Adaptive Offset Subspace Self-Organizing Map: An Application to Handwritten Digit Recognition

Abstract

An Adaptive-Subspace Self-Organizing Map (ASSOM) can learn a set of ordered linear subspaces which correspond to invariant classes. However the basic ASSOMcannot properly learn linear manifolds that are shifted away from the origin of the input space. In this paper, we propose an improvement on ASSOM to amend this deficiency. The new network, named AOSSOM for Adaptive Offset Subspace Self-Organizing Map, minimizes a projection error function in a gradient-descent fashion. In each learning step, the winning module and its neighbors update their offset vectors and basis vectors of the target manifolds towards the negative gradient of the error function. We show by experiments that the AOSSOM can learn clusters aligned on linear manifolds shifted away from the origin and separate them accordingly. The proposed AOSSOM is applied to handwritten digit recognition and shows promising results.