Parametric Cluster Analysis and Mixture Regression

Abstract

This chapter is about advanced parametric clustering techniques based on the concept of mixture distributions. The first section introduces mixture distributions from a general perspective, followed by two popular applications in clustering: normal mixture models (latent profile analysis) for metric input variables and multinomial mixture models (latent class analysis) for categorical variables. Subsequently, these ideas are extended to mixed input scale levels. In the following section, the mixture distribution concept is embedded into a regression framework. In mixture regression models, clustering and estimation of regression parameters are performed simultaneously. By means of Dirichlet process regression, we add another complexity layer to the modeling framework by letting an algorithm determine the optimal number of clusters. Finally, the focus is on latent Dirichlet allocations: topic models for clustering text data.