \lambda _ { 2 } , \dotsb \lambda _ { T } \}$ , where $\lambda _ { t }$ is a scalar attentional weight for $\mathbf { x } _ { t }$ . Then the aggregated video-level representation is given by
+
+$$
+\overline { { \mathbf { x } } } = \sum _ { t = 1 } ^ { T } \lambda _ { t } \mathbf { x } _ { t } ,
+$$
+
+as illustrated in Figure 1 (a). Different from the conventional aggregation mechanism, the proposed MAA module aggregates the features by firstly generating a set of binary indicators to determine whether a snippet should be sampled or not. The model then computes the average aggregation of these sampled snippet-level representations. Lastly, the model computes the expectation (marginalization) of the aggregated average feature for all the possible subsets, and obtains the proposed marginalized average aggregated feature. Formally, in the proposed MAA module, we first define a set of probabilities $\{ p _ { 1 } , p _ { 2 } , \cdot \cdot \cdot p _ { T } \}$ , where each $p _ { t } \in [ 0 , 1 ]$ is a scalar corresponding to $\mathbf { x _ { t } }$ , similar to the notation $\lambda _ { t }$ mentioned previously. We then sample a set of random variables $\{ z _ { 1 } , z _ { 2 } , \cdot \cdot \cdot z _ { T } \}$ , where $z _ { t } \sim B e r n o u l l i ( p _ { t } )$ , i.e., $z _ { t } \in \{ 0 , 1 \}$ with probability $P ( z _ { t } = 1 ) = p _ { t }$ . The sampled set is used to represent the subset selection of snippet-level features, in which $z _ { t } = 1$ indicates $\mathbf { x } _ { t }$ is selected, otherwise not. Therefore, the average aggregation of the sampled subset of snipped-level representations is given by $\begin{array} { r } { \overline { { \bf s } } = \sum _ { i = 1 } ^ { T } z _ { i } { \bf x } _ { i } / \sum _ { i = 1 } ^ { T } z _ { i } } \end{array}$ , and our proposed aggregated feature, defined as the expectation of all the possible subset-level average aggregated representations, is given by
+
+$$
+\overline { { \mathbf { x } } } = \mathbb { E } [ \overline { { \mathbf { s } } } ] = \mathbb { E } \left[ \frac { \sum _ { i = 1 } ^ { T } z _ { i } \mathbf { x } _ { i } } { \sum _ { i = 1 } ^ { T } z _ { i } } \right] ,
+$$
+
+which is illustrated in Figure 1 (b).
+
+# 2.2 PARTIAL ORDER PRESERVATION AND DOMINANT RESPONSE SUPPRESSION
+
+Direct learning and prediction with the attention weights $\lambda$ in Eq. (1) in weakly-supervised action localization leads to an over-response in the most salient regions. The MAA in Eq. (2) has two properties that alleviate the domination effect of the most salient regions. First, the partial order preservation property, i.e., the latent discriminative probabilities preserve the partial order with respect to their attention weights. Second, the dominant response suppression property, i.e., the differences in the latent discriminative probabilities between the most salient items and others are smaller than the differences between their attention weights. The partial order preservation property guarantees that it does not mix up the action and non-action snippets by assigning a high latent discriminative probability to a snippet with low response. The dominant response suppression property reduces the dominant effect of the most salient regions and encourages the identification of dense and more integral action regions. Formally, we present the two properties in Proposition 1 and Proposition 2, respectively. Detailed proofs can be found in Appendix A and Appendix B respectively.
+
+Proposition 1. Let $z _ { i } \sim B e r n o u l l i ( p _ { i } )$ for $i \in \{ 1 , . . . , T \}$ . Then for $T \geq 2$ , Eq. (3) holds true, and $p _ { i } \geq p _ { j } \Leftrightarrow c _ { i } \geq c _ { j } \Leftrightarrow \lambda _ { i } \geq \lambda _ { j }$ .
+
+$$
+\mathbb { E } \left[ \frac { \sum _ { i = 1 } ^ { T } z _ { i } \mathbf { x } _ { i } } { \sum _ { i = 1 } ^ { T } z _ { i } } \right] = \sum _ { i = 1 } ^ { T } c _ { i } p _ { i } \mathbf { x } _ { i } = \sum _ { i = 1 } ^ { T } \lambda _ { i } \mathbf { x } _ { i } ,
+$$
+
+where $\begin{array} { r } { c _ { i } = \mathbb { E } \left[ 1 / ( 1 + \sum _ { k = 1 , k \neq i } ^ { T } z _ { k } ) \right] } \end{array}$ and $\lambda _ { i } = c _ { i } p _ { i }$ for $i \in \{ 1 , . . . , T \}$
+
+Proposition 1 shows that the latent discriminative probabilities $\{ p _ { i } \}$ preserve the partial order of the attention weights $\{ \lambda _ { i } \}$ . This means that a large attention weight corresponds to a large discriminative probability, which guarantees that the latent discriminative probabilities preserve the ranking of the action prediction response. Eq. (3) can be seen as a factorization of the attention weight $\lambda _ { i }$ into the multiplication of two components, $p _ { i }$ and $c _ { i }$ , for $i \in \{ 1 , . . . , T \}$ . $p _ { i }$ is the latent discriminative probability related to the feature of snippet $i$ itself. The factor $c _ { i }$ captures the contextual information of snippet $i$ from the other snippets. This factorization can be considered to be introducing structural information into the aggregation. Factor $c _ { i }$ can be considered as performing a structural regularization for learning the latent discriminative probabilities $p _ { i }$ for $i \in \{ 1 , . . . , T \}$ , as well as for learning a more informative aggregation.
+
+Proposition 2. Let $z _ { i } \sim B e r n o u l l i ( p _ { i } )$ for $i \in \{ 1 , . . . , T \}$ . Denote $\begin{array} { r } { c _ { i } = \mathbb { E } \left[ 1 / ( 1 + \sum _ { k = 1 , k \neq i } ^ { T } z _ { k } ) \right] } \end{array}$ and $\lambda _ { i } = c _ { i } p _ { i }$ for $i \in \{ 1 , . . . , T \}$ . Denote $\begin{array} { r } { \mathcal { T } = \Big \{ i \Big | c _ { i } \geq 1 / ( \sum _ { t = 1 } ^ { T } p _ { t } ) \Big \} } \end{array}$ as an index set. Then $\mathcal T \neq \emptyset$ and for $\forall i \in \mathcal { Z }$ , $\forall j \in \{ 1 , . . . , T \}$ inequality (4) holds true.
+
+$$
+\left| \frac { p _ { i } } { \sum _ { t = 1 } ^ { T } p _ { t } } - \frac { p _ { j } } { \sum _ { t = 1 } ^ { T } p _ { t } } \right| \leq \left| \frac { \lambda _ { i } } { \sum _ { t = 1 } ^ { T } \lambda _ { t } } - \frac { \lambda _ { j } } { \sum _ { t = 1 } ^ { T } \lambda _ { t } } \right|
+$$
+
+The index set $\mathcal { T }$ can be viewed as the most salient features set. Proposition 2 shows that the difference between the normalized latent discriminative probabilities of the most salient regions and others is smaller than the difference between their attention weights. It means that the prediction for each snippet using the latent discriminative probability can reduce the gap between the most salient featuress and the others compared to conventional methods that are based on attention weights. Thus, MAAN suppresses the dominant responses of the most salient featuress and encourages it to identify dense and more integral action regions.
+
+Directly learning the attention weights $\lambda$ leans to an over response to the most salient region in weakly-supervised temporal localization. Namely, the attention weights for only a few snippets are too large and dominate the others, while attention weights for most of the other snippets that also belong to the true action are underestimated. Proposition 2 shows that latent discriminative probabilities are able to reduce the gap between the most salient features and the others compared to the attention weights. Thus, by employing the latent discriminative probabilities for prediction instead of the attention weights, our method can alleviate the dominant effect of the most salient region in weakly-supervised temporal localization.
+
+# 2.3 RECURRENT FAST COMPUTATION
+
+Given a video containing $T$ snippet-level representations, there are $2 ^ { T }$ possible configurations for the subset selection. Directly summing up all the $2 ^ { T }$ configurations to calculate $\overline { { \mathbf { x } } }$ has a complexity of $O ( 2 ^ { T } )$ . In order to reduce the exponential complexity, we propose an iterative method to calculate $\overline { { \mathbf { x } } }$ with ${ \dot { O } } ( T ^ { 2 } )$ complexity. Let us denote the aggregated feature of $\{ \mathbf { x } _ { 1 } , \mathbf { x } _ { 2 } , \cdots \mathbf { x } _ { t } \}$ with length $t$ as $\mathbf { h } _ { t }$ , and denote $\mathbf { Y _ { t } } = \sum _ { i = 1 } ^ { t } z _ { i } \mathbf { x } _ { i }$ and $Z _ { t } = \sum _ { i = 1 } ^ { t } z _ { i }$ for simplicity, then we have a set of
+
+$$
+\mathbf { h } _ { t } = \mathbb { E } \left[ \frac { \sum _ { i = 1 } ^ { t } z _ { i } \mathbf { x } _ { i } } { \sum _ { i = 1 } ^ { t } z _ { i } } \right] = \mathbb { E } \left[ \frac { \mathbf { Y _ { t } } } { Z _ { t } } \right] , t \in \{ 1 , 2 , \cdots , T \} ,
+$$
+
+
+Figure 2: The purple box demonstrates the marginalized average aggregation module, where the inputs are $\{ p _ { i } \} _ { i = 1 } ^ { 4 }$ and $\bf { \dot { \{ x _ { i } \} } _ { i = 1 } ^ { 4 } }$ and the output is $\mathbf { h } _ { 4 }$ . The two black boxes demonstrate the computation graphs of $q _ { i } ^ { t }$ and $\bf { m _ { i } ^ { t } }$ , respectively. The black hollow point indicates its value is 0, while the value of the black solid point is non-zero. $q _ { 0 } ^ { 0 }$ is initialized as 1.
+
+and the aggregated feature of $\{ \mathbf { x } _ { 1 } , \mathbf { x } _ { 2 } , \cdot \cdot \cdot \mathbf { x } _ { T } \}$ can be obtained as $\overline { { \mathbf { x } } } = \mathbf { h } _ { T }$ . In Eq. (5), $Z _ { t }$ is the summation of all the $z _ { i }$ , which indicates the number of elements selected in the subset. Although there are $2 ^ { t }$ distinct configurations for $\{ z _ { 1 } , z _ { 2 } , \cdot \cdot \cdot z _ { t } \}$ , it has only $t + 1$ distinct values for $Z _ { t }$ , i.e. $0 , 1 , \cdots , t$ . Therefore, we can divide all the $2 ^ { t }$ distinct configurations into $t + 1$ groups, where the configurations sharing with the same $Z _ { t }$ fall into the same group. Then the expectation $\mathbf { h } _ { t }$ can be calculated as the summation of the $t + 1$ parts. That is, $\begin{array} { r } { \mathbf { \dot { h } } _ { t } = \mathbb { E } \left[ \mathbb { E } \left[ \left. \frac { \mathbf { Y _ { t } } } { Z _ { t } } \right| Z _ { t } = i \right] \right] = \sum _ { i = 0 } ^ { t } \mathbf { m } _ { i } ^ { t } } \end{array}$ , where the $\mathbf { m } _ { i } ^ { t }$ , indicating the $i ^ { t h }$ part of $\mathbf { h } _ { t }$ for group $Z _ { t } = i$ , is shown in Eq. (6).
+
+$$
+\mathbf { m } _ { i } ^ { t } = P \left( Z _ { t } = i \right) \mathbb { E } \left[ \frac { \mathbf { Y _ { t } } } { Z _ { t } } \bigg | Z _ { t } = i \right] .
