Correntropy induced metric based graph regularized non-negative matrix factorization

Non-negative matrix factorization (NMF) is an efficient dimension reduction method and plays an important role in many pattern recognition and computer vision tasks. However, conventional NMF methods are not robust since the objective functions are sensitive to outliers and do not consider the geometric structure in datasets. In this paper, we proposed a correntropy graph regularized NMF (CGNMF) to overcome the aforementioned problems. CGNMF maximizes the correntropy between data matrix and its reconstruction to filter out the noises of large magnitudes, and expects the coefficients to preserve the intrinsic geometric structure of data. We also proposed a modified version of our CGNMF which construct the adjacent graph by using sparse representation to enhance its reliability. Experimental results on popular image datasets confirm the effectiveness of CGNMF.

[1]  David J. Kriegman,et al.  Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection , 1996, ECCV.

[2]  J KriegmanDavid,et al.  Eigenfaces vs. Fisherfaces , 1997 .

[3]  Xuelong Li,et al.  General Tensor Discriminant Analysis and Gabor Features for Gait Recognition , 2007, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[4]  Fionn Murtagh,et al.  Cluster Dissection and Analysis: Theory, Fortran Programs, Examples. , 1986 .

[5]  E. Oja,et al.  Kullback-Leibler Divergence for Nonnegative for Nonnegative Matrix Factorization , 2011 .

[6]  Zhigang Luo,et al.  Manifold Regularized Discriminative Nonnegative Matrix Factorization With Fast Gradient Descent , 2011, IEEE Transactions on Image Processing.

[7]  Jun Yu,et al.  Click Prediction for Web Image Reranking Using Multimodal Sparse Coding , 2014, IEEE Transactions on Image Processing.

[8]  John Shawe-Taylor,et al.  MahNMF: Manhattan Non-negative Matrix Factorization , 2012, ArXiv.

[9]  Andy Harter,et al.  Parameterisation of a stochastic model for human face identification , 1994, Proceedings of 1994 IEEE Workshop on Applications of Computer Vision.

[10]  Weifeng Liu,et al.  Multiview Hessian Regularization for Image Annotation , 2013, IEEE Transactions on Image Processing.

[11]  Ran He,et al.  Two-Stage Sparse Representation for Robust Recognition on Large-Scale Database , 2010, AAAI.

[12]  Zhigang Luo,et al.  Online Nonnegative Matrix Factorization With Robust Stochastic Approximation , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[13]  G. Seber Multivariate observations / G.A.F. Seber , 1983 .

[14]  H. Sebastian Seung,et al.  Algorithms for Non-negative Matrix Factorization , 2000, NIPS.

[15]  Yuan Yan Tang,et al.  Multiview Hessian discriminative sparse coding for image annotation , 2013, Comput. Vis. Image Underst..

[16]  TaoDacheng,et al.  Large-Margin Multi-ViewInformation Bottleneck , 2014 .

[17]  Jun Yu,et al.  Modern Machine Learning Techniques and Their Applications in Cartoon Animation Research , 2013 .

[18]  Dacheng Tao,et al.  Large-Margin Multi-ViewInformation Bottleneck , 2014, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[19]  H. Sebastian Seung,et al.  Learning the parts of objects by non-negative matrix factorization , 1999, Nature.

[20]  Yuan Yan Tang,et al.  High-Order Distance-Based Multiview Stochastic Learning in Image Classification , 2014, IEEE Transactions on Cybernetics.

[21]  Zhigang Luo,et al.  Correntropy supervised non-negative matrix factorization , 2015, 2015 International Joint Conference on Neural Networks (IJCNN).

[22]  Xuelong Li,et al.  Geometric Mean for Subspace Selection , 2009, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[23]  Feiping Nie,et al.  Robust Manifold Nonnegative Matrix Factorization , 2014, ACM Trans. Knowl. Discov. Data.

[24]  Zhigang Luo,et al.  Non-Negative Patch Alignment Framework , 2011, IEEE Transactions on Neural Networks.

[25]  Weifeng Liu,et al.  Correntropy: Properties and Applications in Non-Gaussian Signal Processing , 2007, IEEE Transactions on Signal Processing.

[26]  Xiaojun Wu,et al.  Graph Regularized Nonnegative Matrix Factorization for Data Representation , 2017, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[27]  Martial Hebert,et al.  Self-explanatory Sparse Representation for Image Classification , 2014, ECCV.

[28]  Chao Liu,et al.  Distributed nonnegative matrix factorization for web-scale dyadic data analysis on mapreduce , 2010, WWW '10.

[29]  Xuelong Li,et al.  Asymmetric bagging and random subspace for support vector machines-based relevance feedback in image retrieval , 2006, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[30]  Dacheng Tao,et al.  Multi-View Intact Space Learning , 2015, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[31]  Stan Z. Li,et al.  Learning spatially localized, parts-based representation , 2001, Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001.

[32]  Bao-Gang Hu,et al.  Robust feature extraction via information theoretic learning , 2009, ICML '09.

[33]  Ran He,et al.  Maximum Correntropy Criterion for Robust Face Recognition , 2011, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[34]  Xuelong Li,et al.  Constrained Nonnegative Matrix Factorization for Image Representation , 2012, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[35]  Y. Rui,et al.  Learning to Rank Using User Clicks and Visual Features for Image Retrieval , 2015, IEEE Transactions on Cybernetics.

[36]  Zhigang Luo,et al.  NeNMF: An Optimal Gradient Method for Nonnegative Matrix Factorization , 2012, IEEE Transactions on Signal Processing.

[37]  Honggang Zhang,et al.  Graph Regularized Non-negative Matrix Factorization By Maximizing Correntropy , 2014, J. Comput..

[38]  Meng Wang,et al.  Adaptive Hypergraph Learning and its Application in Image Classification , 2012, IEEE Transactions on Image Processing.

[39]  Dacheng Tao,et al.  Slow Feature Analysis for Human Action Recognition , 2012, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[40]  Stefanos Zafeiriou,et al.  Discriminant Nonnegative Tensor Factorization Algorithms , 2009, IEEE Transactions on Neural Networks.

[41]  Zhigang Luo,et al.  Correntropy induced metric based graph regularized non-negative matrix factorization , 2014, Proceedings 2014 IEEE International Conference on Security, Pattern Analysis, and Cybernetics (SPAC).

[42]  Dietrich Lehmann,et al.  Nonsmooth nonnegative matrix factorization (nsNMF) , 2006, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[43]  Xian-Sheng Hua,et al.  Ensemble Manifold Regularization , 2009, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[44]  Bin Shen,et al.  Learning dictionary on manifolds for image classification , 2013, Pattern Recognit..