Self-Organizing Clustering with Map of Nonlinear Varieties Representing Variation in One Class

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 linear manifold instead of the linear subspace, has been proposed. The linear manifold in a unit is represented by a mean vector and a set of basis vectors. After training, these units result in a set of linear variety detectors. In another point of view, we can consider the AMSOM represents the latent commonality of data as linear structures. In numerous cases, however, these are not enough to describe the latent commonality of data because of its linearity. In this paper, the nonlinear variety is considered in order to represent a diversity of data in a class. The effectiveness of the proposed method is verified by applying it to some simple classification problems.