Pablo García Bringas

This manuscript provides a comprehensive exploration of Probabilistic latent semantic analysis (PLSA), highlighting its strengths, drawbacks, and challenges. The PLSA, originally a tool for information retrieval, provides a probabilistic sense for a table of co-occurrences as a mixture of multinomial distributions spanned over a latent class variable and adjusted with the expectation–maximization algorithm. The distributional assumptions and the iterative nature lead to a rigid model, dividing enthusiasts and detractors. Those drawbacks have led to several reformulations: the extension of the method to normal data distributions and a non-parametric formulation obtained with the help of Non-negative matrix factorization (NMF) techniques. Furthermore, the combination of theoretical studies and programming techniques alleviates the computational problem, thus making the potential of the method explicit: its relation with the Singular value decomposition (SVD), which means that PLSA can be used to satisfactorily support other techniques, such as the construction of Fisher kernels, the probabilistic interpretation of Principal component analysis (PCA), Transfer learning (TL), and the training of neural networks, among others. We also present open questions as a practical and theoretical research window.