A nonlinear principal component analysis on image data

Principal component analysis (PCA) has been applied in various areas such as pattern recognition and data compression. In some cases, however, PCA does not extract the characteristic of the data-distribution efficiently. In order to overcome this problem, we have proposed a novel method of nonlinear PCA which preserves the order of principal components. In this paper, we reduce the dimensionality of image data with the proposed method, and examine its effectiveness in compression and recognition of the images

[1]  Gunnar Rätsch,et al.  Kernel PCA and De-Noising in Feature Spaces , 1998, NIPS.

[2]  Shigeo Abe DrEng.  Pattern Classification , 2001, Springer London.

[3]  Michael E. Tipping.  Sparse Kernel Principal Component Analysis , 2000, NIPS.

[4]  H. Hotelling.  Analysis of a complex of statistical variables into principal components. , 1933 .

[5]  Shuji Hashimoto,et al.  On the evaluation of a nonlinear principal component analysis , 2004, Neural Networks and Computational Intelligence.

[6]  Juha Karhunen,et al.  Generalizations of principal component analysis, optimization problems, and neural networks , 1995, Neural Networks.

[7]  D. B. Graham,et al.  Characterising Virtual Eigensignatures for General Purpose Face Recognition , 1998 .

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

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

[10]  D. B. Gerham.  Characterizing virtual eigensignatures for general purpose face recognition , 1998 .

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

[12]  Ramanathan Gnanadesikan,et al.  Methods for statistical data analysis of multivariate observations , 1977, A Wiley publication in applied statistics.

[13]  Ryo Saegusa,et al.  Nonlinear principal component analysis to preserve the order of principal components , 2003, Neurocomputing.

[14]  Terence D. Sanger,et al.  Optimal unsupervised learning in a single-layer linear feedforward neural network , 1989, Neural Networks.

[15]  Mitsuo Kawato,et al.  Acquisition of internal representation by multilayered perceptrons , 1991 .