A new fuzzy clustering algorithm with entropy regularization

The Fuzzy k-Means (FkM) algorithm is a tool for clustering n objects into k homogeneous groups. FkM is able to detect only spherical shaped clusters, hence it may not work properly when clusters have different shapes. For this purpose a variant of FkM is the Gustafson-Kessel (GK) algorithm, which can recognize theshapes of the clusters by the computation of the covariance matrix for each cluster. The fuzziness of the FkM and GK partitions is tuned by the so-called parameter of fuzziness which is an artificial device lacking a physical meaning. In order to avoidthis inconvenience a fuzzy clustering algorithm with entropy regularization can be used. The idea consists in tuning the amount of fuzziness of the obtained partition by the concept of entropy. Unfortunately, such a clustering algorithm can identify only spherical clusters. In this respect, we introduce a GK-like algorithm with entropy regularization capable to discover non-spherical clusters.