Online Kernel Principal Component Analysis: A Reduced-Order Model
Copyright policy )Online Kernel Principal Component Analysis: A Reduced-Order Model
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.
online kernel principal component analysis, non-stationarity, reduced-order model, [INFO.INFO-TS] Computer Science [cs]/Signal and Image Processing, data analysis, Principal component analysis, reduced order systems, classical kernel-PCA, pre-image problem, synthetic data set, [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, adaptive filtering, Algorithm design and analysis, principal function approximation, dimensionality reduction techniques, Oja rule, iterative kernel-PCA, [SPI.SIGNAL] Engineering Sciences [physics]/Signal and Image processing, handwritten digit image, Eigenvalues and eigenfunctions, recursive algorithm, Training data, Oja's rule, sparsity, kernel-based machines, reproducing kernel, Data models, function approximation, [INFO.INFO-LG] Computer Science [cs]/Machine Learning [cs.LG], Kernel, online algorithm, recursive algorithm., machine learning, linear principal axe extraction, Dictionaries, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing, Index Terms-Principal component analysis
online kernel principal component analysis, non-stationarity, reduced-order model, [INFO.INFO-TS] Computer Science [cs]/Signal and Image Processing, data analysis, Principal component analysis, reduced order systems, classical kernel-PCA, pre-image problem, synthetic data set, [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, adaptive filtering, Algorithm design and analysis, principal function approximation, dimensionality reduction techniques, Oja rule, iterative kernel-PCA, [SPI.SIGNAL] Engineering Sciences [physics]/Signal and Image processing, handwritten digit image, Eigenvalues and eigenfunctions, recursive algorithm, Training data, Oja's rule, sparsity, kernel-based machines, reproducing kernel, Data models, function approximation, [INFO.INFO-LG] Computer Science [cs]/Machine Learning [cs.LG], Kernel, online algorithm, recursive algorithm., machine learning, linear principal axe extraction, Dictionaries, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing, Index Terms-Principal component analysis
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).77 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
Citations provided by BIP!Popularity provided by BIP!