A hyperbolic topographic mapping for proximity data

Abstract

In this paper a hyperbolic variant of the Topographic Mapping of Proximity Data (HTMP) is proposed. HTMP is based on a tessellation of the hyperbolic plane (IH) with equilateral triangles. In addition to promising options for data clustering and visualization, HTMP provides a convenient interface for the exploration of large data collections. It combines advantages of other recently proposed methods whose development has been stimulated by the extraordinary characteristics of spaces with non-euclidian geometry. The method is applied to data from dynamic contrast enhanced MRI (DCE-MRI). It is demonstrated how HTMP can be used to visualize data similarities based on the Earth Mover’s Distance.