Smoothly distributed fuzzy c-means:: a new self-organizing map

This paper presents a new self-organizing map algorithm. Unlike the well-known method of Kohonen, the new algorithm corresponds to the optimization of an unambiguously defined cost function. It consists of a modified version of the widely used fuzzy c-means functional, where the code vectors are distributed on a regular low-dimensional grid, and a penalization term is added in order to guarantee a smooth distribution for the values of the code vectors on the grid. The mapping properties of the new method. similar to those of Kohonen's algorithm, are illustrated with several data sets. Computer programs (source code and executables) and data are available upon request to the authors. (C) 2001 Pattern Recognition Society. Published by Elsevier Science Ltd. All rights reserved.