A novel optimal discriminant principle in high dimensional spaces

A novel optimal discriminant principle and algorithm in high dimensional space are presented in this paper. The new optimal discriminant vectors have the property: in their spanned space, the within-class distance of training samples equals to zero while the between-class distance doesn't equal to zero. We also illustrate how many optimal discriminant vectors satisfying property above can be obtained. We apply this method to the face recognition and the experimental result shows the performance is superior to the existed methods.

[1]  R. Fisher.  THE USE OF MULTIPLE MEASUREMENTS IN TAXONOMIC PROBLEMS , 1936 .

[2]  John W. Sammon,et al.  An Optimal Discriminant Plane , 1970, IEEE Transactions on Computers.

[3]  John W. Sammon,et al.  An Optimal Set of Discriminant Vectors , 1975, IEEE Transactions on Computers.

[4]  Josef Kittler.  On the Discriminant Vector Method of Feature Selection , 1977, IEEE Transactions on Computers.

[5]  Qi Tian,et al.  Image Classification By The Foley-Sammon Transform , 1986 .

[6]  Q. Tian,et al.  Comparison of statistical pattern-recognition algorithms for hybrid processing. II: Eigenvector-based algorithm , 1988 .

[7]  Zi-Quan Hong,et al.  Algebraic feature extraction of image for recognition , 1991, Pattern Recognit..

[8]  M. Turk,et al.  Eigenfaces for Recognition , 1991, Journal of Cognitive Neuroscience.

[9]  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..

[10]  Jing-Yu Yang,et al.  A generalized optimal set of discriminant vectors , 1992, Pattern Recognit..

[11]  Yong-Qing Cheng,et al.  An Efficient Algorithm for Foley-Sammon Optimal Set of Discriminant Vectors by Algebraic Method , 1992, Int. J. Pattern Recognit. Artif. Intell..

[12]  Jing-Yu Yang,et al.  Optimal fisher discriminant analysis using the rank decomposition , 1992, Pattern Recognit..

[13]  Jing-Yu Yang,et al.  Algebraic feature extraction for image recognition based on an optimal discriminant criterion , 1993, Pattern Recognit..

[14]  Ferdinando Silvestro Samaria,et al.  Face recognition using Hidden Markov Models , 1995 .

[15]  Rama Chellappa,et al.  Discriminant Analysis for Recognition of Human Face Images (Invited Paper) , 1997, AVBPA.

[16]  Ah Chung Tsoi,et al.  Face recognition: a convolutional neural-network approach , 1997, IEEE Trans. Neural Networks.

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