From the idea of "sparse representation" to a representation-based transformation method for feature extraction

Transformation methods have been widely used in biometrics such as face recognition, gait recognition and palmprint recognition. It seems that conventional transformation methods seem to be ''optimal'' for training samples but not for every test sample to be classified. The reason is that conventional transformation methods use only the information of training samples to obtain transform axes. For example, if the transformation method is linear discriminant analysis (LDA), then in the new space obtained using the corresponding transformation, the training samples must have the maximum between-class distance and the minimum within-class distance. However, it is hard to guarantee that the transformation also maximizes the between-class distance and minimizes the within-class distance of the test samples in the new space. Another example is that principal component analysis (PCA) can best represent the training samples with the minimum error; however, it is not guaranteed that every test sample can be also represented with the minimum error. In this paper, we propose to improve conventional transformation methods by relating the training phase with the test sample. The proposed method simultaneously uses both the training samples and test sample to obtain an ''optimal'' representation of the test sample. In other words, the proposed method not only is an improvement to the conventional transformation method but also has the merits of the representation-based classification, which has shown very good performance in various problems. Differing from conventional distance-based classification, the proposed method evaluates only the distances between the test sample and the ''closest'' training samples and depends on only them to perform classification. Moreover, the proposed method uses the weighted distance to classify the test sample. The weight is set to the representation coefficient of a linear combination of the training samples that can well represent the test sample.

[1]  Mohammed Bennamoun,et al.  Linear Regression for Face Recognition , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[2]  David Zhang,et al.  Local Linear Discriminant Analysis Framework Using Sample Neighbors , 2011, IEEE Transactions on Neural Networks.

[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]  Lei Zhang,et al.  Gabor Feature Based Sparse Representation for Face Recognition with Gabor Occlusion Dictionary , 2010, ECCV.

[5]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[6]  Zoubin Ghahramani,et al.  Combining active learning and semi-supervised learning using Gaussian fields and harmonic functions , 2003, ICML 2003.

[7]  Lei Zhang,et al.  A multi-manifold discriminant analysis method for image feature extraction , 2011, Pattern Recognit..

[8]  Xinbo Gao,et al.  Incremental tensor biased discriminant analysis: A new color-based visual tracking method , 2010, Neurocomputing.

[9]  Bernhard Schölkopf,et al.  Learning with Local and Global Consistency , 2003, NIPS.

[10]  Shing-Tai Pan,et al.  Application of Integer FFT on Performance Improvement of Speech Recognition Chip Implementation , 2011, J. Inf. Hiding Multim. Signal Process..

[11]  Chuan-Yu Chang,et al.  Applications of Block Linear Discriminant Analysis for Face Recognition , 2011, J. Inf. Hiding Multim. Signal Process..

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

[13]  Dong Xu,et al.  Multilinear Discriminant Analysis for Face Recognition , 2007, IEEE Transactions on Image Processing.

[14]  Xuelong Li,et al.  Supervised Tensor Learning , 2005, ICDM.

[15]  Xuelong Li,et al.  KPCA for semantic object extraction in images , 2008, Pattern Recognit..

[16]  Geoffrey J. McLachlan,et al.  Discriminant Analysis and Statistical Pattern Recognition: McLachlan/Discriminant Analysis & Pattern Recog , 2005 .

[17]  Philip S. Yu,et al.  Incremental tensor analysis: Theory and applications , 2008, TKDD.

[18]  Wen Gao,et al.  Adaptive discriminant analysis for face recognition from single sample per person , 2011, Face and Gesture 2011.

[19]  Stan Z. Li,et al.  The HFB Face Database for Heterogeneous Face Biometrics research , 2009, 2009 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops.

[20]  Chengjun Liu,et al.  Gabor feature based classification using the enhanced fisher linear discriminant model for face recognition , 2002, IEEE Trans. Image Process..

[21]  Bernhard Schölkopf,et al.  Nonlinear Component Analysis as a Kernel Eigenvalue Problem , 1998, Neural Computation.

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

[23]  Bernt Schiele,et al.  Introducing a weighted non-negative matrix factorization for image classification , 2003, Pattern Recognit. Lett..

