Kernel self-organising maps for classification

Abstract

In this paper, we review two recently developed kernel self-organising maps (SOMs) for classification and further establish their link with an energy function. We demonstrate that the kernel SOM can be derived naturally by minimising the energy function, and the resulting kernel SOM unifies the approaches to kernelise the SOM and can be performed entirely in the feature space. Different forms of kernel functions can be readily adopted. Various kernel SOMs, as well as the original SOM, are compared on classifying several benchmark datasets. The performance of the kernel SOMs depends on the choices of kernel functions and their parameters, as well as the ways to classify the neurons. Although the proposed energy based kernel SOM can produce better classification results than other SOMs in some cases, there is no clear evidence showing that the kernel SOMs are always superior to the common SOM. The computational cost to kernelise the SOM, however, increases significantly.