Fractal approach for determining the optimal number of topics in the field of topic modeling.

Abstract

In this paper we apply multifractal formalism to the analysis of statistical behaviour of topic models under condition of varying number of topics. Our analysis reveals the existence of two self-similar regions and one transition region in the function of density-of-states depending on the number of topics. As earlier a function that can be expressed through density-of-states was successfully used to determine the optimal number of topics, we test the applicability of the density-of-states function for the same purpose. We provide numerical results for three topic models (PLSA, ARTM, and LDA Gibbs sampling) on two marked-up collections containing texts in two different languages. Our experiments show that the “true” number of topics, as determined by the human mark-up, occurs in the transition region.