+$$
+
+In order to calculate $\begin{array} { r } { \mathbf { h } _ { t + 1 } = \sum _ { i = 0 } ^ { t + 1 } \mathbf { m } _ { i } ^ { t + 1 } } \end{array}$ , given $\mathbf { m } _ { i } ^ { t }$ , $i \in \{ 0 , \cdots , t \}$ , we can calculate t+1i , i ∈ $\{ 0 , 1 , \cdots , t + 1 \}$ recurrently. The key idea here is that $\mathbf { m } _ { i } ^ { t + 1 }$ comes from two cases: if $z _ { t + 1 } = 0$ , then $\mathbf { m } _ { i } ^ { t + 1 }$ is the same as $\mathbf { m } _ { i } ^ { t }$ ; if $z _ { t + 1 } = 1$ , then $\mathbf { m } _ { i } ^ { t + 1 }$ is the weighted average of $\mathbf { m } _ { i - 1 } ^ { t }$ and $\mathbf { x } _ { t + 1 }$ . The latter case is also related to the probability $P \left( Z _ { t } = i - 1 \right)$ . By denoting $q _ { i - 1 } ^ { t } = P \left( Z _ { t } = i - 1 \right)$ for simplicity, we can obtain $\mathbf { m } _ { i } ^ { t + 1 }$ as a function of several elements:
+
+$$
+\mathbf { m } _ { i } ^ { t + 1 } = f ( \mathbf { m } _ { i - 1 } ^ { t } , \mathbf { m } _ { i } ^ { t } , \mathbf { x } _ { t + 1 } , p _ { t + 1 } , q _ { i - 1 } ^ { t } ) .
+$$
+
+Similarly, the computation of $q _ { i } ^ { t + 1 } = P \left( Z _ { t + 1 } = i \right)$ comes from two cases: the probability of selecting $i - 1$ items from the first $t$ items and selecting the $\left( t + 1 \right) ^ { t h }$ item, i.e., $q _ { i - 1 } ^ { t } p _ { t + 1 }$ ; and the probability of selecting $i$ items all from the first $t$ items and not selecting the $\left( t + 1 \right) ^ { t h }$ item, i.e., $q _ { i } ^ { t } \left( 1 - p _ { t + 1 } \right)$ . We derive the function of $\mathbf { m } _ { i } ^ { t + 1 }$ and $\boldsymbol q _ { i } ^ { t + 1 }$ in Proposition 3. Detailed proofs can be found in Appendix C.
+
+Proposition 3. Let zt ∼ Bernoulli(pt) , $Z _ { t } = \sum _ { i = 1 } ^ { t } z _ { i }$ and $\mathbf { Y _ { t } } = \sum _ { i = 1 } ^ { t } z _ { i } \mathbf { x } _ { i }$ for $t \in \{ 1 , . . . , T \}$ . Define $\mathbf { m } _ { i } ^ { t }$ $\mathbf { n } _ { i } ^ { t } \ , i \in \{ 0 , \cdot \cdot \cdot \ , t \}$ as Eq. (6) and $q _ { i } ^ { t } = P \left( Z _ { t } = i \right)$ , then $\mathbf { m } _ { i } ^ { t + 1 } \ i \in \{ 0 , 1 , \cdots , t + 1 \}$ can be obtained recurrently by Eq. (8) and Eq. (9).
+
+$$
+\begin{array} { r l } & { \mathbf { m } _ { i } ^ { t + 1 } = p _ { t + 1 } \left( b _ { i - 1 } \mathbf { m } _ { i - 1 } ^ { t } + ( 1 - b _ { i - 1 } ) q _ { i - 1 } ^ { t } \mathbf { x } _ { t + 1 } \right) + ( 1 - p _ { t + 1 } ) \mathbf { m } _ { i } ^ { t } , } \\ & { ~ q _ { i } ^ { t + 1 } = p _ { t + 1 } q _ { i - 1 } ^ { t } + \left( 1 - p _ { t + 1 } \right) q _ { i } ^ { t } , } \end{array}
+$$
+
+where $\begin{array} { r } { b _ { i } = \frac { i } { i + 1 } } \end{array}$ , ${ q _ { - 1 } ^ { t } = 0 }$ , $q _ { t + 1 } ^ { t } = 0$ , $q _ { 0 } ^ { 0 } = 1$ , $\mathbf { m } _ { 0 } ^ { t } = \mathbf { 0 }$ , and $\mathbf { m } _ { t + 1 } ^ { t } = \mathbf { 0 }$ .
+
+Proposition 3 provides a recurrent formula to calculate $\mathbf { m } _ { i } ^ { t }$ . With this recurrent formula, we calculate the aggregation obtain the aggre $\mathbf { h } _ { T }$ by iteratived feature of $\mathbf { m } _ { i } ^ { t }$ fras $i = 1$ $t$ $t = 1$ to The $T$ . Therefore, we canerative computation $\{ \mathbf { x } _ { 1 } , \mathbf { x } _ { 2 } , \cdot \cdot \cdot \mathbf { x } _ { T } \}$ $\begin{array} { r } { \overline { { \mathbf { x } } } = \mathbf { h } _ { T } = \sum _ { i = 0 } ^ { T } \mathbf { m } _ { i } ^ { T } } \end{array}$ procedure is summarized in Algorithm 1 in Appendix E. The time complexity is .
+
+With the fast iterative algorithm in Algorithm 1, the MAA becomes practical for end-to-end training. A demonstration of the computation graph for $\boldsymbol q _ { i } ^ { t + 1 }$ in Eq. (9) and $\mathbf { \dot { m } } _ { i } ^ { t + 1 }$ in Eq. (8) is presented in the left and right-hand sides of Figure 2, respectively. From Figure 2, we can see clearly that, to compute $\mathbf { m } _ { 2 } ^ { 3 }$ (the big black node on the right), it needs $\mathbf { m } _ { 1 } ^ { 2 }$ , $\mathbf { m } _ { 2 } ^ { 2 }$ , x3, $p _ { 3 }$ , and $q _ { 1 } ^ { 2 }$ . The MAA can be easily implemented as a subnetwork for end-to-end training and can be used to replace the operation of other feature aggregators.
+
+
+Figure 3: Network architecture for the weakly-supervised action localization.
+
+
+Figure 4: The feature aggregators used in STPN and MAAN.
+
+2.4 NETWORK ARCHITECTURE AND TEMPORAL ACTION LOCALIZATION
+
+Network Architecture: We now describe the network architecture that employs the MAA module described above for weakly-supervised temporal action localization. We start from a previous stateof-the-art base architecture, the sparse temporal pooling network (STPN) (Nguyen et al., 2018). As shown in Figure 3, it first divides the input video into several non-overlapped snippets and extracts the I3D (Carreira & Zisserman, 2017) feature for each snippet. Each snippet-level feature is then fed to an attention module to generate an attention weight between 0 and 1. STPN then uses a feature aggregator to calculate a weighted sum of the snippet-level features with these class-agnostic attention weights to create a video-level representation, as shown on the left in Figure 4. The video-level representation is then passed through an FC layer followed by a sigmoid layer to obtain class scores. Our MAAN uses the attention module to generate the latent discriminative probability $p _ { t }$ and replaces the feature aggregator from the weighted sum aggregation by the proposed marginalized average aggregation, which is demonstrated on the right in Figure 4.
+
+Training with video-level class labels: Formally, the model first performs aggregation of the i.e. . Th $\mathbf { x } _ { 1 } , \mathbf { x } _ { 2 } , \cdots \mathbf { x } _ { T }$ ) to obtain the video-level reprogistic regression layer (FC layer entation sigmoid) $\bar { \textbf { x } } ( \bar { \textbf { x } } =$ $\mathbb { E } [ \bar { \sum _ { i = 1 } ^ { T } } z _ { i } \mathbf { x } _ { i } / \sum _ { i = 1 } ^ { T } z _ { i } ] )$ $^ +$ video-level classification prediction probability. Specifically, the prediction probability for class $c \in \{ 1 , 2 , \cdot \cdot \cdot C \}$ is parameterized as $\bar { \sigma } _ { j } ^ { c } = \sigma ( \bar { \mathbf { w } _ { c } ^ { \top } } \bar { \mathbf { x } } _ { j } )$ , where $\overline { { \mathbf { x } } } _ { j }$ is the aggregated feature for video $j \in \{ 1 , . . . , N \}$ . Suppose each video $\overline { { \mathbf { x } } } _ { j }$ is i.i.d and each action class is independent from the other, the negative log-likelihood function (cross-entropy loss) is given as follows:
+
+$$
+\mathcal { L } ( \mathbf { W } ) = - \sum _ { j = 1 } ^ { N } \sum _ { c = 1 } ^ { C } \left( y _ { j } ^ { c } \log \sigma _ { j } ^ { c } + ( 1 - y _ { j } ^ { c } ) \log ( 1 - \sigma _ { j } ^ { c } ) \right) ,
+$$
+
+where $y _ { j } ^ { c } \in \{ 0 , 1 \}$ is the ground-truth video-level label for class $c$ happening in video $j$ and $\mathbf { W } =$ $\left[ \mathbf { w } _ { 1 } , . . . , \mathbf { w } _ { C } \right]$ .
+
+Temporal Action Localization: Let $\boldsymbol { s } ^ { c } = \mathbf { w } _ { c } ^ { \top } \overline { { \mathbf { x } } }$ be the video-level action prediction score, and $\sigma ( s ^ { c } ) = \sigma ( \mathbf { w } _ { c } ^ { \top } \overline { { \mathbf { x } } } )$ be the video-level action prediction probability. In STPN, as $\begin{array} { r } { \bar { \mathbf { x } } = \sum _ { t = 1 } ^ { T } \lambda _ { t } \mathbf { x } _ { t } } \end{array}$ , the $s ^ { c }$ can be rewritten as:
+
+$$
+s ^ { c } = \mathbf w _ { c } ^ { \top } \overline { { \mathbf x } } = \sum _ { t = 1 } ^ { T } \lambda _ { t } \mathbf w _ { c } ^ { \top } \mathbf x _ { t } ,
+$$
+
+In STPN, the prediction score of snippet $t$ for action class $\mathrm { c }$ in a video is defined as:
+
+$$
+\begin{array} { r } { s _ { t } ^ { c } = \lambda _ { t } \sigma \big ( \mathbf { w } _ { c } ^ { \top } \mathbf { x } _ { t } \big ) , } \end{array}
+$$
+
+where $\sigma ( \cdot )$ denotes the sigmoid function. In MAAN, as $\bar { \mathbf { x } } = \mathbb { E } [ \sum _ { i = 1 } ^ { T } z _ { i } \mathbf { x } _ { i } / \sum _ { i = 1 } ^ { T } z _ { i } ]$ , according to Proposition 1, the can be rewritten as:
+
+$$
+s ^ { c } = \mathbf { w } _ { c } ^ { \top } \overline { { \mathbf { x } } } = \mathbf { w } _ { c } ^ { \top } \mathbb { E } [ \sum _ { i = 1 } ^ { T } z _ { i } \mathbf { x } _ { i } / \sum _ { i = 1 } ^ { T } z _ { i } ] = \sum _ { t = 1 } ^ { T } c _ { t } p _ { t } \mathbf { w } _ { c } ^ { \top } \mathbf { x } _ { t } .
+$$
+
+The latent discriminative probability $p _ { t }$ corresponds to the class-agnostic attention weight for snippet $t$ . According to Proposition 1 and Proposition 2, $c _ { t }$ does not relate to snippet $t$ , but captures the context of other snippets. ${ \bf w } _ { c }$ corresponds to the class-specific weights for action class $c$ for all the snippets, and $\mathbf { w } _ { c } ^ { \top } \mathbf { x } _ { t }$ indicates the relevance of snippet $t$ to class $c$ . To generate temporal proposals, we compute the prediction score of snippet $t$ belonging to action class $c$ in a video as:
+
+$$
+s _ { t } ^ { c } = p _ { t } \sigma ( \mathbf { w } _ { c } ^ { \top } \mathbf { x } _ { t } ) .
+$$
+
+We denote the $\mathbf { s } ^ { c } = ( s _ { 1 } ^ { c } , s _ { 2 } ^ { c } , . . . , s _ { T } ^ { c } ) \top$ as the class activation sequence (CAS) for class $c$ . Similar to STPN, the threshold is applied to the CAS for each class to extract the one-dimensional connected components to generate its temporal proposals. We then perform non-maximum suppression among temporal proposals of each class independently to remove highly overlapped detections.
+
+Compared to STPN (Eq. (12)), MAAN (Eq. (14)) employs the latent discriminative probability $p _ { t }$ instead of directly using the attention weight $\lambda _ { t }$ (equivalent to $c _ { t } p _ { t } \mathrm { . }$ ) for prediction. Proposition 2 suggests that MAAN can suppress the dominant response $s _ { t } ^ { c }$ compared to STPN. Thus, MAAN is more likely to achieve a better performance in weakly-supervised temporal action localization.
+
+# 3 EXPERIMENTS
+
+This section discusses the experiments on the weakly-supervised temporal action localization problem, which is our main focus. We have also extended our algorithm on addressing the weakly-supervised image object detection problem and the relevant experiments are presented in Appendix F.
