Exploring Topology Preservation of SOMs with a Graph Based Visualization

Abstract

The Self-Organizing Map (SOM), which projects a (high-dimensional) data manifold onto a lower-dimensional (usually 2-d) rigid lattice, is a commonly used manifold learning algorithm. However, a postprocessing --- that is often done by interactive visualization schemes --- is necessary to reveal the knowledge of the SOM. Thanks to the SOM property of producing (ideally) a topology preserving mapping, existing visualization schemes are often designed to show the similarities local to the lattice without considering the data topology. This can produce inadequate tools to investigate the detailed data structure and to what extent the topology is preserved during the SOM learning. A recent graph based SOM visualization, CONNvis [1], which exploits the underutilized knowledge of data topology, can be a suitable tool for such investigation. This paper discusses that CONNvis can represent the data topology on the SOM lattice despite the rigid grid structure, and hence can show the topology preservation of the SOM and the extent of topology violations.