  We propose a geometric algorithm for topic learning and inference that is
built on the convex geometry of topics arising from the Latent Dirichlet
Allocation (LDA) model and its nonparametric extensions. To this end we study
the optimization of a geometric loss function, which is a surrogate to the
LDA's likelihood. Our method involves a fast optimization based weighted
clustering procedure augmented with geometric corrections, which overcomes the
computational and statistical inefficiencies encountered by other techniques
based on Gibbs sampling and variational inference, while achieving the accuracy
comparable to that of a Gibbs sampler. The topic estimates produced by our
method are shown to be statistically consistent under some conditions. The
algorithm is evaluated with extensive experiments on simulated and real data.
