Application of R\'enyi and Tsallis Entropies to Topic Modeling Optimization

Thus, large arrays of textual data, which have been rapidly accumulating on the Internet in the last decade, require ever more complex methods for their automatic processing and modeling. For this, a wide range of mathematical tools, including topic models, is used [1], but their properties and behavior remain little studied so far, which makes it impossible to choose the optimal parameters of such models. If, however, we consider the results of topic modeling as nonequilibrium complex systems (since these, as will be shown below, have the characteristics of such systems), this would make it possible to apply to them a whole range of approaches from statistical physics. First of all, these are models for analyzing the processes of self-organization of large ensembles. The basis for such an analysis may be an approach in which the behavior of the topic model of a textual collection as a word ensemble would be determined by thermodynamic functions, such as entropy or free energy. It is known that complex systems can be characterized by exponential and power law distributions, which is especially characteristic for social [2, 3], biological [4, 5] and economic systems [6, 7].