Features extraction via wavelet kernel PCA for data classification

The performance of a kernel-based method is usually sensitive to a choice of the values of the hyper parameters of a kernel function. In this paper, we present a novel framework of using wavelet kernels in the kernel principal component analysis (KPCA) in order to better explain the nonlinear relationships among original multivariate data. We propose to introduce dilation and translation factors into a wavelet kernel function, in order to narrow down the search for kernel parameters required to calculate the kernel matrix. We tested the hypothesis of implementing a wavelet kernel PCA (WKPCA) to extract the feature information using a set of simulated multi-scale clustered data. We show that WKPCA is an effective feature extraction method for transforming a variety of multi-dimensional clustered data into data with a higher level of linearity among the data attributes. That brings to an improvement in the accuracy of linear classifiers.