Fuzzy c-means clustering with regularization by K-L information

The Gaussian mixture model or Gaussian mixture density decomposition(GMDD) use the likelihood function as a measure of fit. We show that just the same algorithm as the GMDD can be derived from a modified objective function of fuzzy c-means (FCM) clustering with the regularizer by K-L information, only when the parameter λ equals 2. Although the fixed-point iteration scheme of FCM is similar to that of the GMDD, the FCM has more flexible structure since the algorithm is based on the objective function method. In a slightly different manner such as installing a deterministic annealing or an addition of Gustafson and Kessel´s (1979) constraint, the proposed algorithm is likely to provide more valid clustering results.