Fuzzy clustering based on modified distance measures

Abstract

The well-known fuzzy c-means algorithm is an objective function based fuzzy clustering technique that extends the classical k-means method to fuzzy partitions. By replacing the Euclidean distance in the objective function other cluster shapes than the simple (hyper-)spheres of the fuzzy c-means algorithm can be detected, for instance ellipsoids, lines or shells of circles and ellipses. We propose a modified distance function that is based on the dot product and allows to detect a new kind of cluster shape and also lines and (hyper-)planes.