Reviews: Geometric Dirichlet Means Algorithm for topic inference

I like this paper for two different reasons. After RecoverKL and the spectral algorithm, this paper brings a very novel and useful perspective into the topic inference problem for LDA, without apparently making strong assumptions about topics, such as separability via anchor words, etc. Secondly, it seems to be extremely good in practice meeting the speed of RecoverKL with the accuracy of Gibbs sampling algorithms. A. The algorithm: Aspects of this work were known before. For example, Blei pointed out the convex geometry in the original LDA paper, and the connection between LDA/NMF and K-Means was also known. However, the novel aspect of this paper is that it has used these connections to propose an inference algorithm for LDA completely based on the geometry of the topic and word simplexes. This is done by making an additional connection between the topic inference problem and that of Centroidal Voronoi Tesselations of a convex simplex.