Geodesic Nonlinear Mapping Using the Neural Gas Network

A geodesic nonlinear projection method based on self-organizing neural networks is proposed. Firstly, the neural gas (NG) algorithm is used to obtain codebook vectors, and a graph is concurrently created by using the competitive Hebbian rule. Secondly, the nonlinear mapping is created by applying an adaptation rule for codebook positions in the projection space. The algorithm minimizes a cost function that favors the preservation of the local topology, using geodesic distances in the input space. The proposed method, called GNLP-NG, is an enhancement over curvilinear distance analysis (CDA). The mapping quality obtained with GNLP-NG outperforms CDA and Isotop, in terms of the trustworthiness, continuity and topology preservation measures.