Conic Scan Coverage algorithm for nonparametric topic modeling

In this paper we propose new algorithms for topic modeling when number of topics is not known. 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 the topics. The resulting algorithm is shown in practice to have accuracy comparable to that of a Gibbs sampler in terms of topic estimation, which requires the number of topics be given. Moreover, our algorithm is the fastest among a variety of state of the art parametric techniques. The consistency of the estimates produced by our method is established under some conditions.