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Gaussian Mixture PDF Approximation and Fuzzy c-Means Clustering with Entropy Regularization

EM algorithm is a popular density estimation method that uses the likelihood function as the measure of fit. Fuzzy c-Means (FCM) is also a popular clustering algorithm by the distance-based objective function methods. This paper discusses about similarity between the Gaussian mixture model with EM algorithm and the FCM based on the Mahalanobis distance with the entropy regularization. We show that the same algorithm as the EM algorithm can be derived from a modified FCM with regularization by K-L information. And, then we apply it to Fuzzy c-Varieties (FCV) which is a clustering algorithm to obtain linear or ellipsoidal clusters.