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.
Plate notation representing the PLSA model ("asymmetric" formulation). is the document index variable, is a word's topic drawn from the document's topic distribution, , and is a word drawn from the word distribution of this word's topic, . The and are observable variables, the topic is a latent variable.
Considering observations in the form of co-occurrences of words and documents, PLSA models the probability of each co-occurrence as a mixture of conditionally independent multinomial distributions:
with 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 and are both generated from the latent class in similar ways (using the conditional probabilities and ), whereas the second formulation is the asymmetric formulation, where, for each document , a latent class is chosen conditionally to the document according to , and a word is then generated from that class according to . Although we have used words and documents in this example, the co-occurrence of any couple of discrete variables may be modelled in exactly the same way.
So, the number of parameters is equal to . The number of parameters grows linearly with the number of documents. In addition, although PLSA is a generative model of the documents in the collection it is estimated on, it is not a generative model of new documents.
Their parameters are learned using the EM algorithm.
Application
PLSA may be used in a discriminative setting, via Fisher kernels.[1]
Generative models: The following models have been developed to address an often-criticized shortcoming of PLSA, namely that it is not a proper generative model for new documents.
Higher-order data: Although this is rarely discussed in the scientific literature, PLSA extends naturally to higher order data (three modes and higher), i.e. it can model co-occurrences over three or more variables. In the symmetric formulation above, this is done simply by adding conditional probability distributions for these additional variables. This is the probabilistic analogue to non-negative tensor factorisation.
↑ Pinoli, Pietro; et, al. (2013). "Enhanced probabilistic latent semantic analysis with weighting schemes to predict genomic annotations". Proceedings of IEEE BIBE 2013. The 13th IEEE International Conference on BioInformatics and BioEngineering. IEEE. pp.1–4. doi:10.1109/BIBE.2013.6701702. ISBN978-147993163-7.
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