Clustering with Non-Convex Penalized Gaussian Graphical Models for Simultaneous Parameter Estimation and Pursuit of Sparseness

• Activity Number: 649
• Type: Contributed
• Date/Time: Thursday, August 4, 2016 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Chen Gao* and Wei Pan and Xiaotong Shen and Yunzhang Zhu
• Companies: University of Minnesota and University of Minnesota and University of Minnesota and The Ohio State University
• Keywords: model-based clustering ; mixture model ; Gaussian graphical model ; non-convex penalty ; glioblastoma ; gene expression

Abstract

Gaussian mixture model-based clustering is able to depict the network structure of variables while partitioning data into several clusters. However, estimating a positive-definite covariance matrix in Gaussian models is a challenging task. Here we employ a recently proposed method of estimating positive-definite precision matrix and apply it to Gaussian mixture model-based clustering. Unlike other competing methods, our method uses a non-convex penalty to pursue sparseness and detect similarity of entries in each precision matrix between different clusters. Some numerical examples have shown that our method possesses the impressive property to distinguish between zero and non-zero entries when estimating precsion matrices in each cluster. We also apply our method to a data set from a gene expression study for glioblastoma. From the case study using this data set and subsequent simulations, our clustering method is able to reveal the network structure of each cluster while achieving sparseness and grouping simultaneously.