title: On the equivalence between kernel self-organising maps and self-organising mixture density networks.
abstract: The kernel method has become a useful trick and has been widely applied to various learning models to extend their nonlinear approximation and classification capabilities. Such extensions have also recently occurred to the Self-Organising Map (SOM). In this paper, two recently proposed kernel SOMs are reviewed, together with their link to an energy function. The Self-Organising Mixture Network is an extension of the SOM for mixture density modelling. This paper shows that with an isotropic, density-type kernel function, the kernel SOM is equivalent to a homoscedastic Self-Organising Mixture Network, an entropy-based density estimator. This revelation on the one hand explains that kernelising SOM can improve classification performance by acquiring better probability models of the data; but on the other hand it also explains that the SOM already naturally approximates the kernel method.
authors.affiliation: School of Electrical and Electronic Engineering, University of Manchester, Manchester, M60 1QD, United Kingdom. h.yin@manchester.ac.uk
authors.forename: Hujun
authors.initials: H
authors.lastname: Yin
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D016000:Cluster Analysis; D016571:Neural Networks, Computer; D010363:Pattern Recognition, Automated