+
+# 3.1 EXPERIMENTAL SETTINGS
+
+Datasets. We evaluate MAAN on two popular action localization benchmark datasets, THUMOS14 (Jiang et al., 2014) and ActivityNet1.3 (Heilbron et al., 2015). THUMOS14 contains 20 action classes for the temporal action localization task, which consists of 200 untrimmed videos (3,027 action instances) in the validation set and 212 untrimmed videos (3,358 action instances) in the test set. Following standard practice, we train the models on the validation set without using the temporal annotations and evaluate them on the test set. ActivityNet1.3 is a large-scale video benchmark for action detection which covers a wide range of complex human activities. It provides samples from 200 activity classes with an average of 137 untrimmed videos per class and 1.41 activity instances per video, for a total of 849 video hours. This dataset contains 10,024 training videos, 4,926 validation videos and 5,044 test videos. In the experiments, we train the models on the training videos and test on the validation videos.
+
+Evaluation Metrics. We follow the standard evaluation metric by reporting mean average precision (mAP) values at several different levels of intersection over union (IoU) thresholds. We use the benchmarking code provided by ActivityNet1 to evaluate the models.
+
+Implementation Details. We use two-stream I3D networks (Carreira & Zisserman, 2017) pre-trained on the Kinetics dataset (Kay et al., 2017) to extract the snippet-level feature vectors for each video. All the videos are divided into sets of non-overlapping video snippets. Each snippet contains 16 consecutive frames or optical flow maps. We input each 16 stacked RGB frames or flow maps into the I3D RGB or flow models to extract the corresponding 1024 dimensional feature vectors. Due to the various lengths of the videos, in the training, we uniformly divide each video into $T$ non-overlapped segments, and randomly sample one snippet from each segment. Therefore, we sample $T$ snippets for each video as the input of the model for training. We set $T$ to 20 in our MAAN model. The attention module in Figure 3 consists of an FC layer of $1 0 2 4 \times 2 5 6$ , a LeakyReLU layer, an FC layer of $2 5 6 \times 1$ , and a sigmoid non-linear activation, to generate the latent discriminative probability $p _ { t }$ We pass the aggregated video-level representation through an FC layer of $1 0 2 4 \times C$ followed by a sigmoid activation to obtain class scores. We use the ADAM optimizer (Kingma & Ba, 2014) with an initial learning rate of $5 \times 1 0 ^ { - 4 }$ to optimize network parameters. At the test time, we first reject classes whose video-level probabilities are below 0.1. We then forward all the snippets of the video to generate the CAS for the remaining classes. We generate the temporal proposals by cutting the CAS with a threshold th. The combination ratio of two-stream modalities is set to 0.5 and 0.5. Our algorithm is implemented in PyTorch 2. We run all the experiments on a single NVIDIA Tesla M40 GPU with a $2 4 \mathrm { G B }$ memory.
+
+Table 1: Comparison of the proposed MAAN with four baseline feature aggregators on the THUMOS14 test set. All values are reported in percentage. The last column is the classification mAP.
+
+| Supervision | Methods | AP@IoU |
| 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 0.9 |
| Fully Supervised | Richard et al. (Richard & Gall, 2016) | 39.7 | 35.7 | 30.0 | 23.2 | 15.2 | - | - | | ■ |
| Shou et al. (Shou et al.,2016) | 47.7 | 43.5 | 36.3 | 28.7 | 19.0 | 10.3 | 5.3 | = | = |
| Yeung et al. (Yeung et al.,2016) | 48.9 | 44.0 | 36.0 | 26.4 | 17.1 | - | - | - | = |
| Yuan et al.(Yuan et al.,2016) | 51.4 | 42.6 | 33.6 | 26.1 | 18.8 | = | - | = | |
| Shou et al. (Shou et al., 2017) | - | - | 40.1 | 29.4 | 23.3 | 13.1 | 7.9 | | |
| Yuan et al. (Yuan et al.,2017b) | 51.0 | 45.2 | 36.5 | 27.8 | 17.8 | = | - | = | |
| Xu et al. (Xu et al.,2017) | 54.5 | 51.5 | 44.8 | 35.6 | 28.9 | | | | |
| Zhao et al. (Zhao et al.,2017) | 66.0 | 59.4 | 51.9 | 41.0 | 29.8 | ■ | = | = | |
| Weakly Supervised | Wang et al. (Wang et al., 2017) | 44.4 | 37.7 | 28.2 | 21.1 | 13.7 | = | | | |
| Singh & Lee (Singh& Lee,2017) | 36.4 | 27.8 | 19.5 | 12.7 | 6.8 | = | | | = |
| STPN (Nguyen et al.,2018) (UN) | 45.3 | 38.8 | 31.1 | 23.5 | 16.2 | 9.8 | 5.1 | 2.0 | 0.3 |
| STPN (Nguyen et al., 2018) (I3D) | 52.0 | 44.7 | 35.5 | 25.8 | 16.9 | 9.9 | 4.3 | 1.2 | 0.1 |
| STPN (Nguyen et al.,2018) (ours) | 57.4 | 48.7 | 40.3 | 29.5 | 19.8 | 11.4 | 5.8 | 1.7 | 0.2 |
| AutoLoc (Shou et al.,2018) | ■ | ■ | 35.8 | 29.0 | 21.2 | 13.4 | 5.8 | - | - |
| MAAN (ours) | 59.8 | 50.8 | 41.1 | 30.6 | 20.3 | 12.0 | 6.9 | 2.6 | 0.2 |
+
+Table 3: Comparison of our algorithm to the state-of-the-art approaches on ActivityNet1.3 validation set. AP $( \% )$ is reported for different IoU threshold $\alpha$ . (“ours” means our implementation.)
+
+| Supervision | Methods | AP@IoU |
| 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 0.9 |
| Fully Supervised | Richard et al. (Richard & Gall, 2016) | 39.7 | 35.7 | 30.0 | 23.2 | 15.2 | - | - | | ■ |
| Shou et al. (Shou et al.,2016) | 47.7 | 43.5 | 36.3 | 28.7 | 19.0 | 10.3 | 5.3 | = | = |
| Yeung et al. (Yeung et al.,2016) | 48.9 | 44.0 | 36.0 | 26.4 | 17.1 | - | - | - | = |
| Yuan et al.(Yuan et al.,2016) | 51.4 | 42.6 | 33.6 | 26.1 | 18.8 | = | - | = | |
| Shou et al. (Shou et al., 2017) | - | - | 40.1 | 29.4 | 23.3 | 13.1 | 7.9 | | |
| Yuan et al. (Yuan et al.,2017b) | 51.0 | 45.2 | 36.5 | 27.8 | 17.8 | = | - | = | |
| Xu et al. (Xu et al.,2017) | 54.5 | 51.5 | 44.8 | 35.6 | 28.9 | | | | |
| Zhao et al. (Zhao et al.,2017) | 66.0 | 59.4 | 51.9 | 41.0 | 29.8 | ■ | = | = | |
| Weakly Supervised | Wang et al. (Wang et al., 2017) | 44.4 | 37.7 | 28.2 | 21.1 | 13.7 | = | | | |
| Singh & Lee (Singh& Lee,2017) | 36.4 | 27.8 | 19.5 | 12.7 | 6.8 | = | | | = |
| STPN (Nguyen et al.,2018) (UN) | 45.3 | 38.8 | 31.1 | 23.5 | 16.2 | 9.8 | 5.1 | 2.0 | 0.3 |
| STPN (Nguyen et al., 2018) (I3D) | 52.0 | 44.7 | 35.5 | 25.8 | 16.9 | 9.9 | 4.3 | 1.2 | 0.1 |
| STPN (Nguyen et al.,2018) (ours) | 57.4 | 48.7 | 40.3 | 29.5 | 19.8 | 11.4 | 5.8 | 1.7 | 0.2 |
| AutoLoc (Shou et al.,2018) | ■ | ■ | 35.8 | 29.0 | 21.2 | 13.4 | 5.8 | - | - |
| MAAN (ours) | 59.8 | 50.8 | 41.1 | 30.6 | 20.3 | 12.0 | 6.9 | 2.6 | 0.2 |
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| Fully Supervised | Richard et al. (Richard & Gall, 2016) | 39.7 | 35.7 | 30.0 | 23.2 | 15.2 | - | - | | ■ |
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| Yeung et al. (Yeung et al.,2016) | 48.9 | 44.0 | 36.0 | 26.4 | 17.1 | - | - | - | = |
| Yuan et al.(Yuan et al.,2016) | 51.4 | 42.6 | 33.6 | 26.1 | 18.8 | = | - | = | |
| Shou et al. (Shou et al., 2017) | - | - | 40.1 | 29.4 | 23.3 | 13.1 | 7.9 | | |
| Yuan et al. (Yuan et al.,2017b) | 51.0 | 45.2 | 36.5 | 27.8 | 17.8 | = | - | = | |
| Xu et al. (Xu et al.,2017) | 54.5 | 51.5 | 44.8 | 35.6 | 28.9 | | | | |
| Zhao et al. (Zhao et al.,2017) | 66.0 | 59.4 | 51.9 | 41.0 | 29.8 | ■ | = | = | |
| Weakly Supervised | Wang et al. (Wang et al., 2017) | 44.4 | 37.7 | 28.2 | 21.1 | 13.7 | = | | | |
| Singh & Lee (Singh& Lee,2017) | 36.4 | 27.8 | 19.5 | 12.7 | 6.8 | = | | | = |
| STPN (Nguyen et al.,2018) (UN) | 45.3 | 38.8 | 31.1 | 23.5 | 16.2 | 9.8 | 5.1 | 2.0 | 0.3 |
| STPN (Nguyen et al., 2018) (I3D) | 52.0 | 44.7 | 35.5 | 25.8 | 16.9 | 9.9 | 4.3 | 1.2 | 0.1 |
| STPN (Nguyen et al.,2018) (ours) | 57.4 | 48.7 | 40.3 | 29.5 | 19.8 | 11.4 | 5.8 | 1.7 | 0.2 |
| AutoLoc (Shou et al.,2018) | ■ | ■ | 35.8 | 29.0 | 21.2 | 13.4 | 5.8 | - | - |
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| 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 0.9 |
| Fully Supervised | Richard et al. (Richard & Gall, 2016) | 39.7 | 35.7 | 30.0 | 23.2 | 15.2 | - | - | | ■ |
| Shou et al. (Shou et al.,2016) | 47.7 | 43.5 | 36.3 | 28.7 | 19.0 | 10.3 | 5.3 | = | = |
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| Weakly Supervised | Wang et al. (Wang et al., 2017) | 44.4 | 37.7 | 28.2 | 21.1 | 13.7 | = | | | |
| Singh & Lee (Singh& Lee,2017) | 36.4 | 27.8 | 19.5 | 12.7 | 6.8 | = | | | = |
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+ "html": "| Algorithm 1: Style clustering | |
| Input: n images x1,x2,., xn ∈ X and respective class labels yi ∈ [k] Number of styles per class l ∈N |
| Feature extraction function : X → Rd | |
| Output: Per class style labels γ : [n] → [k] ×[] | |
| ∀i∈[n],fi←(xi) // | extract features from images |
| ∀j∈[k],ti ←k-meanst({filyi=j}）// cluster class j into l styles | |
| Vi∈[n],ψ(i)←(yi,ti) // assign joint class and style labels | |
+
+We provide samples in Fig. 16 of clustering shoe images with $\mathbf { k }$ -means $k = 2 , l = 1 0 0$ ) using style features (Li et al., 2017) extracted from a pretrained VGG model.
+
+# A.9 DOMAIN TRANSLATION RESULTS
+
+We extend our unsupervised domain translation approach to support multi-attribute class labeling. We use the 40 annotated attributes in CelebA and use them to supervise 40 different shared class embeddings in addition to a single content embedding optimized per image. We demonstrate the effectiveness of this extended LORD approach in translating males to females and vice versa in Fig. 17.
+
+
+Figure 14: Qualitative comparison on CelebA between our method and 3 of our ablation baselines. Fully-amortized models (a, b) fail to preserve the class (person identity) across different content codes and introduce several artifacts, showing their lower degree of disentanglement. Semiamortized model regularized with asymmetric noise (c) transfers over unreliable properties between identities (such as hair style). Our model (d) learns to disentangle the intrinsic characteristics of each identity and provides the best disentanglement and highest quality.
