Fuzzy and robust formulations of maximum-likelihood-based Gaussian mixture decomposition

We show that maximum-likelihood-based Gaussian mixture decomposition (GMD) can be viewed as a probabilistic clustering algorithm. Furthermore, we formulate a fuzzy version of the GMD algorithm, and present the similarities and differences between the fuzzy C-means (FCM) algorithm and the fuzzy GMD method. In order to provide a good initial point, we propose a new initialization method for the fuzzy GMD algorithm. We also derive the objective function and update equations for a robust version of the FCM and the fuzzy GMD. The robust versions can be used when the data set is expected to be noisy.