Regularized Class-Specific Subspace Classifier

In this paper, we mainly focus on how to achieve the translated subspace representation for each class, which could simultaneously indicate the distribution of the associated class and the differences from its complementary classes. By virtue of the reconstruction problem, the class-specific subspace classifier (CSSC) problem could be represented as a series of biobjective optimization problems, which minimize and maximize the reconstruction errors of the related class and its complementary classes, respectively. Besides, the regularization term is specifically introduced to ensure the whole system’s stability. Accordingly, a regularized class-specific subspace classifier (RCSSC) method can be further proposed based on solving a general quadratic ratio problem. The proposed RCSSC method consistently converges to the global optimal subspace and translation under the variations of the regularization parameter. Furthermore, the proposed RCSSC method could be extended to the unregularized case, which is known as unregularized CSSC (UCSSC) method via orthogonal decomposition technique. As a result, the effectiveness and the superiority of both proposed RCSSC and UCSSC methods can be verified analytically and experimentally.

[1]  Xuelong Li,et al.  L1-Norm-Based 2DPCA , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

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

[3]  Alexandros Iosifidis,et al.  Class-Specific Reference Discriminant Analysis With Application in Human Behavior Analysis , 2015, IEEE Transactions on Human-Machine Systems.

[4]  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.

[5]  Songhwai Oh,et al.  Elastic-net regularization of singular values for robust subspace learning , 2015, 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[6]  Feiping Nie,et al.  Discriminative Embedded Clustering: A Framework for Grouping High-Dimensional Data , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[7]  I. Jolliffe.  Principal Component Analysis , 2002 .

[8]  Feiping Nie,et al.  Optimal Mean Robust Principal Component Analysis , 2014, ICML.

[9]  Xuelong Li,et al.  Sparse kernel entropy component analysis for dimensionality reduction of biomedical data , 2015, Neurocomputing.

[10]  Yun Fu,et al.  Robust Subspace Discovery through Supervised Low-Rank Constraints , 2014, SDM.

[11]  Feiping Nie,et al.  Flexible Shift-Invariant Locality and Globality Preserving Projections , 2014, ECML/PKDD.

[12]  Alejandro F. Frangi,et al.  Two-dimensional PCA: a new approach to appearance-based face representation and recognition , 2004 .

[13]  Ian T. Jolliffe,et al.  Principal Component Analysis , 2002, International Encyclopedia of Statistical Science.

[14]  Yun Fu,et al.  Low-Rank Common Subspace for Multi-view Learning , 2014, 2014 IEEE International Conference on Data Mining.

[15]  Tao Jiang,et al.  Efficient and robust feature extraction by maximum margin criterion , 2003, IEEE Transactions on Neural Networks.

[16]  Anastasios Tefas,et al.  Class-Specific Kernel-Discriminant Analysis for Face Verification , 2007, IEEE Transactions on Information Forensics and Security.

[17]  Feiping Nie,et al.  Trace Ratio Problem Revisited , 2009, IEEE Transactions on Neural Networks.

[18]  Keinosuke Fukunaga,et al.  Introduction to statistical pattern recognition (2nd ed.) , 1990 .

[19]  Feiping Nie,et al.  Semi-supervised orthogonal discriminant analysis via label propagation , 2009, Pattern Recognit..

[20]  Xuelong Li,et al.  Pixel-to-Model Distance for Robust Background Reconstruction , 2016, IEEE Transactions on Circuits and Systems for Video Technology.

[21]  Ja-Chen Lin,et al.  A new LDA-based face recognition system which can solve the small sample size problem , 1998, Pattern Recognit..

[22]  Xuelong Li,et al.  Binary Two-Dimensional PCA , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[23]  Feiping Nie,et al.  Low-Rank Matrix Recovery via Efficient Schatten p-Norm Minimization , 2012, AAAI.

[24]  Feiping Nie,et al.  Efficient and Robust Feature Selection via Joint ℓ2, 1-Norms Minimization , 2010, NIPS.

[25]  Feiping Nie,et al.  Robust Principal Component Analysis with Non-Greedy l1-Norm Maximization , 2011, IJCAI.

[26]  Feiping Nie,et al.  Orthogonal vs. uncorrelated least squares discriminant analysis for feature extraction , 2012, Pattern Recognit. Lett..

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

[28]  Xiao-Yuan Jing,et al.  Kernel Uncorrelated Adjacent-class Discriminant Analysis , 2010, 2010 20th International Conference on Pattern Recognition.

[29]  Jieping Ye,et al.  Generalized Low Rank Approximations of Matrices , 2004, Machine Learning.

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

[31]  Dacheng Tao,et al.  Classification with Noisy Labels by Importance Reweighting , 2014, IEEE Transactions on Pattern Analysis and Machine Intelligence.