On Tsallis Entropy-based and Bezdek-type Fuzzy Latent Semantics Analysis

In this study, we present two types of fuzzy counterparts to the probabilistic latent semantic analysis (pLSA) approach. The first type is derived by solving the optimization problem of Tsallis entropy-penalizing free energy of a pseudo pLSA model using a modified i.i.d. assumption; this derivation is similar to that of the conventional fuzzy counterpart of the pLSA that involves solving the optimization problem of Shannon entropy-penalizing free energy. The second proposed approach is derived from the first approach by letting the fuzzification parameter approach infinity; this derivation is similar to the derivation of a fuzzy clustering algorithm from another fuzzy clustering algorithm by letting the fuzzification parameter approach infinity. Furthermore, some numerical examples for the proposed methods are presented.