Feature extraction based on Laplacian bidirectional maximum margin criterion

Maximum margin criterion (MMC) based feature extraction is more efficient than linear discriminant analysis (LDA) for calculating the discriminant vectors since it does not need to calculate the inverse within-class scatter matrix. However, MMC ignores the discriminative information within the local structures of samples and the structural information embedding in the images. In this paper, we develop a novel criterion, namely Laplacian bidirectional maximum margin criterion (LBMMC), to address the issue. We formulate the image total Laplacian matrix, image within-class Laplacian matrix and image between-class Laplacian matrix using the sample similar weight that is widely used in machine learning. The proposed LBMMC based feature extraction computes the discriminant vectors by maximizing the difference between image between-class Laplacian matrix and image within-class Laplacian matrix in both row and column directions. Experiments on the FERET and Yale face databases show the effectiveness of the proposed LBMMC based feature extraction method.

[1]  Bruce A. Draper,et al.  Recognizing faces with PCA and ICA , 2003, Comput. Vis. Image Underst..

[2]  Shuicheng Yan,et al.  Classification and Feature Extraction by Simplexization , 2008, IEEE Transactions on Information Forensics and Security.

[3]  Fei Wang,et al.  Feature Extraction by Maximizing the Average Neighborhood Margin , 2007, 2007 IEEE Conference on Computer Vision and Pattern Recognition.

[4]  Jian-Huang Lai,et al.  1D-LDA vs. 2D-LDA: When is vector-based linear discriminant analysis better than matrix-based? , 2008, Pattern Recognit..

[5]  Shuicheng Yan,et al.  A Convengent Solution to Tensor Subspace Learning , 2007, IJCAI.

[6]  Daoqiang Zhang,et al.  Efficient and robust feature extraction by maximum margin criterion , 2003, IEEE Transactions on Neural Networks.

[7]  P. Jonathon Phillips,et al.  Empirical Evaluation Methods in Computer Vision , 2002 .

[8]  Richard O. Duda,et al.  Pattern classification and scene analysis , 1974, A Wiley-Interscience publication.

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

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

[11]  Anil K. Jain,et al.  39 Dimensionality and sample size considerations in pattern recognition practice , 1982, Classification, Pattern Recognition and Reduction of Dimensionality.

[12]  H. Damasio,et al.  IEEE Transactions on Pattern Analysis and Machine Intelligence: Special Issue on Perceptual Organization in Computer Vision , 1998 .

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

[14]  David Zhang,et al.  Sequential row-column independent component analysis for face recognition , 2009, Neurocomputing.

[15]  Jian Yang,et al.  BDPCA plus LDA: a novel fast feature extraction technique for face recognition , 2006, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[16]  Jing-Yu Yang,et al.  Face recognition based on the uncorrelated discriminant transformation , 2001, Pattern Recognit..

[17]  Dong Xu,et al.  Trace Ratio vs. Ratio Trace for Dimensionality Reduction , 2007, 2007 IEEE Conference on Computer Vision and Pattern Recognition.

[18]  Jian Yang,et al.  Two-dimensional PCA: a new approach to appearance-based face representation and recognition , 2004, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[19]  J. Friedman.  Regularized Discriminant Analysis , 1989 .

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

[21]  David Zhang,et al.  Directional independent component analysis with tensor representation , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.

[22]  Kuanquan Wang,et al.  Bidirectional PCA with assembled matrix distance metric for image recognition , 2006, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[23]  M. Omair Ahmad,et al.  Two-dimensional FLD for face recognition , 2005, Pattern Recognit..

[24]  Shuicheng Yan,et al.  Correlation Metric for Generalized Feature Extraction , 2008, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[25]  J. Tenenbaum,et al.  A global geometric framework for nonlinear dimensionality reduction. , 2000, Science.

[26]  Jian Yang,et al.  Globally Maximizing, Locally Minimizing: Unsupervised Discriminant Projection with Applications to Face and Palm Biometrics , 2007, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[27]  Jian Yang,et al.  Two-dimensional discriminant transform for face recognition , 2005, Pattern Recognit..

