Self-organising map as a natural kernel method

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 a symmetric 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.