DocumentCode :
1409524
Title :
Online Kernel Principal Component Analysis: A Reduced-Order Model
Author :
Honeine, Paul
Author_Institution :
Lab. de Modelisation et Surete des Syst., Univ. de Technol. de Troyes, Troyes, France
Volume :
34
Issue :
9
fYear :
2012
Firstpage :
1814
Lastpage :
1826
Abstract :
Kernel principal component analysis (kernel-PCA) is an elegant nonlinear extension of one of the most used data analysis and dimensionality reduction techniques, the principal component analysis. In this paper, we propose an online algorithm for kernel-PCA. To this end, we examine a kernel-based version of Oja´s rule, initially put forward to extract a linear principal axe. As with most kernel-based machines, the model order equals the number of available observations. To provide an online scheme, we propose to control the model order. We discuss theoretical results, such as an upper bound on the error of approximating the principal functions with the reduced-order model. We derive a recursive algorithm to discover the first principal axis, and extend it to multiple axes. Experimental results demonstrate the effectiveness of the proposed approach, both on synthetic data set and on images of handwritten digits, with comparison to classical kernel-PCA and iterative kernel-PCA.
Keywords :
data analysis; function approximation; principal component analysis; reduced order systems; Oja rule; classical kernel-PCA; data analysis; dimensionality reduction techniques; handwritten digit image; iterative kernel-PCA; kernel-based machines; linear principal axe extraction; online algorithm; online kernel principal component analysis; principal function approximation; reduced-order model; synthetic data set; Algorithm design and analysis; Data models; Dictionaries; Eigenvalues and eigenfunctions; Kernel; Principal component analysis; Training data; Oja´s rule; Principal component analysis; machine learning; online algorithm; recursive algorithm.; reproducing kernel;
fLanguage :
English
Journal_Title :
Pattern Analysis and Machine Intelligence, IEEE Transactions on
Publisher :
ieee
ISSN :
0162-8828
Type :
jour
DOI :
10.1109/TPAMI.2011.270
Filename :
6112772
Link To Document :
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