Topology-Preserving mappings for data visualisation

Abstract

We present a family of topology preserving mappings similar to the Self-Organizing Map (SOM) and the Generative Topographic Map (GTM). These techniques can be considered as a non-linear projection from input or data space to the output or latent space (usually 2D or 3D), plus a clustering technique, that updates the centres. A common frame based on the GTM structure can be used with different clustering techniques, giving new properties to the algorithms. Thus we have the topographic product of experts (ToPoE) with the Product of Experts substituting the Mixture of Experts of the GTM, two versions of the Harmonic Topographic Mapping (HaToM) that utilise the K-Harmonic Means (KHM) clustering, and the faster Topographic Neural Gas (ToNeGas), with the inclusion of Neural Gas in the inner loop. We also present the Inverse-weighted K-means Topology-Preserving Map (IKToM), based on the same structure for non-linear projection, that makes use of a new clustering technique called The Inverse Weighted K-Means. We apply all the algorithms to a high dimensional dataset, and compare it as well with the Self-Organizing Map, in terms of visualisation, clustering and topology preservation.