Linear Fuzzy Clustering with Regularization by K-L information

Abstract

FCM-type fuzzy clustering approaches are closely related to Gaussian Mixture Models (GMMs) and the objective function of Fuzzy c-Means with regularization by K-L information (KFCM) is optimized by an EM-like algorithm. In this paper, we propose to apply probabilistic PCA mixture models to linear clustering following the discussion on the relationship between Local PCA and linear fuzzy clustering. Although the proposed method is a kind of the constrained model of KFCM, the algorithm includes a similar formulation with the Fuzzy c-Varieties (FCV) algorithm as a special case. Then the algorithm can be regarded as a modified FCV algorithm with regularization by K-L information, which makes it possible to tune the cluster shapes adaptively.