Model-Based Clustering via Multinomial Logistic Cluster Probabilities for Gaussian Data

• Activity Number: 85
• Type: Contributed
• Date/Time: Sunday, August 3, 2014 : 4:00 PM to 5:50 AM
• Sponsor: Section on Statistics and the Environment
• Author(s): Lulu Wang*+ and Jennifer A. Hoeting
• Companies: Colorado State University and Colorado State University
• Keywords: Model-based Clustering ; Classification EM Algorithm ; Multinomial Logistic ; Noise Cluster ; Stochastic CEM

Abstract

Parametric model-based clustering methods are becoming more common. Model-based clustering allows incorporation of the uncertainty of parameter estimates and also allows estimation of uncertainty about cluster membership for each observation. There are many potential applications of model-based clustering including social network, gene expression, animal migration and so on. In some applications it makes sense to incorporate covariates to predict cluster assignment. For clustering spatial location data, we often find that the correlation between important covariates and locations (the response) is very low. In this case, previously proposed linear regression-based model clustering does not work well. We propose a new model using multinomial logistic regression to capture the relation between covariates and locations based on the cluster assignments. We will also introduce an extended version of this model that allows some data to be classified into a noise cluster. We propose a Classification EM-algorithm (CEM) approach and also a stochastic EM algorithm to estimate parameters for our model-based clustering via the multinomial logistic cluster probabilities for Gaussian data.