Summary
Recently, the the support vector machine (SVM) has become a popular tool in time series forecasting. In developing a successful SVM forecaster, the first step is feature extraction. This paper proposes the applications of principal component analysis (PCA), kernel principal component analysis (KPCA) and independent component analysis (ICA) to SVM for feature extraction. The PCA linearly transforms the original inputs into new uncorrelated features. The KPCA is a nonlinear PCA developed by using the kernel method. In ICA, the original inputs are linearly transformed into features which are mutually statistically independent. By examining the sunspot data, Santa Fe data set A and five real futures contracts, the experiment shows that SVM by feature extraction using PCA, KPCA or ICA can perform better than that without feature extraction. Furthermore, among the three methods, there is the best performance in the KPCA feature extraction, followed by the ICA feature extraction.
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An Empirical Study of Dimensionality Reduction in Support Vector Machine*
1. Introduction
Recently, support vector machine (SVM) has become a popular tool in time series forecasting [18, 19, 20, 26, 27], due to its remarkable characteristics such as good generalization performance, the absence of local minima and the sparse representation of solution. Unlike most of the traditional methods which implement the Empirical Risk Minimization Principal, SVM implements the Structural Risk Minimization Principal which seeks to minimize an upper bound of the generalization error rather than minimize the training error [31]. This eventually results in a better generalization performance in SVM than other traditional methods. As the training of SVM is equivalent to solving a linearly constrained convex quadratic programming problem, the solution of SVM is always global optimal and absent ...See the full content of this document
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