Decision Manifolds: Classification Inspired by Self-Organization

Abstract

We present a classifier algorithm that approximates the decision surface of labeled data by a patchwork of separating hyperplanes. The hyperplanes are arranged in a way inspired by how Self-Organizing Maps are trained. We take advantage of the fact that the boundaries can often be approximated by linear ones connected by a low-dimensional nonlinear manifold. The resulting classifier allows for a voting scheme that averages over the classifiction results of neighboring hyperplanes. Our algorithm is computationally efficient both in terms of training and classification. Further, we present a model selection framework for estimation of the paratmeters of the classification boundary, and show results for artificial and real-world data sets.