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Hierarchical topic modeling is a potentially powerful instrument fordetermining the topical structure of text collections that allows constructinga topical hierarchy representing levels of topical abstraction. However, tuningof parameters of hierarchical models, including the number of topics on eachhierarchical level, remains a challenging task and an open issue. In thispaper, we propose a Renyi entropy-based approach for a partial solution to theabove problem. First, we propose a Renyi entropy-based metric of quality forhierarchical models. Second, we propose a practical concept of hierarchicaltopic model tuning tested on datasets with human mark-up. In the numericalexperiments, we consider three different hierarchical models, namely,hierarchical latent Dirichlet allocation (hLDA) model, hierarchical Pachinkoallocation model (hPAM), and hierarchical additive regularization of topicmodels (hARTM). We demonstrate that hLDA model possesses a significant level ofinstability and, moreover, the derived numbers of topics are far away from thetrue numbers for labeled datasets. For hPAM model, the Renyi entropy approachallows us to determine only one level of the data structure. For hARTM model,the proposed approach allows us to estimate the number of topics for twohierarchical levels.

Analysis and tuning of hierarchical topic models based on Renyi entropy approach