  We introduce a Bayesian model for inferring mixtures of subspaces of
different dimensions. The key challenge in such a mixture model is
specification of prior distributions over subspaces of different dimensions. We
address this challenge by embedding subspaces or Grassmann manifolds into a
sphere of relatively low dimension and specifying priors on the sphere. We
provide an efficient sampling algorithm for the posterior distribution of the
model parameters. We illustrate that a simple extension of our mixture of
subspaces model can be applied to topic modeling. We also prove posterior
consistency for the mixture of subspaces model. The utility of our approach is
demonstrated with applications to real and simulated data.
