Refining Gaussian mixture model based on enhanced manifold learning

Gaussian mixture model (GMM) has been widely used for data analysis in various domains including text documents, face images and genes. GMM can be viewed as a simple linear superposition of Gaussian components, each of which represents a data cluster. Recent models, namely Laplacian regularized GMM (LapGMM) and locally consistent GMM (LCGMM) have been proposed to preserve the local manifold structure of the data for modeling Gaussian mixtures, and show superior performance than the original GMM. However, these two models ignore the global manifold structure without consideration of the widely separated points. In this paper, we introduce refined Gaussian mixture model (RGMM), which explicitly places separated points far apart from each other as well as brings nearby points closer together according to the probability distributions of Gaussians, in the hope of fully discovering the discriminating power of manifold learning for estimating Gaussian mixtures. We use EM algorithm to optimize the maximum likelihood function of RGMM. Experimental results on three real-world data sets demonstrate the effectiveness of RGMM in data clustering.