[28]  Anil K. Jain,et al.  Small Sample Size Effects in Statistical Pattern Recognition: Recommendations for Practitioners , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[29]  Deng Cai,et al.  Tensor Subspace Analysis , 2005, NIPS.

[30]  John M. Lee.  Riemannian Manifolds: An Introduction to Curvature , 1997 .

[31]  Stephen Lin,et al.  Graph Embedding and Extensions: A General Framework for Dimensionality Reduction , 2007, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[32]  Bruce A. Draper,et al.  Analyzing PCA-based Face Recognition Algorithms: Eigenvector Selection and Distance Measures , 2003 .

[33]  Jian Yang,et al.  Why can LDA be performed in PCA transformed space? , 2003, Pattern Recognit..

[34]  David Zhang,et al.  Face recognition using FLDA with single training image per person , 2008, Appl. Math. Comput..

[35]  Hyeonjoon Moon,et al.  The FERET evaluation methodology for face-recognition algorithms , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[36]  R. Tibshirani,et al.  Flexible Discriminant Analysis by Optimal Scoring , 1994 .

[37]  Dao-Qing Dai,et al.  Improved discriminate analysis for high-dimensional data and its application to face recognition , 2007, Pattern Recognit..

[38]  Jing-Yu Yang,et al.  Optimal discriminant plane for a small number of samples and design method of classifier on the plane , 1991, Pattern Recognit..

[39]  Yun Fu,et al.  Image Classification Using Correlation Tensor Analysis , 2008, IEEE Transactions on Image Processing.

[40]  Paul D. Minton,et al.  Statistics: The Exploration and Analysis of Data , 2002, Technometrics.

[41]  Xiaolong Teng,et al.  Face recognition using discriminant locality preserving projections , 2006, Image Vis. Comput..

[42]  Yuxiao Hu,et al.  Learning a locality preserving subspace for visual recognition , 2003, Proceedings Ninth IEEE International Conference on Computer Vision.

[43]  Hua Yu,et al.  A direct LDA algorithm for high-dimensional data - with application to face recognition , 2001, Pattern Recognit..

[44]  Juyang Weng,et al.  Using Discriminant Eigenfeatures for Image Retrieval , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

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

[46]  Hau-San Wong,et al.  Face recognition based on 2D Fisherface approach , 2006, Pattern Recognit..

[47]  Jian Yang,et al.  Minimal local reconstruction error measure based discriminant feature extraction and classification , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.

[48]  B. Ripley,et al.  Pattern Recognition , 1968, Nature.

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

[50]  Dao-Qing Dai,et al.  Inverse Fisher discriminate criteria for small sample size problem and its application to face recognition , 2005, Pattern Recognit..

[51]  Honggang Zhang,et al.  Comments on "Globally Maximizing, Locally Minimizing: Unsupervised Discriminant Projection with Application to Face and Palm Biometrics" , 2007, IEEE Trans. Pattern Anal. Mach. Intell..

[52]  Shuicheng Yan,et al.  Graph embedding: a general framework for dimensionality reduction , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[53]  Lawrence Sirovich,et al.  Application of the Karhunen-Loeve Procedure for the Characterization of Human Faces , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[54]  Avinash C. Kak,et al.  PCA versus LDA , 2001, IEEE Trans. Pattern Anal. Mach. Intell..

[55]  Xuelong Li,et al.  Effective Feature Extraction in High-Dimensional Space , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[56]  Mikhail Belkin,et al.  Laplacian Eigenmaps for Dimensionality Reduction and Data Representation , 2003, Neural Computation.

[57]  Deli Zhao,et al.  Linear Laplacian Discrimination for Feature Extraction , 2007, 2007 IEEE Conference on Computer Vision and Pattern Recognition.

[58]  R. Tibshirani,et al.  Penalized Discriminant Analysis , 1995 .

[59]  S T Roweis,et al.  Nonlinear dimensionality reduction by locally linear embedding. , 2000, Science.

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

[61]  Hwann-Tzong Chen,et al.  Local discriminant embedding and its variants , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).