CSDL Home IEEE Transactions on Pattern Analysis & Machine Intelligence 2012 vol.34 Issue No.09  Sept.
Issue No.09  Sept. (2012 vol.34)
pp: 18141826
P. Honeine , Lab. de Modelisation et Surete des Syst., Univ. de Technol. de Troyes, Troyes, France
ABSTRACT
Kernel principal component analysis (kernelPCA) 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 kernelPCA. To this end, we examine a kernelbased version of Oja's rule, initially put forward to extract a linear principal axe. As with most kernelbased 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 reducedorder 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 kernelPCA and iterative kernelPCA.
INDEX TERMS
reduced order systems, data analysis, function approximation, principal component analysis, iterative kernelPCA, online kernel principal component analysis, reducedorder model, data analysis, dimensionality reduction techniques, online algorithm, Oja rule, linear principal axe extraction, kernelbased machines, principal function approximation, synthetic data set, handwritten digit image, classical kernelPCA, Kernel, Principal component analysis, Eigenvalues and eigenfunctions, Dictionaries, Algorithm design and analysis, Data models, Training data, recursive algorithm., Principal component analysis, online algorithm, machine learning, reproducing kernel, Oja's rule
CITATION
P. Honeine, "Online Kernel Principal Component Analysis: A ReducedOrder Model", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.34, no. 9, pp. 18141826, Sept. 2012, doi:10.1109/TPAMI.2011.270
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