Balanced Self-Paced Learning for Generative Adversarial Clustering Network

Clustering is an important problem in various machine learning applications, but still a challenging task when dealing with complex real data. The existing clustering algorithms utilize either shallow models with insufficient capacity for capturing the non-linear nature of data, or deep models with large number of parameters prone to overfitting. In this paper, we propose a deep Generative Adversarial Clustering Network (ClusterGAN), which tackles the problems of training of deep clustering models in unsupervised manner. \emph{ClusterGAN} consists of three networks, a discriminator, a generator and a clusterer (i.e. a clustering network). We employ an adversarial game between these three players to synthesize realistic samples given discriminative latent variables via the generator, and learn the inverse mapping of the real samples to the discriminative embedding space via the clusterer. Moreover, we utilize a conditional entropy minimization loss to increase/decrease the similarity of intra/inter cluster samples. Since the ground-truth similarities are unknown in clustering task, we propose a novel balanced self-paced learning algorithm to gradually include samples into training from easy to difficult, while considering the diversity of selected samples from all clusters. Therefore, our method makes it possible to efficiently train clusterers with large depth by leveraging the proposed adversarial game and balanced self-paced learning algorithm. According our experiments, ClusterGAN achieves competitive results compared to the state-of-the-art clustering and hashing models on several datasets.

[1]  Gérard Govaert,et al.  Assessing a Mixture Model for Clustering with the Integrated Completed Likelihood , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[2]  Chao Li,et al.  A Self-Paced Multiple-Instance Learning Framework for Co-Saliency Detection , 2015, 2015 IEEE International Conference on Computer Vision (ICCV).

[3]  Piotr Indyk,et al.  Similarity Search in High Dimensions via Hashing , 1999, VLDB.

[4]  Heng Huang,et al.  Conditional generative adversarial network for gene expression inference , 2018, Bioinform..

[5]  Antonio Torralba,et al.  Spectral Hashing , 2008, NIPS.

[6]  Soumith Chintala,et al.  Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks , 2015, ICLR.

[7]  Michael I. Jordan,et al.  On Spectral Clustering: Analysis and an algorithm , 2001, NIPS.

[8]  Jimmy Ba,et al.  Adam: A Method for Stochastic Optimization , 2014, ICLR.

[9]  Alex Krizhevsky,et al.  Learning Multiple Layers of Features from Tiny Images , 2009 .

[10]  Fei Wang,et al.  Efficient multiclass maximum margin clustering , 2008, ICML '08.

[11]  Yi Yang,et al.  Image Clustering Using Local Discriminant Models and Global Integration , 2010, IEEE Transactions on Image Processing.

[12]  Li Fei-Fei,et al.  ImageNet: A large-scale hierarchical image database , 2009, CVPR.

[13]  Jonathon Shlens,et al.  Conditional Image Synthesis with Auxiliary Classifier GANs , 2016, ICML.

[14]  Jiayu Zhou,et al.  Learning A Task-Specific Deep Architecture For Clustering , 2015, SDM.

[15]  Ali Farhadi,et al.  Unsupervised Deep Embedding for Clustering Analysis , 2015, ICML.

[16]  Shiguang Shan,et al.  Self-Paced Learning with Diversity , 2014, NIPS.

[17]  Ivor W. Tsang,et al.  Spectral Embedded Clustering: A Framework for In-Sample and Out-of-Sample Spectral Clustering , 2011, IEEE Transactions on Neural Networks.

[18]  Jia Wang,et al.  Unsupervised Triplet Hashing for Fast Image Retrieval , 2017, ACM Multimedia.

[19]  Masashi Sugiyama,et al.  Learning Discrete Representations via Information Maximizing Self-Augmented Training , 2017, ICML.

[20]  Eric P. Xing,et al.  Structured Generative Adversarial Networks , 2017, NIPS.

[21]  Jiwen Lu,et al.  Learning Compact Binary Descriptors with Unsupervised Deep Neural Networks , 2016, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[22]  Chen Huang,et al.  Unsupervised Learning of Discriminative Attributes and Visual Representations , 2016, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[23]  Shih-Fu Chang,et al.  Semi-supervised hashing for scalable image retrieval , 2010, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[24]  Enhong Chen,et al.  Learning Deep Representations for Graph Clustering , 2014, AAAI.

[25]  Honglak Lee,et al.  An Analysis of Single-Layer Networks in Unsupervised Feature Learning , 2011, AISTATS.

