Probabilistic Assessment of Model-Based Clustering

• Activity Number: 638
• Type: Topic Contributed
• Date/Time: Thursday, August 13, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Xuwen Zhu* and Volodymyr Melnykov
• Companies: The University of Alabama and The University of Alabama
• Keywords: model-based clustering ; classification ; influential observations ; diagnostics ; Gaussian mixture models

Abstract

Finite mixtures provide a powerful tool for modeling heterogeneous data. Model-based clustering is a broadly used grouping technique that assumes the existence of the one-to-one correspondence between clusters and mixture model components. Although there are many directions of active research in the model-based clustering framework, very little attention has been paid to studying the specific nature of detected clustering solutions. We develop an approach for assessing the variability in classifications carried out by the Bayes decision rule. The proposed technique allows assessing significance of each assignment made. We also apply the developed instrument for identifying influential observations that have impact on the structure of the detected partitioning. The proposed diagnostic methodology is studied and illustrated on synthetic data and applied to the analysis of two well-known classification datasets.