  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 automatically inferred.
We derive a simple inference scheme for this model which analytically
integrates out both the mixture parameters and the warping function. We show
that our model is effective for density estimation, performs better than
infinite Gaussian mixture models at recovering the true number of clusters, and
produces interpretable summaries of high-dimensional datasets.
