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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 of words and documents, PLSA models the probability of each co-occurrence as a mixture of conditionally independent multinomial distributions: : being c the words' topic. 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. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Probabilistic latent semantic analysis」の詳細全文を読む スポンサード リンク
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