Reviews: Scalable inference of topic evolution via models for latent geometric structures

This is a very well written paper, both in style and substance. There are a few stylistic peculiarities that could surely be ruled out by thorough proof-reading. The authors present a nice introduction into the idea of modelling sets of topics, i.e. sets of points on a simplex, as the geometric structure of a polytope. They go on to describe, how evolution of such a polytope can be modelled over time by embedding a unit hypersphere into the simplex and modelling polytope evolution as random trajectories over this sphere. They further present a non-parametric hierarchical model for capturing polytopes with a varying number of topics and also multiple polytopes arising from different corpora.