pLSI Model Training Algorithm

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A pLSI Model Training Algorithm is a latent semantic analysis algorithm that can be applied by a pLSI Model Training System (to solve a pLSI Model Training Task that generates a probabilistic latent semantic indexing model).



References

2011

  • (Wkipedia, 2011) ⇒ http://en.wikipedia.org/wiki/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. PLSA evolved from Latent semantic analysis, adding a sounder probabilistic model. PLSA has applications in information retrieval and filtering, natural language processing, machine learning from text, and related areas. It was introduced in 1999 by Jan Puzicha and Thomas Hofmann, and it is related to non-negative matrix factorization. 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. This results in a more principled approach which has a solid foundation in statistics. Considering observations in the form of co-occurrences [math]\displaystyle{ (w,d) }[/math] of words and documents, PLSA models the probability of each co-occurrence as a mixture of conditionally independent multinomial distributions: [math]\displaystyle{ P(w,d) = \sum_c P(c) P(d|c) P(w|c) = P(d) \sum_c P(c|d) P(w|c) }[/math] The first formulation is the symmetric formulation, where [math]\displaystyle{ w }[/math] and [math]\displaystyle{ d }[/math] are both generated from the latent class [math]\displaystyle{ c }[/math] in similar ways (using the conditional probabilities [math]\displaystyle{ P(d|c) }[/math] and [math]\displaystyle{ P(w|c) }[/math]), whereas the second formulation is the asymmetric formulation, where, for each document [math]\displaystyle{ d }[/math], a latent class is chosen conditionally to the document according to [math]\displaystyle{ P(c|d) }[/math], and a word is then generated from that class according to [math]\displaystyle{ P(w|c) }[/math].

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1999