Adaptive Affine Subspace Self-organizing Map with Kernel Method

Abstract

Adaptive Subspace Self-organizing Map (ASSOM) is an evolution of Self-Organizing Map, where each computational unit defines a linear subspace. Recently, its modified version, where each unit defines an affine subspace instead of the subspace, has been proposed. The affine subspace in a unit is represented by a mean vector and a set of basis vectors. After training, these units result in a set of affine subspace detectors. In numerous cases, however, these are not enough to describe a class of patterns because of its linearity. In this paper, the Adaptive Affine Subspace SOM (AASSOM) on the high-dimensional space with kernel method is proposed in order to achieve efficient classification. By using the kernel method, linear affine subspaces in the AASSOM can be extended to nonlinear affine subspaces easily. The effectiveness of the proposed method is verified by applying it to some simple classification problems.