Probabilistic latent semantic analysis
Probabilistic latent semantic analysis (PLSA), also known as probabilistic latent semantic indexing (PLSI, especially in information retrieval circles) is a statistical technique for the analysis of two-mode and co-occurrence data. In effect, one can derive a low-dimensional representation of the observed variables in terms of their affinity to certain hidden variables, just as in latent semantic analysis, from which PLSA evolved. Compared to standard latent semantic analysis which stems from linear algebra and downsizes the occurrence tables (usually via a singular value decomposition), probabilistic latent semantic analysis is based on a mixture decomposition  derived from a latent class model. Model. Considering observations in the form of co-occurrences formula_1 of words and documents, PLSA models the probability of each co-occurrence as a mixture of conditionally independent multinomial distributions: with 'c' being the words' topic. Note that the number of topics is a hyperparameter that must be chosen in advance and is not estimated from the data. The first formulation is the "symmetric" formulation, where formula_3 and formula_4 are both generated from the latent class formula_5 in similar ways (using the conditional probabilities formula_6 and formula_7), whereas the second formulation is the "asymmetric