+
+
+Figure 15: A visualization of the degradation in reconstruction and disentanglement quality in cases where classes exhibit intra-class variations. It can be observed that the car model is not preserved well across different content codes.
+
+
+Figure 16: Random samples from clusters of shoe images formed by $\mathbf { k }$ -means on style features extracted from a pretrained VGG model.
+
+
+(b) Females to Males
+Figure 17: Examples of translations between genders of faces from CelebA using our method.
\ No newline at end of file
diff --git a/parse/train/Hyl9xxHYPr/Hyl9xxHYPr_content_list.json b/parse/train/Hyl9xxHYPr/Hyl9xxHYPr_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..0dab7bf762c0044792b7165239ba068e50a14e1a
--- /dev/null
+++ b/parse/train/Hyl9xxHYPr/Hyl9xxHYPr_content_list.json
@@ -0,0 +1,1827 @@
+[
+ {
+ "type": "text",
+ "text": "DEMYSTIFYING INTER-CLASS DISENTANGLEMENT ",
+ "text_level": 1,
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+ {
+ "type": "text",
+ "text": "Aviv Gabbay Yedid Hoshen School of Computer Science and Engineering The Hebrew University of Jerusalem, Israel ",
+ "bbox": [
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+ "page_idx": 0
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+ {
+ "type": "text",
+ "text": "ABSTRACT ",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 0
+ },
+ {
+ "type": "text",
+ "text": "Learning to disentangle the hidden factors of variations within a set of observations is a key task for artificial intelligence. We present a unified formulation for class and content disentanglement and use it to illustrate the limitations of current methods. We therefore introduce LORD, a novel method based on Latent Optimization for Representation Disentanglement. We find that latent optimization, along with an asymmetric noise regularization, is superior to amortized inference for achieving disentangled representations. In extensive experiments, our method is shown to achieve better disentanglement performance than both adversarial and non-adversarial methods that use the same level of supervision. We further introduce a clustering-based approach for extending our method for settings that exhibit in-class variation with promising results on the task of domain translation. ",
+ "bbox": [
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+ "page_idx": 0
+ },
+ {
+ "type": "text",
+ "text": "Project webpage: http://www.vision.huji.ac.il/lord ",
+ "bbox": [
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+ "page_idx": 0
+ },
+ {
+ "type": "text",
+ "text": "1 INTRODUCTION ",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 0
+ },
+ {
+ "type": "text",
+ "text": "Objects in the real world encompass many different attributes mixed together. Some of the attributes are permanent i.e. the class identity of the object, whereas others are transitory e.g. the pose of the object. Humans can often effectively separate between the class identity of the object, and the transitory pose of the object, even from a single observation. A key task for artificial intelligence is to empower computers to learn to separate between different attributes of observed data, often referred to as disentanglement. In this paper, we present a new method for achieving disentanglement between the class of an object and the sample-specific content. We restrict our attention to images, however some of our ideas may carry over to other modalities. ",
+ "bbox": [
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+ "page_idx": 0
+ },
+ {
+ "type": "text",
+ "text": "There are multiple settings for disentanglement. The simplest is fully supervised - for each training image both the class and content are given as labels. A fully supervised scheme (e.g. deep encoders) may be trained to recover the class and content information from a single image. Conversely, a generative model can be trained to generate an image given input class and content information. On the other extreme, fully unsupervised disentanglement takes as input a set of images with no further information. A successful unsupervised disentanglement algorithm will be able to learn a representation in which different factors of variation such as class and content will be represented separately. Fully unsupervised disentanglement is highly ambitious and is work in progress, current methods typically do not produce consistently good results in this setting (Locatello et al., 2019). ",
+ "bbox": [
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+ "page_idx": 0
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+ {
+ "type": "text",
+ "text": "In this work, we deal with the class-supervised disentanglement task. In this setting, the class label for each image in the training set is given. Such supervision can be easily obtained in practice e.g. tracking an object in a video obtains multiple images in multiple poses of the same class (for example, person identity). The objective of the disentanglement task is to learn a representation containing all the information not available in the class label, denoted as content. In the case of faces, this content includes: head pose, facial expression, etc. We begin by carefully analyzing the information contained in the class and content representations. We show that current methods allow information to leak between the representations leading to imperfect disentanglement. We therefore introduce LORD, a novel method which carefully ensures no information leakage between the class and content representations. ",
+ "bbox": [
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+ "page_idx": 0
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+ {
+ "type": "text",
+ "text": "Our method differs from previous methods by several methodological improvements. i) We leverage latent optimization to learn a single representation for each class which is shared between all its samples. We show and discuss the benefits of this approach over the amortized techniques. ii) We introduce asymmetric regularization on the content latent codes to achieve class-invariant representations. We show the superiority of this technique over adversarial constraints and the KLdivergence. Latent optimization is very effective at learning disentangled representations at training time, however, it is not useful for obtaining class and content codes of unseen test images. Optimizing over the latent codes at test time (without class supervision which exists at training time), leads to overfitting which results in entangled representations. We overcome this challenge by introducing a second stage in which we use the class and content codes learned by our model in the first stage for training feed-forward class and content encoders. The encoders generalize well to unseen images and significantly reduce the inference time on new samples. ",
+ "bbox": [
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+ "text": "",
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+ "type": "text",
+ "text": "Our method is evaluated qualitatively and quantitatively in terms of generation of novel samples of observed classes. We also quantitatively evaluate the quality of disentanglement of learned features by classifying class labels from content codes and vice versa. Our method is shown to significantly outperform other adversarial and non-adversarial methods. Disentangling class and content representations assumes that intra-class variation is significantly lower than inter-class variation. We discover that this assumption can be relaxed by clustering in-class styles into separate classes. We demonstrate promising results of our approach on unsupervised domain mapping. ",
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+ "text": "Our contributions in this work are as follows: i) An insightful analysis of class-conditional disentanglement. ii) LORD: a new well-motivated non-adversarial method for disentanglement achieving SOTA results by shared latent optimization and an asymmetric regularization. iii) Second stage amortization for single-shot class generalization. iv) The first effective method for disentanglement between 10k classes. v) A clustering based extension for style disentanglement. ",
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+ "type": "text",
+ "text": "1.1 RELATED WORK ",
+ "text_level": 1,
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "Our work deals with class-supervised disentanglement. Several works based on variational autoencoders (VAEs) (Kingma & Welling, 2014) have attempted disentanglement with no supervision e.g. $\\beta$ -VAE (Higgins et al., 2017) and factor-VAE (Kim & Mnih, 2018). In an extensive comparative study, Locatello et al. (2019) show that none of the compared methods have been successful on all the datasets examined. It therefore seems likely that some supervision is required for effective disentanglement. Many works (including ours) provide only class supervision e.g. when the identity of a face is given but not its transitory attributes. The disentanglement between the factors of variation is enforced by adversarial constraints (Mathieu et al., 2016; Szabo et al., 2018; Denton & Birodkar, ´ 2017; Hadad et al., 2018) or by non-adversarial constraints e.g. cycle (Harsh Jha et al., 2018) or variational group codes (Bouchacourt et al., 2018). Differently from the above works, we learn perclass codes rather than per-image class. Similar design choice were taken by cGAN and cVAE, but for the application of image generation rather than disentanglement. cGAN and cVAE require the latent space to be Gaussian, which hurts disentanglement performance. ",
+ "bbox": [
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+ "type": "text",
+ "text": "Many disentanglement methods use adversarial training (Goodfellow et al., 2014). Success was achieved on image generation (Brock et al., 2019), image mapping (Isola et al., 2017) and domain alignment (Liu et al., 2017). Adversarial methods are notoriously hard to optimize, require very careful architecture and hyper-parameters tuning due to their min-max nature. To overcome these issues, non-adversarial methods have been proposed to achieve better results on tasks previously dominated by adversarial networks e.g. image synthesis (Bojanowski et al., 2018; Razavi et al., 2019), image-to-image mapping (Hoshen & Wolf, 2018) and word translation (Mukherjee et al., 2018). In this paper, we present a non-adversarial method achieving state-of-the-art performance on disentanglement. ",
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+ "type": "text",
+ "text": "2 CLASS AND CONTENT DISENTANGLEMENT ",
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+ "text": "Assume that we are given a collection of $n$ images $x _ { 1 } , x _ { 2 } , . . . , x _ { n } \\in { \\mathcal { X } }$ . For each image $x _ { i }$ , we are given a class label $y _ { i } \\in [ k ]$ . We assume that every image belongs to a single class, although this requirement can be relaxed. Note that many images may share the same class label (e.g. faces of the same person at different poses). We denote the embedding of a given class $y$ as $e _ { y }$ . We assume that the images can be disentangled into representations in two latent spaces $\\mathcal { V }$ and $\\mathcal { C }$ . Therefore, our objective it to find a class representation $e _ { y _ { i } } \\in \\mathcal { V }$ and a content representations $c _ { i } \\in \\mathcal { C }$ for each image $x _ { i }$ . Let us define the information that we wish each representation to contain. As there is some inconsistency in the notation used in the style-content, pose-content and domain translation literature, we will define our terms precisely. ",
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+ "text": "The image class representation $e _ { y _ { i } }$ , needs to include all information that is shared by all images sharing the same class e.g. if classes correspond to different facial identities, then the class representation must include all the time-invariant facial information. The content representation $c _ { i }$ includes all the information that is unchanged if the image is transferred between classes. This information must be independent of the class-information. E.g for faces, content corresponds to time-varying facial information such as head pose and expression. Besides the class and content representations, images may contain other image-specific information, which is not represented by the class-label and is not expected to be transferred across classes. The difference between content and style is semantic and requires careful design. In the facial identity example the style may include noise, lighting conditions or nuisance background features. We denote the style representation as $s _ { i } \\in S$ . ",
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+ "text": "We define a generator $G$ , a neural network parameterized by $\\theta$ , which transforms the disentangled representations into an image. Given our definitions above each image can be modeled by: ",
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+ "text": "$$\nx _ { i } = G _ { \\theta } ( e _ { y _ { i } } , s _ { i } , c _ { i } ) \\quad x _ { i } \\in \\mathcal { X } \\enspace e _ { y _ { i } } \\in \\mathcal { Y } \\enspace s _ { i } \\in \\mathcal { S } \\enspace c _ { i } \\in \\mathcal { C }\n$$",
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+ "text": "The content must be independent of the class and style, however the style may be class dependent. E.g. if the classes are shoe images and edge images, styles within the shoes class may include particular colors and textures, which are typical of shoes but not of edge images. More formally, the mutual information between $c$ and $e _ { y }$ , $s$ should be zero: ",
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+ "img_path": "images/a4a820fe06f323fd3124f5386c9804af73f20ca49e0361dfe1dca79e9508319a.jpg",
+ "text": "$$\nI ( c ; e _ { y } ) = 0 \\qquad I ( c ; s ) = 0\n$$",
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+ "text": "Adversarial Methods: One way to ensure the independence between the content and class/style representations is using adversarial discriminators. We will summarize the ideas proposed in DrNet (Denton & Birodkar, 2017) as this approach has the best performance of all adversarial methods. These techniques do not learn a class representation explicitly but instead strongly constrain a style encoding. The model of this method is described by: ",