[26]  Aaron C. Courville,et al.  Adversarially Learned Inference , 2016, ICLR.

[27]  Andreas Krause,et al.  Discriminative Clustering by Regularized Information Maximization , 2010, NIPS.

[28]  Jian Sun,et al.  K-Means Hashing: An Affinity-Preserving Quantization Method for Learning Binary Compact Codes , 2013, 2013 IEEE Conference on Computer Vision and Pattern Recognition.

[29]  Heng Huang,et al.  Semi-Supervised Generative Adversarial Network for Gene Expression Inference , 2018, KDD.

[30]  Dale Schuurmans,et al.  Maximum Margin Clustering , 2004, NIPS.

[31]  Shih-Fu Chang,et al.  Spherical hashing , 2012, 2012 IEEE Conference on Computer Vision and Pattern Recognition.

[32]  Yoshua Bengio,et al.  Gradient-based learning applied to document recognition , 1998, Proc. IEEE.

[33]  Rob Fergus,et al.  Deep Generative Image Models using a Laplacian Pyramid of Adversarial Networks , 2015, NIPS.

[34]  Jitendra Malik,et al.  Normalized cuts and image segmentation , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[35]  Pietro Perona,et al.  Self-Tuning Spectral Clustering , 2004, NIPS.

[36]  Simon Haykin,et al.  GradientBased Learning Applied to Document Recognition , 2001 .

[37]  Deli Zhao,et al.  Agglomerative clustering via maximum incremental path integral , 2013, Pattern Recognit..

[38]  Maoguo Gong,et al.  Multi-Objective Self-Paced Learning , 2016, AAAI.

[39]  Cheng Deng,et al.  Unsupervised Deep Generative Adversarial Hashing Network , 2018, 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition.

[40]  Shin Ishii,et al.  Distributional Smoothing with Virtual Adversarial Training , 2015, ICLR 2016.

[41]  Daphne Koller,et al.  Self-Paced Learning for Latent Variable Models , 2010, NIPS.

[42]  Xin Liu,et al.  Document clustering based on non-negative matrix factorization , 2003, SIGIR.

[43]  Pieter Abbeel,et al.  InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets , 2016, NIPS.

[44]  Dhruv Batra,et al.  Joint Unsupervised Learning of Deep Representations and Image Clusters , 2016, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[45]  Simon Osindero,et al.  Conditional Generative Adversarial Nets , 2014, ArXiv.

[46]  Yoshua Bengio,et al.  Generative Adversarial Nets , 2014, NIPS.

[47]  George Trigeorgis,et al.  A Deep Semi-NMF Model for Learning Hidden Representations , 2014, ICML.

[48]  Dong Cao,et al.  Self-Paced Cross-Modal Subspace Matching , 2016, SIGIR.

[49]  Jun Zhu,et al.  Triple Generative Adversarial Nets , 2017, NIPS.

[50]  Jiwen Lu,et al.  Deep hashing for compact binary codes learning , 2015, 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[51]  Yang Yu,et al.  Mixture of GANs for Clustering , 2018, IJCAI.

[52]  Cheng Deng,et al.  Deep Clustering via Joint Convolutional Autoencoder Embedding and Relative Entropy Minimization , 2017, 2017 IEEE International Conference on Computer Vision (ICCV).

[53]  David J. C. MacKay,et al.  Unsupervised Classifiers, Mutual Information and 'Phantom Targets' , 1991, NIPS.

[54]  Jason Weston,et al.  Curriculum learning , 2009, ICML '09.

[55]  Wojciech Zaremba,et al.  Improved Techniques for Training GANs , 2016, NIPS.

[56]  Andreas Krause,et al.  Advances in Neural Information Processing Systems (NIPS) , 2014 .

[57]  Xinlei Chen,et al.  Large Scale Spectral Clustering with Landmark-Based Representation , 2011, AAAI.

[58]  Harold W. Kuhn,et al.  The Hungarian method for the assignment problem , 1955, 50 Years of Integer Programming.

[59]  Rui Xu,et al.  Survey of clustering algorithms , 2005, IEEE Transactions on Neural Networks.

[60]  Svetlana Lazebnik,et al.  Iterative quantization: A procrustean approach to learning binary codes , 2011, CVPR 2011.

[61]  John Salvatier,et al.  Theano: A Python framework for fast computation of mathematical expressions , 2016, ArXiv.