Numerical Evaluation of Clustering Methods with Kernel PCA

Abstract

Kernel methods are ones that, by replacing the inner product with positive definite function, implicitly perform a nonlinear mapping of the input data into a high-dimensional feature space. The clustering methods using kernel function (kernel clustering methods) are superior in accuracy to the conventional ones such as K-Means (KM) and Neural-Gas (NG). But, it seems that kernel clustering methods do not always show sufficient ability of clustering. One method to improve them is to find expression of approximation for data in the feature space. In this paper, we introduce the kernel PCA and apply it to clustering methods as KM and NG. Further, we apply it to derived kernel method, which means twice application of kernel functions. The simulation results show that the proposed clustering methods are superior in terms of accuracy to the conventional methods.