KERNEL SELF-ORGANISING MAPS AND MIXTURE NETWORKS

Abstract – Kernel methods have been widely applied to various learning models to extend their nonlinear approximation abilities. Such extensions have also recently occurred to the Self-Organising Map (SOM). In this paper, two recent kernel SOMs are reviewed and it is shown that the kernel SOMs can be formally derived from an energy function of the SOM in the feature space. Various kernel functions are readily applicable to the kernel SOM, while their performance and choices of kernel parameters depend on the problem. This paper shows that with an isotropic and density-type kernel function, the kernel SOM is equivalent to a homoscedastic Self-Organising Mixture Network, an entropy-based density estimator. It also explains that the SOM approximates naturally a kernel method