This paper discusses the relationship between the K-L information based FCM method and a mixture distribution model with the EM algorithm when a noise cluster is assumed. Equivalence between the two methods in the sense that the derived solutions are the same is proved. From the equivalence a parameter in the fuzzy model can be estimated by using the mixture distribution model. A regularized FCM algorithm with the noise cluster is moreover derived for which the equivalent statistical model with the EM algorithm does not exist.