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+ "text": "They attempt to ensure the similarity of styles of images in the class using a similarity constraint $\\mathcal { L } _ { s i m i l a r i t y } = \\| s _ { i } - s _ { j } \\| ^ { 2 }$ if $y _ { i } ~ = ~ y _ { j }$ . To ensure independence between $s$ and $c$ , an adversarial discriminator $D _ { y } ( c _ { i } , c _ { j } )$ is trained to discover if two images are from the same class. If the content representation is truly disentangled, then no class information is available in the content code and the discriminator accuracy will not be greater than a random chance. This approach has two weaknesses: i) It does not directly prevent content information from leaking into the style representation (but only through a weak pairwise constraint). ii) Adversarial methods are notoriously hard to optimize and require careful hyper-parameter tuning due to the challenging saddle point optimization problem. ",
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+ "text": "Non-Adversarial Methods: Due to the difficulty of adversarial training, non-adversarial methods have attracted attention. We will review the ideas in Multi-Level VAE (ML-VAE) (Bouchacourt et al., 2018), which performs the best of the non-adversarial methods and is most related to ours. ML-VAE also does not learn a class-representation, but a style representation $s _ { i }$ via amortized inference. However, in order to limit the content information which flows to the generator from the style code, it relies on the presence of samples from the same class in a mini-batch during training and accumulates their style encodings using a product of normal densities before feeding the generator (the entire process is described in the original paper). To summarize, ML-VAE approximates the style representation $\\bar { s } _ { M }$ of a group of observations $M$ from the same class, and generates the image: ",
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+ "img_path": "images/7248818e23b39958c75f4f06f7fb1e44b902adc1e31f9510affaebcab6402e10.jpg",
+ "text": "$$\nx _ { i } = G _ { \\theta } \\left( 0 , \\bar { s } _ { M _ { i } } , c _ { i } \\right) ~ M _ { i } = \\{ j | y _ { i } = y _ { j } \\}\n$$",
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+ "text": "It limits the information in the content representation $c _ { i }$ by constraining its distribution using KLdivergence with the standard normal distribution. This approach suffers from significant drawbacks: i) It uses grouped amortized encoding for inferring $\\bar { s } _ { M }$ . As the size of a mini-batch is limited, this either limits the group accumulation to be over a few samples which is biased, or limits batchdiversity by only including a few classes which hurts optimization. ii) In our experiments, the KL-divergence does not sufficiently constrain the information in $c _ { i }$ i.e. in practice class information is found in $c _ { i }$ . ",
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+ "type": "text",
+ "text": "3 LORD: LATENT OPTIMIZATION FOR REPRESENTATION DISENTANGLEMENT ",
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+ "text": "In Sec. 2, we analyzed the task of disentanglement between class and content. Our analysis highlighted the issues faced by current state-of-the-art methods. In this section, we introduce a novel method motivated by the insights from the previous section. ",
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+ "text": "3.1 LATENT OPTIMIZATION FOR CLASS SUPERVISION ",
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+ "text": "We make explicit the assumption that inter-class variation is significantly larger than intra-class variation. This allows us to model images as a combination of class and content codes: ",
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+ "img_path": "images/d05b7a64cbd3ac5f9f8b5a9366d1d940bccd5f1bb3520b71709c653833d9bc98.jpg",
+ "text": "$$\nx _ { i } = G _ { \\theta } ( e _ { y _ { i } } , 0 , c _ { i } )\n$$",
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+ "text": "Shared Latent Optimization: We model the class representation as an embedding $e _ { y }$ that is shared between all images belonging to the same class $\\{ x _ { i } | y _ { i } = y \\}$ . Instead of using amortized inference (learning a mapping from the image to the class codes using an encoder), we optimize over the class embeddings directly using latent optimization. This has several important benefits: i) As the code is shared exactly between all images belonging to the same class (each having different content), it is impossible to include any content information in the class code. ii) As we learn per-class representations directly rather than using previous techniques as group averaging, each mini-batch can contain images randomly sampled from all classes allowing maximal diversity. ",
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+ "text": "We learn the content representation by optimizing over per-sample content embeddings directly using latent optimization and not in an amortized fashion using an image to content encoder. As we show in the experimental section, a model trained with latent optimization preserves a very high degree of disentanglement along the training and is less sensitive to hyperparameter choices. ",
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+ "text": "Asymmetric Noise Regularization: Latent optimization over the class embeddings ensures that no content information is present in the class representation. To ensure that class information does not leak into the content representation, we regularize the content code to enforce minimality of information. Previous approaches attempted to minimize content information by setting a bottleneck of a small content code or by matching the content distribution to a prior normal distribution using KLdivergence. Using a small noiseless bottleneck, does not however reduce information significantly. A continuous variable may in fact store an infinite amount of information (although the amount of information the generator may extract is limited by other factors). In our experiments, we found that regularizing with KL-divergence (as done by previous works) led to a partial posterior collapse i.e. nearly all means and standard deviations learned by the encoder defaulted to 0 and 1 respectively, satisfying a perfect standard normal distribution. For a few components, the encoder learned large means and very small standard deviations. The KL-divergence therefore learned behavior similar to a small-size bottleneck. This phenomenon implies that regularizing the distribution of the content codes with KL-divergence may require additional attention and a careful hyperparameter tuning. We present the experimental evidence in the Appendix A.3. ",
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+ "text": "In our approach, we regularize the content code with an additive Gaussian noise of a fixed variance, and an activation decay penalty. In contrast to a variational auto-encoder, we do not learn the variance, but rather keep it fixed. This prevents the possibility of the variance decreasing to a small value, ensuring that noise is applied equally on all components. Our objective function becomes: ",
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+ "type": "image",
+ "img_path": "images/54fe648be34a4f231649f23cc71864475ff6e0bfad8dcb6cb7c299b138bd4c1d.jpg",
+ "image_caption": [
+ "Figure 1: A sketch of the first stage: all class and content embeddings and the generator are jointly optimized. All images of the same class share a single class embedding. The content embeddings are regularized by a gaussian noise. By the end of this stage, the latent space of the training set is disentangled. Note that the second stage is not shown. "
+ ],
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+ "type": "equation",
+ "img_path": "images/1cdf5c179ae1a0fa49efa3e3f967719248c4408db5f6a78b69204b6e55d59f1e.jpg",
+ "text": "$$\n\\mathcal { L } = \\sum _ { i = 1 } ^ { n } \\| G _ { \\theta } ( e _ { y _ { i } } , 0 , c _ { i } + z _ { i } ) - x _ { i } \\| + \\lambda \\| c _ { i } \\| ^ { 2 } \\quad z _ { i } \\sim \\mathcal { N } ( 0 , \\sigma ^ { 2 } I )\n$$",
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+ "text": "The first loss terms uses a VGG perceptual loss as implemented by Hoshen & Malik (2019). Unless stated otherwise, we optimize over class and content codes $( e _ { y _ { i } }$ and $c _ { i }$ ) directly using latent optimization. All latent codes and the parameters of the generator are learned end-to-end using stochastic gradient descent: ",
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+ "type": "equation",
+ "img_path": "images/809550c242d098628f4ba350b02ce48558afbefac08cd08b396131576771d017.jpg",
+ "text": "$$\n\\{ e _ { 1 } ^ { * } , . . , e _ { k } ^ { * } , c _ { 1 } ^ { * } . . , c _ { n } ^ { * } , \\theta ^ { * } \\} = a r g \\operatorname* { m i n } _ { e , c , \\theta } \\mathcal { L }\n$$",
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+ "type": "text",
+ "text": "3.2 AMORTIZATION FOR ONE-SHOT INFERENCE ",
+ "text_level": 1,
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+ "type": "text",
+ "text": "Latent optimization, which is used effectively for training, requires optimization for every image (including at inference time). In the training set, a class embedding is shared across multiple images, which prevents the embedding from including content information. However, at inference time, a single image from an unknown class is observed. Optimizing over the latent codes for a single image leads to overfitting which results in entangled representations. Moreover, it requires iterative test-time inference since it does not perform amortized inference. ",
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+ "type": "text",
+ "text": "To this end, we introduce a second stage which learns class and content encoders that directly infer class $e _ { y _ { i } }$ and content $c _ { i }$ representations from a single image $x _ { i }$ . The second stage effectively amortizes the results of the first stage and generalizes well to unseen classes and images. We train encoders $E _ { y } : \\mathcal { X } \\mathcal { V }$ and $E _ { c } : \\mathcal { X } \\mathcal { C }$ , which take as input an image $x _ { i }$ and output its class and content embeddings that were learned by our method in the first stage. We also use a reconstruction loss, to ensure the representations learned in the second stage must reconstruct the original image $x _ { i }$ . The optimization objective is presented in Eq. 8. The optimization is over the parameters of encoders $E _ { y }$ and $E _ { c }$ (which are randomly initialized) and the parameters of the generator $G$ (which are initialized from the first stage). Note that the given $e _ { y _ { i } }$ and $c _ { i }$ are the representations we have learned during the previous stage. ",
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+ "img_path": "images/f7626f6c38e1db67963b5ab465614e1e03ae2cbfc17e3a8ac1686915776c9614.jpg",
+ "text": "$$\n\\mathcal { L } _ { E } = \\sum _ { i = 1 } ^ { n } \\| G _ { \\theta } ( E _ { y } ( x _ { i } ) , 0 , E _ { c } ( x _ { i } ) ) - x _ { i } \\| + \\alpha _ { 1 } \\cdot \\| E _ { y } ( x _ { i } ) - e _ { y _ { i } } \\| ^ { 2 } + \\alpha _ { 2 } \\cdot \\| E _ { c } ( x _ { i } ) - c _ { i } \\| ^ { 2 }\n$$",
+ "text_format": "latex",
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+ "type": "text",
+ "text": "After training, we can preserve the class of a new test image $\\hat { x _ { 1 } }$ and transfer over the content from another image $\\hat { x _ { 2 } }$ by decomposing the images into their disentangled class and content representa",
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+ "img_path": "images/8cc80b0622be21614b3de64abd85180d1a99c516f618dde3cd1c90feddfb3261.jpg",
+ "image_caption": [
+ "Figure 2: Comparison between our method and baselines on Cars3D (top) and SmallNorb (bottom). "
+ ],
+ "image_footnote": [],
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+ {
+ "type": "text",
+ "text": "tions and regenerating them as follows: ",
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+ "page_idx": 5
+ },
+ {
+ "type": "equation",
+ "img_path": "images/8587199609bb55a8f87e89fdd37ff99e87431d0b8bc780f2345c8b4d1eafcd3c.jpg",
+ "text": "$$\n\\hat { x } _ { 1 2 } = G _ { \\theta } ( E _ { y } ( \\hat { x _ { 1 } } ) , 0 , E _ { c } ( \\hat { x _ { 2 } } ) )\n$$",
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+ {
+ "type": "text",
+ "text": "4 EXPERIMENTS ",
+ "text_level": 1,
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+ "type": "text",
+ "text": "Our method is evaluated against SOTA techniques for class-supervised disentanglement. We do not compare to methods for fully-unsupervised disentanglement as the results are not directly comparable and their performance is inferior on the following benchmarks due to lower level of supervision. All the implementation details are provided in the Appendix A.1. ",
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+ "text": "Datasets: We evaluate the performance of our method and the baselines on several datasets (each with the appropriate class labels): Cars3D (car model as class label, azimuth and elevation as content), SmallNorb (object type $\\times$ lighting $\\times$ elevation as class labels, azimuth as content), SmallNorbPoses (object type $\\times$ lighting as class labels, azimuth and elevation as content), CelebA (person identity as class label, other unlabeled transitory facial attributes e.g. head pose and expression as content), KTH (person identity as class label, other unlabeled transitory attributes e.g skeleton position as content), RaFD (facial expression as class label, rest as varied content). A more detailed description of each dataset and configuration can be found in the Appendix A.2. ",
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+ "type": "text",
+ "text": "Baselines: We compare our method against SOTA methods for class-supervised disentanglement. DrNet (Denton & Birodkar, 2017) and Szabo et al. (2018) encourage disentanglement by adversar- ´ ial constraints, and ML-VAE (Bouchacourt et al., 2018) and Cycle-VAE (Harsh Jha et al., 2018) use variants of VAE equipped with grouped class accumulation and cycle constraints to discourage degenerate solutions. We also compare against StarGAN (Choi et al., 2018) in Multi-Domain translation. For fairness, we evaluate each baseline with $L _ { 1 }$ and perceptual loss and report the best. ",
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+ "type": "text",
+ "text": "Quantitative Experiments: ",
+ "text_level": 1,
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+ {
+ "type": "text",
