  We propose new algorithms for topic modeling when the number of topics is
unknown. Our approach relies on an analysis of the concentration of mass and
angular geometry of the topic simplex, a convex polytope constructed by taking
the convex hull of vertices representing the latent topics. Our algorithms are
shown in practice to have accuracy comparable to a Gibbs sampler in terms of
topic estimation, which requires the number of topics be given. Moreover, they
are one of the fastest among several state of the art parametric techniques.
Statistical consistency of our estimator is established under some conditions.
