Path finding on a spherical SOM using the distance transform and floodplain analysis

Abstract

Data visualization has become an important tool for analyzing very complex data. In particular, spatial visualization enables users to view data in a intuitive manner. It has typically been used to externalize clusters and their relationships which exist in highly complex multidimensional data. We envisage that not only cluster formation and relationships but also other types of information, such as temporal changes of datum, can be extracted through the spatialization. In this paper, we investigate an application of trajectory/path analysis carried out using a Self-Organizing Map as a spatialization method. We propose an application of distance transformations to the Geodesic Self-Organizing Map. This new approach allows a user to visually inspect the trajectory of multidimensional knowledge pieces on a two-dimensional space. The trajectories discovered through this approach are essentially the shortest paths between two points on the Self-Organizing Map. However, those paths might go outside of the input dataspace due to the connectivity of neurons imposed by the grid structure. We also present a method to find the shortest path, which falls within the input dataspace using simple floodplain analysis.