+ "text": "Content transfer experiments: To test the quality of disentanglement, we measure the quality of content transfer in terms of perceptual similarity by LPIPS (Zhang et al., 2018). We use the content labels available in the Cars3D and SmallNorb datasets as ground truth for content transfer. For given test images $x _ { i }$ and $x _ { j }$ , we measure the similarity between $\\boldsymbol { x } _ { 1 2 } = G _ { \\theta } ( E _ { y } ( x _ { i } ) , 0 , E _ { c } ( x _ { j } ) )$ and another image from the same class of $x _ { i }$ matching the same content of $x _ { j }$ . For CelebA, given two images of the same person, we infer the class (identity) representation from the first image and aim at reconstructing the second by extracting the content representation from an image of a different identity which has the most similar pose (nearest neighbour in the 68 facial-landmarks space). Results are reported in Tab. 1. It can be seen that we strongly outperform all the baselines. ",
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+ {
+ "type": "image",
+ "img_path": "images/456face1d74a0224867ce68234287a02d182ee33cc46dfa2693347f18930b400.jpg",
+ "image_caption": [
+ "Figure 3: Comparison between our method and baselines on KTH (top) and CelebA (bottom). "
+ ],
+ "image_footnote": [],
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+ "text": "",
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+ },
+ {
+ "type": "text",
+ "text": "Classification experiments: To assess the disentanglement of our learned representations, we follow the protocol in Harsh Jha et al. (2018) and train a classifier to classify class labels from content codes and vice versa. Results can be seen in Tab. 2. On all datasets, our model achieves near perfect disentanglement as the classifier could barely guess class labels from content codes by a random chance (same for the other direction). All the baselines fail to zero out the mutual information between the two representations. To conclude, our method is able to learn the most disentangled features without introducing adversarial constraints. For CelebA, in order to test if the content of an image is predictable from the class code we train a linear regression model to regress the position of 68 facial landmarks. It can be seen that the linear regression results in the highest error on our class representations, indicating the highest degree of disentanglement of our method. It should be noted that all methods could classify class labels from class codes and content labels from content codes very accurately (not shown). ",
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+ },
+ {
+ "type": "text",
+ "text": "Facial expression transfer experiment: We compare our method against StarGAN in the task of Multi-Domain translation. We follow the protocol in Choi et al. (2018) and compute the classification error of a facial expression classifier (trained on real images from RaFD) on synthesized images. We train both image translation models using the same training set and perform image translation on the same, unseen test set. As can be seen in Tab. 4, our model achieves lower classification error than StarGAN, indicating that our model produces more realistic facial expressions without using adversarial training. ",
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+ },
+ {
+ "type": "text",
+ "text": "Qualitative Experiments: We visually evaluate the results of our method against DrNet (strongest adversarial baseline) and ML-VAE (strongest non-adversarial baseline) in Fig. 2 and 3. In each experiment, we visualize switching between class (left column) and content (top row) codes for each pair within a set of 5 test images. On Cars3D, our method achieves excellent content transfer while keeping the class fixed. DrNet is mostly able to transfer the content, but it does not keep the car model fixed. ML-VAE results are of lower fidelity. On SmallNorb, our method works well, whereas the baseline methods struggle with preserving the identity of the object in some rotations (e.g. bottom row). On KTH both our method as well as DrNet perform well, although our method achieves more accurate transfer (e.g. last image in the top row). ML-VAE fails to transfer the skeleton on some identities (e.g. last row). On CelebA, the baselines generally transfer head pose but do not preserve the person identity. Our method achieves better pose transfer than both baselines, and is able to maintain the identity. ",
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+ },
+ {
+ "type": "table",
+ "img_path": "images/6a918b7dfe91e281d945e04afd3d102bb18c4af794736e16662b4469c0c97062.jpg",
+ "table_caption": [
+ "Table 1: Content transfer reconstruction error (LPIPS ↓) "
+ ],
+ "table_footnote": [],
+ "table_body": "| Algorithm 1: Style clustering | |
| Input: n images x1,x2,., xn ∈ X and respective class labels yi ∈ [k] Number of styles per class l ∈N |
| Feature extraction function : X → Rd | |
| Output: Per class style labels γ : [n] → [k] ×[] | |
| ∀i∈[n],fi←(xi) // | extract features from images |
| ∀j∈[k],ti ←k-meanst({filyi=j}）// cluster class j into l styles | |
| Vi∈[n],ψ(i)←(yi,ti) // assign joint class and style labels | |
",
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+ {
+ "type": "text",
+ "text": "We provide samples in Fig. 16 of clustering shoe images with $\\mathbf { k }$ -means $k = 2 , l = 1 0 0$ ) using style features (Li et al., 2017) extracted from a pretrained VGG model. ",
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+ {
+ "type": "text",
+ "text": "A.9 DOMAIN TRANSLATION RESULTS ",
+ "text_level": 1,
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+ "page_idx": 18
+ },
+ {
+ "type": "text",
+ "text": "We extend our unsupervised domain translation approach to support multi-attribute class labeling. We use the 40 annotated attributes in CelebA and use them to supervise 40 different shared class embeddings in addition to a single content embedding optimized per image. We demonstrate the effectiveness of this extended LORD approach in translating males to females and vice versa in Fig. 17. ",
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+ {
+ "type": "image",
+ "img_path": "images/6923afbe1984b3120993fcf14d09161ef35c17626e55f8e7df3f383a44ee9148.jpg",
+ "image_caption": [
+ "Figure 14: Qualitative comparison on CelebA between our method and 3 of our ablation baselines. Fully-amortized models (a, b) fail to preserve the class (person identity) across different content codes and introduce several artifacts, showing their lower degree of disentanglement. Semiamortized model regularized with asymmetric noise (c) transfers over unreliable properties between identities (such as hair style). Our model (d) learns to disentangle the intrinsic characteristics of each identity and provides the best disentanglement and highest quality. "
+ ],
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+ {
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+ "img_path": "images/e34680ae4f4ad147ff213cb223fbbd950c2cb1992bc2e7b5277a4b2bea72dab9.jpg",
+ "image_caption": [
+ "Figure 15: A visualization of the degradation in reconstruction and disentanglement quality in cases where classes exhibit intra-class variations. It can be observed that the car model is not preserved well across different content codes. "
+ ],
+ "image_footnote": [],
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+ "img_path": "images/ea4d38282844e45acdfe9eb7d4635e8133ca2552fe9a01de06491ae29f60b0b8.jpg",
+ "image_caption": [
+ "Figure 16: Random samples from clusters of shoe images formed by $\\mathbf { k }$ -means on style features extracted from a pretrained VGG model. "
+ ],
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+ {
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+ "img_path": "images/6ed964c64a59748e2b0f1e81bf79a75775db2b79afe1097edf27c3955594e20a.jpg",
+ "image_caption": [
+ "(b) Females to Males ",
+ "Figure 17: Examples of translations between genders of faces from CelebA using our method. "
+ ],
+ "image_footnote": [],
+ "bbox": [
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+ "page_idx": 21
+ }
+]
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diff --git a/parse/train/Hyl9xxHYPr/Hyl9xxHYPr_middle.json b/parse/train/Hyl9xxHYPr/Hyl9xxHYPr_middle.json
new file mode 100644
index 0000000000000000000000000000000000000000..79127119d56258e1076912cfe154ba4ca8f29e5b
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| Input: n images x1,x2,., xn ∈ X and respective class labels yi ∈ [k] Number of styles per class l ∈N |
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| Output: Per class style labels γ : [n] → [k] ×[] | |
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| ∀j∈[k],ti ←k-meanst({filyi=j}）// cluster class j into l styles | |
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| Input: n images x1,x2,., xn ∈ X and respective class labels yi ∈ [k] Number of styles per class l ∈N |
| Feature extraction function : X → Rd | |
| Output: Per class style labels γ : [n] → [k] ×[] | |
| ∀i∈[n],fi←(xi) // | extract features from images |
| ∀j∈[k],ti ←k-meanst({filyi=j}）// cluster class j into l styles | |
| Vi∈[n],ψ(i)←(yi,ti) // assign joint class and style labels | |
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| Input: n images x1,x2,., xn ∈ X and respective class labels yi ∈ [k] Number of styles per class l ∈N |
| Feature extraction function : X → Rd | |
| Output: Per class style labels γ : [n] → [k] ×[] | |
| ∀i∈[n],fi←(xi) // | extract features from images |
| ∀j∈[k],ti ←k-meanst({filyi=j}）// cluster class j into l styles | |
| Vi∈[n],ψ(i)←(yi,ti) // assign joint class and style labels | |
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+# Local $K$ -means: An Efficient Optimization Algorithm And Its Generalization
+
+Anonymous Author(s)
+Affiliation
+Address
+email
+
+# Abstract
+
+1 Until now, $k$ -means is still one of the most popular clustering algorithms because of
+2 its simplicity and efficiency, although it has been proposed for a long time. In this
+3 paper, we considered a variant of $k$ -means that takes the $k$ -nearest neighbor $k$ -NN)
+4 graph as input and proposed a novel clustering algorithm called Local K-Means
+5 (LKM). We also developed a general model that unified LKM, KSUMS, and SC,
+6 and discussed the connection among them. In addition, we proposed an efficient
+7 optimization algorithm for the unified model. Thus, not only LKM but also SC can
+8 be optimized with a linear time complexity with respect to the number of samples.
+9 Specifically, the computational overhead is $O ( n k )$ , where $n$ and $k$ are denote the
+10 number of samples and nearest neighbors, respectively. Extensive experiments
+11 have been conducted on 11 synthetic and 16 benchmark datasets from the literature.
+12 The effectiveness, efficiency, and robustness to outliers of the proposed method
+13 have been verified by the experimental results.
+
+# 14 1 Introduction
+
+15 Clustering is one of the fundamental tasks of machine learning [10]. It plays a very important role in
+16 many applications such as document analysis [6], image processing [14], and recommender system
+17 [12]. Given a dataset with $n$ samples and the number of clusters $c$ , its purpose is to split these samples
+18 into $c$ disjoint groups, so that the samples within the same group are similar to each other, and the
+19 samples between different groups are not. Although there are lots of clustering algorithms have been
+20 proposed, $k$ -means is still getting a lot of attention. In this paper, we proposed an efficient clustering
+21 method called local $k$ -means where a $k$ -NN graph is taken as input. It can be seen as a variant of
+22 traditional $k$ -means. In the following, the two basic materials of our model are firstly described, and
+23 the main contributions of this article will be mentioned at the end of this section.
+24 Notations: Bold capital letters and bold lowercase letters denote matrices and vectors, respectively.
+25 The symbols $n , d$ , and $c$ are respectively used to represent the number of samples of the dataset, the
+26 number of features, and the number of clusters to construct. For matrix A, we call it indicator matrix,
+27 if each row of it has only one element equal to 1. $\Phi ^ { n \times c }$ is the set of all indicator matrices.
+
+# 28 1.1 $k$ -means
+
+29 As one of the most popular clustering algorithms, $k$ -means aims to group n samples into c clusters
+30 where each sample belongs to the cluster with the nearest cluster centers. Let ${ \bf X } \doteq [ { \bf x } _ { 1 } , \cdots , { \bf x } _ { n } ] ^ { T } \in$
+31 $\mathbb { R } ^ { n \times d }$ be a collection of samples to cluster, where $\mathbf { x } _ { i } \in \mathbb { R } ^ { d }$ denotes the $i$ -th sample. Then the objective
+32 function of $k$ -means can be formulated as
+
+$$
+\operatorname* { m i n } _ { A _ { 1 } , \cdots , A _ { c } } \sum _ { k = 1 } ^ { c } \sum _ { \mathbf x _ { i } \in A _ { k } } \| \mathbf x _ { i } - \mathbf m _ { k } \| _ { 2 } ^ { 2 } ,
+$$
+
+Submitted to 35th Conference on Neural Information Processing Systems (NeurIPS 2021). Do not distribute.
+
+
+Figure 1: Community in the social network. There is a connection between two users if they know each other, in other words, the two people are friends with each other. The thicker the line, the more familiar the two users. According to the connections between users, the clustering algorithm divides them into disjoint sets. For example, a partition composed of A, B, C, and $\mathrm { D }$ is a satisfactory clustering result.
+
+where 33 $\mathcal { A } _ { k }$ denotes the set of samples in the $i$ -th cluster, $\mathcal { A } _ { 1 } \bigcup \cdots \bigcup \mathcal { A } _ { c } = \{ \mathbf { x } _ { i } \mid i = 1 , \cdots , n \}$ , and 34 $\mathbf { m } _ { k }$ denotes the mean of samples in $\mathcal { A } _ { k }$ .
+
+35 Although the problem in Eq. (1) is computationally difficult, 1 many efficient optimization algorithms
+36 where a local optimum will be found quickly have been proposed. Among them, Lloyd’s algorithm is
+37 the most widely used. Let $\mathbf { Y } = [ \mathbf { y } _ { 1 } , \therefore \mathbf { \bar { \phi } } , \mathbf { \bar { y } } _ { n } ] ^ { T } = [ \bar { \mathbf { y } } _ { 1 } , \cdots \mathbf { \bar { \phi } } , \bar { \mathbf { y } } _ { c } ] \in \mathbb { R } ^ { n \times c }$ be an indicator matrix, i.e.,
+
+$$
+y _ { i j } = { \left\{ \begin{array} { l l } { 1 } & { \mathbf { x } _ { i } \in \mathcal { A } _ { j } } \\ { 0 } & { { \mathrm { o t h e r w i s e } } } \end{array} \right. } , i = 1 , \cdots , n , j = 1 , \cdots , c ,
+$$
+
+38 the problem in Eq. (1) can be then rewritten as
+
+$$
+\operatorname* { m i n } _ { \mathbf { Y } } \| \mathbf { X } - \mathbf { Y } \mathbf { M } \| _ { 2 } ^ { 2 } ,
+$$
+
+where 39 $\mathbf { M } = ( \mathbf { Y } ^ { T } \mathbf { Y } ) ^ { - 1 } \mathbf { Y } ^ { T } \mathbf { X }$ . In Lloyd’s algorithm, $\mathbf { Y }$ and $\mathbf { M }$ are regarded as two independent 40 variables and be optimized alternately.