[24]  Theofanis Sapatinas,et al.  Discriminant Analysis and Statistical Pattern Recognition , 2005 .

[25]  Jian Yang,et al.  An approach for directly extracting features from matrix data and its application in face recognition , 2008, Neurocomputing.

[26]  Juha Karhunen,et al.  Principal component neural networks — Theory and applications , 1998, Pattern Analysis and Applications.

[27]  Qi Zhu,et al.  A simple and fast representation-based face recognition method , 2013, Neural Computing and Applications.

[28]  Dacheng Tao,et al.  Max-Min Distance Analysis by Using Sequential SDP Relaxation for Dimension Reduction , 2011, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[29]  David Zhang,et al.  Represent and fuse bimodal biometric images at the feature level: complex-matrix-based fusion scheme , 2010 .

[30]  Jing-Yu Yang,et al.  An efficient renovation on kernel Fisher discriminant analysis and face recognition experiments , 2004, Pattern Recognit..

[31]  Bernhard Schölkopf,et al.  Learning from labeled and unlabeled data on a directed graph , 2005, ICML.

[32]  Jeng-Shyang Pan,et al.  AN IMPROVEMENT TO THE NEAREST NEIGHBOR CLASSIFIER AND F ACE RECOGNITION EXPERIMENTS , 2013 .

[33]  Dacheng Tao,et al.  Constrained Empirical Risk Minimization Framework for Distance Metric Learning , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[34]  Jian Yang,et al.  Beyond sparsity: The role of L1-optimizer in pattern classification , 2012, Pattern Recognit..

[35]  Wen Gao,et al.  Unified Principal Component Analysis with generalized Covariance Matrix for face recognition , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.

[36]  Cheng-Chin Chiang,et al.  USING GRADIENT FEATURES FROM SCALE-INVARIANT KEYPOINTS ON FACE RECOGNITION , 2011 .

[37]  G. Baudat,et al.  Generalized Discriminant Analysis Using a Kernel Approach , 2000, Neural Computation.

[38]  Jian Yang,et al.  A Two-Phase Test Sample Sparse Representation Method for Use With Face Recognition , 2011, IEEE Transactions on Circuits and Systems for Video Technology.

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

[40]  Yong Xu.  Quaternion-Based Discriminant Analysis Method for Color Face Recognition , 2012, PloS one.

[41]  Dacheng Tao,et al.  Simple Exponential Family PCA , 2010, IEEE Transactions on Neural Networks and Learning Systems.

[42]  Dacheng Tao,et al.  Empirical Discriminative Tensor Analysis for Crime Forecasting , 2011, KSEM.

[43]  Marco Loog,et al.  Local Discriminant Analysis , 2006, 18th International Conference on Pattern Recognition (ICPR'06).

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

[45]  Allen Y. Yang,et al.  Robust Face Recognition via Sparse Representation , 2009, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[46]  Ming Li,et al.  2D-LDA: A statistical linear discriminant analysis for image matrix , 2005, Pattern Recognit. Lett..

[47]  Alex Pentland,et al.  Face recognition using eigenfaces , 1991, Proceedings. 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[48]  Bernhard Schölkopf,et al.  Kernel Principal Component Analysis , 1997, ICANN.

[49]  Xuelong Li,et al.  Incremental learning of weighted tensor subspace for visual tracking , 2009, 2009 IEEE International Conference on Systems, Man and Cybernetics.

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

[51]  Yuxiao Hu,et al.  Face recognition using Laplacianfaces , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[52]  Xuelong Li,et al.  Bayesian Tensor Approach for 3-D Face Modeling , 2008, IEEE Transactions on Circuits and Systems for Video Technology.

[53]  Stephen A. Billings,et al.  Nonlinear Fisher discriminant analysis using a minimum squared error cost function and the orthogonal least squares algorithm , 2002, Neural Networks.

[54]  David Zhang,et al.  A feature extraction method for use with bimodal biometrics , 2010, Pattern Recognit..

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

[56]  Xuelong Li,et al.  Tensor Rank One Discriminant Analysis - A convergent method for discriminative multilinear subspace selection , 2008, Neurocomputing.