Nonlinear projection using geodesic distances and the neural gas network

Abstract

A nonlinear projection method that uses geodesic distances and the neural gas network is proposed. First, the neural gas algorithm is used to obtain codebook vectors, and a connectivity graph is concurrently created by using competitive Hebbian rule. A procedure is added to tear or break non-contractible cycles in the connectivity graph, in order to project efficiently 'circular' manifolds such as cylinder or torus. In the second step, the nonlinear projection is created by applying an adaptation rule for codebook positions in the projection space. The mapping quality obtained with the proposed method outperforms CDA and Isotop, in terms of the trustworthiness, continuity, and topology preservation measures.