+
+# 41 1.2 Data in the form of graph
+
+42 In fields such as social networks and recommendation systems, the data being studied is often
+43 presented in the form of graphs. In other words, for a single sample, we have no features to describe
+44 it, what we have is only the relationship between it and others, as shown in Figure 1.
+
+In generally, a sparse similarity matrix 45 $\mathbf { W } \in \mathbb { R } ^ { n \times n }$ can be used to describe this kind of data, i.e.,
+
+$$
+\begin{array} { r } { w _ { i j } = \left\{ \begin{array} { l l } { f ( \mathbf { x } _ { i } , \mathbf { x } _ { j } ) } & { \mathrm { I f ~ } \mathbf { x } _ { i } \mathrm { ~ a n d ~ } \mathbf { x } _ { j } \mathrm { ~ a r e ~ d i r e c t l y ~ c o n n e c t e d } } \\ { \qquad 0 } & { \mathrm { O t h e r w i s e } } \end{array} \right. , i , j = 1 , \cdots , n , } \end{array}
+$$
+
+where 46 $f ( \mathbf { x } _ { i } , \mathbf { x } _ { j } )$ represents the similarity between $\mathbf { x } _ { i }$ and $\mathbf { x } _ { j }$ , and its value can be usually obtained 47 directly.
+
+48 Based on the above discussion, a $k$ -means-like algorithm is proposed, which takes the $k$ -NN graph
+49 as input and can be quickly optimized. In addition, we also discussed its connection with other
+50 algorithms, such as KSUMS and spectral clustering. Here, we summarize the main contributions of
+51 the article as follows
+
+• A novel clustering algorithm called Local K-Means (LKM) is proposed. Because only the distances between the sample and its neighbors are considered, LKM is robust to outliers.
+• The relationship between LKM and other algorithms (KSUMS and SC) is discussed, and a unified model is established. An efficient optimization algorithm for the unified model is developed, from which we find that the spectral clustering model can be optimized in the same way as LKM, which means both of them can also be optimized in $O ( n k )$ time.
+
+60 A disadvantage of $k$ -means is that its performance will be affected largely by the initialization of
+61 the cluster center. To this end, a lot of efforts have been made, such as [2, 4, 3]. In these methods,
+62 the cluster center is carefully initialized through a special process. In addition to the more robust
+63 clustering result, an improvement of performance can also be achieved. More related work can be
+64 found here [15, 22].
+65 Since the computational complexity of $k$ -means involves the product of the number of samples
+66 and clusters, it will be very time-consuming if the two numbers are very large. With the help of
+67 techniques that used to accelerate the nearest neighbor search, the nearest center for each sample
+68 can be quickly found without computing distances to all centers [25, 11]. [7] developed a fast
+69 implementation of $k$ -means using coreset. A partition on a small coreset is computed firstly and is
+70 used as an initialization on a larger coreset. In [32], Xia et al. described each cluster by a ball and
+71 proposed Ball $k$ -means which accelerated $k$ -means by reducing the computation of distances between
+72 samples and centers. [13] proposed compressive $k$ -means (CKM) where the centers are estimated
+73 from a sketch (a compressed representation of the original data). Once the sketch is obtained, the
+74 computational overhead is then independent of the size of the original data. Moreover, it’s also a hot
+75 spot to use the advantages of GPU to shorten the time consumed by $k$ -means, such as [17] and [5].
+
+Clustering on graph data is also a hot topic. Some well-known algorithms include [19, 29, 21]. However, these algorithms often have a time complexity that increases quadratically with respect to the number of samples. To this end, many fast versions of them are proposed [33, 20, 9].
+
+# 79 3 The proposed model
+
+80 In our article, how to solve the problem in Eq. (1) has not been paid attention to, but some simple
+81 derivations are firstly made on it. Therefore we can analyze the meaning of the problem from the
+82 perspective of a distance graph. For convenience, we define $\mathcal { N } _ { k } ( \mathbf { x } _ { i } ) \ \bar { = } \ \{ \mathbf { x } _ { j } \ \mid \mathbf { \bar { x } } _ { j }$ is among the
+83 $k$ -nearest neighbors of $\mathbf { x } _ { i }$ or $\mathbf { x } _ { i }$ is among the $k$ -nearest neighbors of $\mathbf { x } _ { j } \}$ , and start from the following
+84 equivalent form of $k$ -means
+
+$$
+\operatorname* { m i n } _ { A _ { 1 } , \cdots , A _ { c } } \sum _ { k = 1 } ^ { c } { \frac { 1 } { | A _ { k } | } } \sum _ { \mathbf { x } _ { i } , \mathbf { x } _ { j } \in A _ { k } } \| \mathbf { x } _ { i } - \mathbf { x } _ { j } \| _ { 2 } ^ { 2 } ,
+$$
+
+With the help of the definition of $\mathbf { Y }$ in Eq. (2), problem (5) can be equivalently expressed as follow
+
+$$
+\begin{array} { r l } & { \underset { { \bf Y } \in \Phi ^ { n \times c } } { \operatorname* { m i n } } d i a g \left( ( { \bf Y } ^ { T } { \bf Y } ) ^ { - 1 } \right) ^ { T } d i a g \left( { \bf Y } ^ { T } { \bf D } { \bf Y } \right) , } \\ & { \Leftrightarrow \underset { { \bf Y } \in \Phi ^ { n \times c } } { \operatorname* { m i n } } T r \left( ( { \bf Y } ^ { T } { \bf Y } ) ^ { - 1 } { \bf Y } ^ { T } { \bf D } { \bf Y } \right) , } \end{array}
+$$
+
+86 where $d i a g ( \mathbf { A } ) = [ a _ { 1 1 } , \cdots , a _ { n n } ] ^ { T }$ . Obviously, if we only consider the distances between the sample
+87 and its neighbors, then the problem in Eq. (7) can be expressed as
+
+$$
+\operatorname* { m i n } _ { \mathbf { Y } \in \Phi ^ { n \times c } } T r \left( ( \mathbf { Y } ^ { T } \mathbf { Y } ) ^ { - 1 } \mathbf { Y } ^ { T } \mathbf { D } ^ { ( k ) } \mathbf { Y } \right) ,
+$$
+
+88 with
+
+$$
+\mathbf { d } _ { i j } ^ { ( k ) } = \left\{ \begin{array} { c c } { \| \mathbf { x } _ { i } - \mathbf { x } _ { j } \| _ { 2 } ^ { 2 } } & { \mathrm { i f } \mathbf { x } _ { i } \in \mathcal { N } _ { k } ( \mathbf { x } _ { j } ) } \\ { \gamma } & { \mathrm { O t h e r w i s e } } \end{array} \right. ,
+$$
+
+where 89 $\gamma$ is the maximum value of set $\{ \| \mathbf { x } _ { i } - \mathbf { x } _ { j } \| _ { 2 } ^ { 2 } \mid \mathbf { x } _ { i } \in \mathcal { N } _ { k } ( \mathbf { x } _ { j } ) , i = 1 , \cdot \cdot \cdot , n \}$ . The Equation (8) 90 is the final objective function of LKM.
+
+91 From the discussion in Section 1.2, we know that only the similarity instead of the distance between
+92 samples can be obtained directly in graph data. Fortunately, in practical applications, we can convert
+93 the similarity to dissimilarity by
+
+$$
+r _ { i j } = \left\{ \begin{array} { c l } { { - l o g ( s _ { i j } ) } } & { { 0 < s _ { i j } } } \\ { { \beta } } & { { s _ { i j } = 0 } } \end{array} , \right.
+$$
+
+where 94 $s _ { i j }$ is the normalized2 similarity between $\mathbf { x } _ { i }$ and $\mathbf { x } _ { j }$ , $\beta$ is the maximum value of set $\{ - l o g ( s _ { i j } ) \ |$ 95 $i , j = 1 , \bar { \cdot } \cdot \cdot , n \}$ . Then the dissimilarity can be used to replace the distance in the model.
+
+$$
+{ } ^ { 2 } s _ { i j } \in [ 0 , 1 ]
+$$
+
+97 It is not difficult to find that LKM, KSUMS [23], and Ratio-cut [29] can all be represented uniformly
+98 by the following model
+
+$$
+\operatorname* { m i n } _ { \mathbf { Y } \in \Phi ^ { n \times c } } T r \left( ( \mathbf { Y } ^ { T } \mathbf { Y } ) ^ { - p } \mathbf { Y } ^ { T } \mathbf { G } ^ { ( k ) } \mathbf { Y } \right) ,
+$$
+
+99 where gij (k) denotes the dissimilarity or distance between $\mathbf { x } _ { i }$ and $\mathbf { x } _ { j }$ , and $p > = 0$ is a parameter. The
+0 meaning of $p$ will be explored in future work.
+
+101 Instances of KSUMS and LKM: The objective function of KSUMS is
+
+$$
+\operatorname* { m i n } _ { \mathbf { Y } \in \Phi ^ { n \times c } } T r \left( \mathbf { Y } ^ { T } \mathbf { D } ^ { ( k ) } \mathbf { Y } \right) ,
+$$
+
+where 102 $\mathbf { D } ^ { ( k ) }$ takes the same expression as that in LKM. Let $g _ { i j _ { \pmb { \mathscr { I } } } } ^ { ( k ) }$ be setted by Eq. (9), the problem (11) 103 is identical with KSUMS (12) if $p = 0$ , and is identical with LKM if $p = 1$ .
+
+4 Instance of Ratio-cut: Benefiting from the introduction of $\mathbf { Y }$ , the problem of ratio-cut (an algorithm
+5 that belongs to the spectral clustering (SC) family) can be expressed as
+
+$$
+\operatorname* { m i n } _ { \mathbf { Y } \in \Phi ^ { n \times c } } T r \left( ( \mathbf { Y } ^ { T } \mathbf { Y } ) ^ { - 1 } \mathbf { Y } ^ { T } ( \pmb { \Delta } - \mathbf { W } ) \mathbf { Y } \right) ,
+$$
+
+where 106 $\pmb { \Delta }$ is a diagonal matrix, $\begin{array} { r } { \Delta _ { i i } = \sum _ { j = 1 } ^ { n } w _ { i j } } \end{array}$ . In generally, the similarity matrix W can be determined by heat kernel, i.e., 107 $w _ { i j } = e ^ { - \frac { \| \mathbf { x } _ { i } - \mathbf { x } _ { j } \| _ { 2 } ^ { 2 } } { t } }$ if $\mathbf { x } _ { i } \in \mathcal { N } _ { k } ( \mathbf { x } _ { j } )$ , $w _ { i j } = 0$ otherwise. Therefore the problem (11) is equivalent with ratio-cut, if 108 $p = 1$ and $g _ { i j } ^ { ( k ) }$ is setted by
+
+$$
+\mathbf { g } _ { i j } ^ { ( k ) } = \left\{ \begin{array} { c c } { \sum _ { j = 1 } ^ { n } w _ { i j } } & { i = j } \\ { - w _ { i j } } & { i \neq j , \mathrm { ~ a n d ~ } \mathbf { x } _ { i } \in \mathcal { N } _ { k } ( \mathbf { x } _ { j } ) } \\ { 0 } & { \mathrm { O t h e r w i s e } } \end{array} \right. .
+$$
+
+# 109 3.2 Optimization
+
+110 From the discussion above, we know that the problem of LKM can be expressed by Eq. (11) with
+111 $p = 1$ . Therefore, an optimization algorithm for problem (11) instead of problem (8) is developed.
