Minimum Volume Topic Modeling
This work addresses topic modeling for text analysis, offering a novel optimization-based method that is incremental in improving efficiency and accuracy.
The authors tackled the problem of topic modeling by proposing a minimum volume approach that reformulates Latent Dirichlet Allocation (LDA) as minimizing the volume of a topic simplex enclosing documents, with a convex relaxation proven to have the same global minimum under certain assumptions. They introduced an ADMM method for solving it, showing benefits in computation time and topic recovery performance in numerical experiments.
We propose a new topic modeling procedure that takes advantage of the fact that the Latent Dirichlet Allocation (LDA) log likelihood function is asymptotically equivalent to the logarithm of the volume of the topic simplex. This allows topic modeling to be reformulated as finding the probability simplex that minimizes its volume and encloses the documents that are represented as distributions over words. A convex relaxation of the minimum volume topic model optimization is proposed, and it is shown that the relaxed problem has the same global minimum as the original problem under the separability assumption and the sufficiently scattered assumption introduced by Arora et al. (2013) and Huang et al. (2016). A locally convergent alternating direction method of multipliers (ADMM) approach is introduced for solving the relaxed minimum volume problem. Numerical experiments illustrate the benefits of our approach in terms of computation time and topic recovery performance.