Laplacian Regularized Gaussian Mixture Model for Data Clustering

Citations Over TimeTop 10% of 2011 papers

Abstract

Gaussian Mixture Models (GMMs) are among the most statistically mature methods for clustering. Each cluster is represented by a Gaussian distribution. The clustering process thereby turns to estimate the parameters of the Gaussian mixture, usually by the Expectation-Maximization algorithm. In this paper, we consider the case where the probability distribution that generates the data is supported on a submanifold of the ambient space. It is natural to assume that if two points are close in the intrinsic geometry of the probability distribution, then their conditional probability distributions are similar. Specifically, we introduce a regularized probabilistic model based on manifold structure for data clustering, called Laplacian regularized Gaussian Mixture Model (LapGMM). The data manifold is modeled by a nearest neighbor graph, and the graph structure is incorporated in the maximum likelihood objective function. As a result, the obtained conditional probability distribution varies smoothly along the geodesics of the data manifold. Experimental results on real data sets demonstrate the effectiveness of the proposed approach.

Related Papers

• → MPI Implementation of Expectation Maximization Algorithm for Gaussian Mixture Models(2014)7 cited
• → An algorithm for estimating number of components of Gaussian mixture model based on penalized distance(2008)7 cited
• Estimating parameters of GMM based on split EM(2012)
• GMM을 위한 점진적 ${\cal}k-means$ 알고리즘에 의해 초기값을 갖는 EM알고리즘과 화자식별에의 적용(2005)
• EM Algorithm with Initialization Based on Incremental ${\cal}k-means$ for GMM and Its Application to Speaker Identification(2005)