A new typicality-based weight function for robust mixture decomposition

One of the fundamental problems in applications of fuzzy set theory is the estimation of membership functions from data. In methods based on probability theory one of the techniques used to estimate probability densities is mixture decomposition. This method assumes that a given data set comes from a distribution that is a convex combination of parametrized components (density functions) such as Gaussians. A similar method can be used to estimate membership functions. In other words, a membership function can be modeled as a convex combination of parametrized models. Therefore, the task of estimating the membership function can be viewed as a mixture decomposition problem. Mixture decomposition involves estimation of the parameters of each component in the mixture. The expectation-maximization (EM) algorithm has been traditionally used for Gaussian mixture decomposition. However, this algorithm is not robust, and gives poor results in the presence of noise. In this paper, we present a robust algorithm for Gaussian mixture decomposition. The algorithm uses robust statistical methods to construct a weight function. Since the weight function is based on the idea of typicality, it gives low weights to noise points and outliers. Thus, the algorithm gives robust estimates of the parameters. The weight function we propose uses the distribution of the distances of good points to component prototypes. We present results of the algorithm for both synthetic and real data sets.