Convex optimization for exact rank recovery in topic models

Topic models are widely used in a variety of applications including document classification and computer vision. The number of topics in the model plays an important role in terms of accuracy. We consider the problem of estimating the number of topics. In [1], a convex optimization approach was proposed to solve the problem via a constrained nuclear norm minimization. A standard semidefinite programming (SDP) was applied to solve the convex optimization only for a small size problem (e.g. 100× 100 matrix) due to its high computational complexity. To extend the applicability of the approach to large scale problems, we propose an accelerated gradient algorithm (AGA). Numerical results show that proposed algorithm can reliably solve a wide range of large scale problems in a shorter time than SDP solvers. Moreover, algorithms applied to a fairly large size real world dataset and results are provided.