Model
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:
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.
Read more about this topic: Probabilistic Latent Semantic Analysis
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