A Bayesian approach to two-mode clustering

We develop a new Bayesian approach to estimate the parameters of a latent-class model for the joint clustering of both modes of two-mode data matrices. Posterior results are obtained using a Gibbs sampler with data augmentation. Our Bayesian approach has three advantages over existing methods. First, we are able to do statistical inference on the model parameters, which would not be possible using frequentist estimation procedures. In addition, the Bayesian approach allows us to provide statistical criteria for determining the optimal numbers of clusters. Finally, our Gibbs sampler has fewer problems with local optima in the likelihood function and empty classes than the EM algorithm used in a frequentist approach. We apply the Bayesian estimation method of the latent-class two-mode clustering model to two empirical data sets. The first data set is the Supreme Court voting data set of Doreian, Batagelj, and Ferligoj (2004). The second data set comprises the roll call votes of the United States House of Representatives in 2007. For both data sets, we show how two-mode clustering can provide useful insights.