Warped Mixtures for Nonparametric Cluster Shapes

A mixture of Gaussians fit to a single curved or heavy-tailed cluster will report that the data contains many clusters. To produce more appropriate clusterings, we introduce a model which warps a latent mixture of Gaussians to produce nonparametric cluster shapes. The possibly low-dimensional latent mixture model allows us to summarize the properties of the high-dimensional clusters (or density manifolds) describing the data. The number of manifolds, as well as the shape and dimension of each manifold is automat-ically inferred. We derive a simple inference scheme for this model which analytically inte-grates out both the mixture parameters and the warping function. We show that our model is effective for density estimation, per-forms better than infinite Gaussian mixture models at recovering the true number of clus-ters, and produces interpretable summaries of high-dimensional datasets.