+112 To begin with, some notations are presented as follows
+
+$$
+\begin{array} { l } { { s _ { i } \triangleq \bar { \bf y } _ { i } ^ { T } { \bf G } ^ { ( k ) } \bar { \bf y } _ { i } , \quad i = 1 , \cdots , c , } } \\ { { n _ { i } \triangleq \bar { \bf y } _ { i } ^ { T } \bar { \bf y } _ { i } , \quad i = 1 , \cdots , c , } } \end{array}
+$$
+
+113 the problem (11) then becomes
+
+$$
+\operatorname* { m i n } _ { \mathbf { Y } \in \Phi ^ { n \times c } } O b j ( \mathbf { Y } ) , \mathrm { w i t h } O b j ( \mathbf { Y } ) = \sum _ { i = 1 } ^ { c } \frac { s _ { i } } { n _ { i } ^ { p } } .
+$$
+
+114 In the following derivation, the $i$ -th row of $\mathbf { Y }$ (i.e., $\mathbf { y } _ { i }$ ) is regarded as the variable to be optimized
+115 while others are fixed, and $\mathbf { y } _ { i } = \mathbf { e } _ { \alpha }$ before updated. Thus $\mathbf { y } _ { i }$ can be updated by
+
+$$
+\begin{array} { r } { { \bf y } _ { i } = { \bf e } _ { \beta } , \quad \beta = \arg \underset { j } { \operatorname* { m i n } } O b j ( { \bf y } _ { i } = { \bf e } _ { j } ) - O b j ( { \bf y } _ { i } = { \bf 0 } ) , } \end{array}
+$$
+
+116 where $\mathbf { e } _ { i } = [ 0 , \cdots , 1 , \cdots , 0 ]$ be a vector with all elements equal to 0, except the $i$ -th, which is 1, and
+117 0 is the column vector of all zeros,
+
+118 Because $O b j ( \mathbf { y } _ { i } = \mathbf { 0 } )$ is constant, the above formula holds. According to Eq. (17), we have
+
+$$
+\begin{array} { r } { O b j ( \mathbf { y } _ { i } = \mathbf { e } _ { j } ) - O b j ( \mathbf { y } _ { i } = \mathbf { 0 } ) = \left\{ \begin{array} { l l } { \frac { s _ { j } + b _ { j } } { ( n _ { j } + 1 ) ^ { p } } - \frac { s _ { j } } { n _ { j } ^ { p } } } & { j \neq \alpha } \\ { \frac { s _ { j } } { n _ { j } ^ { p } } - \frac { s _ { j } - b _ { j } } { ( n _ { j } - 1 ) ^ { p } } } & { j = \alpha } \end{array} , j = 1 , \cdots , c , \right. } \end{array}
+$$
+
+119 with
+
+$$
+\begin{array} { r } { b _ { j } = \left\{ \begin{array} { l l } { 2 \sum _ { \mathbf { x } _ { l } \in A _ { j } } g _ { i l } ^ { ( k ) } + g _ { i i } ^ { ( k ) } } & { j \neq \alpha } \\ { 2 \sum _ { \mathbf { x } _ { l } \in A _ { j } } g _ { i l } ^ { ( k ) } - g _ { i i } ^ { ( k ) } } & { j = \alpha } \end{array} \right. , } \end{array}
+$$
+
+Algorithm 1: An efficient program for solving problem (11).
+
+Note: The vector $\mathbf { y } \in \mathbb { R } ^ { n }$ denotes the clustering result, i.e., $y _ { i }$ is the cluster that $\mathbf { x } _ { i }$ belongs to. The Eq. (15), (16), and (20) involved in the algorithm have high computational complexity, but these can be computed more efficiently if the sparsity of $\mathbf { G } ^ { ( k ) }$ is considered. See the supplementary material for a more detailed algorithm;
+
+Data: Sparse matrix ${ } ^ { 3 } \mathbf { G } ^ { ( k ) } \in \mathbb { R } ^ { n \times n }$ , the number of cluster $c$ Result: The clustering result y
+Initialize y randomly;
+Compute vector s and $\mathbf { n }$ by Eq. (15) and (16), respectively;
+
+while not converge do for $i = 1 , \cdots , n$ do Compute $b _ { j }$ by Eq. (20) for $j \in B _ { i }$ ; Compute $\dot { O b j } ( y _ { i } = j ) - O b j ( y _ { i } = 0 )$ by Eq. (19) for $j \in B _ { i }$ ; Update $y _ { i }$ by Eq. (18); Update s and $\mathbf { n }$ by Eq. (21) and Eq. (22), respectively;
+
+20 Benefiting from the sparsity of $\mathbf { G } ^ { ( k ) }$ , it takes $O ( n k )$ , $O ( k + c )$ , and $O ( k )$ time to compute s, $\mathbf { b }$ , and
+121 n, respectively. Therefore, the proposed optimization algorithm has a computational complexity of
+122 $O ( n ^ { 2 } \dot { k } + n c )$ , which is unbearable, for large-scale datasets. However, if the variables s and $\mathbf { n }$ are
+123 computed in advance and updated following the update of $y _ { i }$ , then the computational complexity of
+124 the algorithm can greatly be reduced. The update rules for s and $\mathbf { n }$ are as follows
+
+$$
+\begin{array} { c c } { { s _ { \alpha } \Leftarrow s _ { \alpha } - b _ { \alpha } , } } & { { s _ { \beta } \Leftarrow s _ { \beta } + b _ { \beta } , } } \\ { { n _ { \alpha } \Leftarrow n _ { \alpha } - 1 , } } & { { n _ { \beta } \Leftarrow n _ { \beta } + 1 , } } \end{array}
+$$
+
+125 Thus, the computational complexity of the optimization algorithm is $O ( n ( k + c ) )$
+
+126 On more step From Eq. (11), we know that only the information of pair $\left( \mathbf { x } _ { i } , \mathbf { x } _ { j } \right)$ is considered in
+127 the model, and there are at most $2 n k$ such pairs. For convenience, we assume that there are exactly
+128 $2 k$ such pairs for each sample $\mathbf { x } _ { i }$ , i.e., $2 k = | \{ ( \mathbf { x } _ { i } , \mathbf { x } _ { j } ) \mid \mathbf { x } _ { j } \in \mathcal { N } _ { k } ( \mathbf { x } _ { i } )$ or $\mathbf { x } _ { i } \in \mathcal { N } _ { k } ( \mathbf { x } _ { j } ) \big \} |$ . For cluster
+129 $j$ , we call it an element of $B _ { i }$ $( j \in B _ { i } )$ ), if there is at least one sample in cluster $j$ belongs to $\mathcal { N } _ { k } ( { \bf x } _ { i } )$
+130 or $\mathbf { x } _ { i }$ belongs to the set of neighbors of these samples. Based on the assumption and notations above,
+131 we know that when updating $\mathbf { y } _ { i }$ by Eq. (18), the size of $B _ { i }$ is at most $2 k$ . However, it does not make
+132 sense to group the sample $\mathbf { x } _ { i }$ into cluster ${ j \not \in B _ { i } }$ , from the perspective of the performance. Therefore,
+133 we only need to pay attention to the cases where $j \in B _ { i }$ . Thus, the computational complexity of the
+134 optimization algorithm can be reduced to $O ( n k )$ .
+135 Time and space complexity From Algorithm 1, we can see that the memory is mainly occupied
+136 by the matrix $\mathbf { G } ^ { ( k ) } \in \mathbb { R } ^ { n \times n }$ , which is equivalent to a sparse matrix, and contains at most $2 n k$
+137 non-constants. The memory overhead caused by other variables is $O ( n )$ at most. For example, y,
+138 $B _ { i }$ , and s require $O ( n ) , O ( k )$ , and $O ( c )$ memory, respectively. Thus the memory overhead of LKM
+139 is $O ( n k )$ . Benefiting from the sparsity of $\mathbf { G } ^ { ( k ) }$ , Eq. (15), (16), and (20) can all be calculated more
+140 efficiently. Specifically, only $O ( \bar { n } k )$ , $O ( n )$ , and $O ( k )$ time are needed respectively, please refer to the
+141 supplementary materials for details. After $y _ { i }$ is updated, only $O ( 1 )$ time is needed to update variables
+142 s and $\mathbf { n }$ . Thus, the computational complexity of LKM is $O ( n k )$ .
+
+# 143 4 Experiments
+
+In this section, the performance of the proposed algorithm, LKM, is verified on eleven synthetic datasets and sixteen benchmark datasets. The rest of this section is organized as follows: First, experiments on synthetic datasets are shown. In short, Mickey, Outlier, and family of Grid datasets are used to verify the effectiveness, robustness, and efficiency of LKM, respectively. Then, we compare 7 popular clustering algorithms with LKM on 16 benchmark datasets, to evaluate the performance of the proposed algorithm.
+
+# 150 4.1 Experiments conducted on synthetic datasets
+
+Experiment on “Mickey” To verify the effectiveness of LKM, a synthetic dataset called “Mickey” is constructed. The distribution of points is shown in Figure 2(a). The triangles representing the means of the clusters are not points of the datasets.
+
+From Figure 2(b) and 2(c), we found that The proposed method LKM successfully found the cluster structure, but $k$ -means did not. $k$ -means still cannot find the correct structure, even with the initialization of the ground truth label. Because the distance between point 1 and the blue triangle (mean of all blue points), $d _ { 1 }$ is greater than the distance between point 1 and the orange triangle (mean of all orange points), $d _ { 2 }$ , $k$ -means will group it into the blue cluster instead of orange. Therefore, $k$ -means cannot handle datasets like this.
+
+
+Figure 2: The performance of $k$ -means and LKM on “Mickey”.
+
+160 Experiment on “Outlier” In order to verify the robustness of our method, we construct a dataset
+161 called “Outlier”. It consists of four clusters with centers $( 0 , 0 )$ , $( 0 , 5 )$ , $( 5 , 0 )$ , and $( 5 , 5 )$ , and an outlier
+162 with the coordinate of (100, 100). The distance between outlier $A$ and other points is not as close as
+163 shown in Figure 3. From Figure 3(b) and 3(c), we can see that the performance of $k \mathrm { . }$ -means is severely
+164 affected by the outlier $A$ , while the performance of LKM is not. In $k$ -means, the center of the cluster
+165 containing abnormal points will largely shift towards the direction of the abnormal points, resulting
+166 in poor performance. In LKM, the distance between $\mathbf { x } _ { i }$ and $\mathbf { x } _ { j }$ is not calculated if $\bar { \mathbf { x } _ { j } } \notin \mathcal { N } _ { k } ( \mathbf { x } _ { i } )$ , but
+167 a parameter $\lambda$ is used instead, so ideally, the distance between any two points belonging to different
+168 clusters is $\lambda$ . In other words, for the sample point $\mathbf { x } _ { i }$ , there is no difference between the outlier and
+169 the samples that do not belong to $\mathcal { N } _ { k } ( { \bf x } _ { i } )$ .
+170 Experiments on the family of “Grid” In order to verify the efficiency of LKM, in this paragraph,
+171 9 synthetic datasets called Toy-1, Toy-2, · · · , Toy-9 are constructed. These datasets share the same
+172 structure, and their distributions are similar to that shown in Figure 4. In these datasets, each cluster
+173 is always composed of 10 points generated by Gaussian distribution. Since the time complexity of
+174 LKM and $k$ -means is closely related to the number of points, we set different sizes for these data
+175 sets, ranging from 1960 to 125440. The number of clusters and the standard deviation involved in the
+176 Gaussian distribution for each dataset is shown in Table 1.
+177 In Table 2, the column named “Ball-Tree” represents the time it takes to construct the graph required
+178 by LKM through Ball-tree with $k = 2 0$ . The column named $^ { 6 6 } \#$ Iter” denotes the number of iterations
+179 required for the algorithm to converge. The total time of LKM refers to the sum of the time consumed
+180 by Ball-Tree and Algorithm 1. The speed-up is the ratio of the time consumed by each iteration of
+181 $k$ -means to the time consumed by each iteration of Algorithm 1. Both $k$ -means and LKM were run
+182 50 times, and the average results were reported.
+183 As shown in Table 2, Algorithm 1 consumes a significantly shorter time than $k$ -means, which is more
+184 obvious on datasets with more clusters. The main reason is that when $y _ { i }$ is going to update, only the
+185 case where $j \in B _ { i }$ is considered. In addition, LKM has a significant improvement in terms of the
+186 quality of the clustering result, compared to $k$ -means, as shown in Table 1 and Figure 4.
+
+
+Figure 3: The performance of $k$ -means and LKM on “Outlier”.
+
+
+Figure 4: The performance of $k$ -means and LKM on Toy-1.
+
+Table 1: Performance of $k$ -means and LKM
+
+