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

This paper presents a new self-organizing map algorithm. Unlike the well-kn own 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 dis tributed on a regular low-dimensional grid, and a penalization term is adde d in order to guarantee a smooth distribution for the values of the code ve ctors on the grid. The mapping properties of the new method. similar to tho se 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 Elsevie r Science Ltd. All rights reserved.