Title: Kernel optimisation for KPCA based on Gaussianity estimation

Authors: Qi Kang; Kang Wang; Bingyao Huang; Jing An

Addresses: Department of Control Science and Engineering, Tongji University, Shanghai 201804, China ' Department of Control Science and Engineering, Tongji University, Shanghai 201804, China ' Department of Electrical and Computer Engineering, Rowan University, Glassboro, NJ 08028, USA ' School of Electrical and Electronic Engineering, Shanghai Institute of Technology, Shanghai 201418, China

Abstract: Kernel-based principle component analysis (KPCA) is an effective feature extraction method. It extends PCA to nonlinear cases using kernel trick. The performance of KPCA relies on the pre-selected parameter of kernel function. In this paper, we propose a kernel parameter optimisation method by using principle component subspace-based Gaussianity estimation, based on the idea that optimal kernel parameters lead the mapped feature space close to Gaussian distribution. By using subspace coordinates in feature space generalised by KPCA, the mapping data problem is properly solved. Further, we estimate the Gaussian distribution approximation degree in subspace by using the establishing condition for multidimensional Gaussian distribution in statistics. Experiment results are shown to verify the kernel parameter optimisation algorithm by testing on both simulation and real-world data.

Keywords: principle component analysis; PCA; feature space; Gaussian distribution estimation; kernel parameter optimisation; feature extraction.

DOI: 10.1504/IJBIC.2014.060620

International Journal of Bio-Inspired Computation, 2014 Vol.6 No.2, pp.91 - 107

Received: 10 Jan 2014
Accepted: 19 Jan 2014
Published online: 27 Sep 2014 *

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