We present a Dirichlet process mixture model over discrete incomplete rankings and study two Gibbs sampling inference techniques for estimating posterior clusterings. The first approach uses a slice sampling subcomponent for estimating cluster parameters. The second approach marginalizes out several cluster parameters by taking advantage of approximations to the conditional posteriors. We empirically demonstrate (1) the effectiveness of this approximation for improving convergence, (2) the benefits of the Dirichlet process model over alternative clustering techniques for ranked data, and (3) the applicability of the approach to exploring large realworld ranking datasets. 1

Clustering ranked preference data using sociodemographic covariates.

Bayesian principal component analysis (BPCA), a probabilistic reformulation of PCA with Bayesian model selection, is a systematic approach to determining the number of essential principal components (PCs) for data representation. However, it assumes that data are Gaussian distributed and thus it cannot handle all types of practical observations, e.g. integers and binary values. In this paper, we propose simple exponential family PCA (SePCA), a generalised family of probabilistic principal component analysers. SePCA employs exponential family distributions to handle general types of observations. By using Bayesian inference, SePCA also automatically discovers the number of essential PCs. We discuss techniques for fitting the model, develop the corresponding mixture model, and show the effectiveness of the model based on experiments. 1