Exponential locality preserving projections for small sample size problem

Locality preserving projections (LPP) is a widely used manifold reduced dimensionality technique. However, it suffers from two problems: (1) small sample size problem and (2) the performance is sensitive to the neighborhood size k. In order to address these problems, we propose an exponential locality preserving projections (ELPP) by introducing the matrix exponential in this paper. ELPP avoids the singular of the matrices and obtains more valuable information for LPP. The experiments are conducted on three public face databases, ORL, Yale and Georgia Tech. The results show that the performances of ELPP is better than those of LPP and the state-of-the-art LPP Improved1.

[1]  Jian Yang,et al.  LPP solution schemes for use with face recognition , 2010, Pattern Recognit..

[2]  Bo Yang,et al.  Sample-dependent graph construction with application to dimensionality reduction , 2010, Neurocomputing.

[3]  Timothy F. Havel,et al.  Derivatives of the Matrix Exponential and Their Computation , 1995 .

[4]  Bin Xu,et al.  Generalized Discriminant Analysis: A Matrix Exponential Approach , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[5]  H. Sebastian Seung,et al.  The Manifold Ways of Perception , 2000, Science.

[6]  Zhongliang Jing,et al.  Local structure based supervised feature extraction , 2006, Pattern Recognit..

[7]  Gene F. Franklin,et al.  Digital control of dynamic systems , 1980 .

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

[9]  Nicholas J. Higham,et al.  The Scaling and Squaring Method for the Matrix Exponential Revisited , 2005, SIAM J. Matrix Anal. Appl..

[10]  Cleve B. Moler,et al.  Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later , 1978, SIAM Rev..

[11]  Xiaoyang Tan,et al.  Pattern Recognition , 2016, Communications in Computer and Information Science.

[12]  W. Stewart,et al.  A numerical study of large sparse matrix exponentials arising in Markov chains 1 1 This work has ben , 1999 .

[13]  C. Loan,et al.  Nineteen Dubious Ways to Compute the Exponential of a Matrix , 1978 .

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

[15]  Xiaofei He,et al.  Locality Preserving Projections , 2003, NIPS.

[16]  Dewen Hu,et al.  A Direct Locality Preserving Projections (DLPP) Algorithm for Image Recognition , 2008, Neural Processing Letters.

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

[18]  Timothy F. Havel,et al.  Matrix decompositions of two-dimensional nuclear magnetic resonance spectra. , 1994, Proceedings of the National Academy of Sciences of the United States of America.