Robust EM Clustering Through a Mixture in Multivariate Regression

• Activity Number: 526
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Ji Young Kim*+ and Xuming He and John Marden
• Companies: Mount Holyoke College and University of Illinois at Urbana-Champaign and University of Illinois at Urbana-Champaign
• Keywords: Robust ; Clustering ; Multivariate Regression ; EM akgirutgn

Abstract

Among a variety of clustering techniques, the mixture model approach provides a sound and flexible option. The normal mixture models fitted through the EM algorithm have been commonly used for clustering. To account for heavier tails, the mixture of t distributions has been used as an alternative. However, data with non-Gaussian tails, asymmetry, or extreme outliers may not be adequately modeled by a mixture of t distributions. In some problems, clustering can be done effectively once after adjusting for certain covariates. We propose a robust clustering method (REM) for high-dimensional data based on the idea of mixtures in a multivariate linear regression setting, designed to reduce the effects of the outliers with Huber's loss function. The model is fitted via the EM (expectation and maximization) algorithm with a new iterative algorithm to solve the optimization problem. In simulation studies, we find that the REM often works better than existing clustering methods. The superior performance of the REM can be attributed to the robustness and the use of covariates. Along with other existing methods, the REM provides an elaborate approach to clustering heterogene