SOM based on Nonlinear Distance Measure Defined by Graph

Abstract

In this paper, a new distance measure for improving the self-organizing map learning process is described. The new distance measure is defined based on data distribution, thus it can be efficiently used for real application, in which data is often distributed in nonlinear manifold. The authors have reported a graph-based distance measure, but it requires high computation performance. To reduce the computational cost, we define an energy function in the data space, and a distance is calculated using the energy function. Experimental results using simple data show effectiveness of the proposed method.