A probabilistic model for Latent Semantic Indexing

Dimension reduction methods, such as Latent Semantic Indexing (LSI), when applied to semantic space built upon text collections, improve information retrieval, information filtering and word sense disambiguation. A new dual probability model based on the similarity concepts is introduced to provide deeper understanding of LSI. Semantic associations can be quantitatively characterized by their statistical significance, the likelihood. Semantic dimensions containing redundant and noisy information can be separated out and should be ignored because their contribution to the overall statistical significance is negative. LSI is the optimal solution of the model. The peak in likelihood curve indicates the existence of an intrinsic semantic dimension. The importance of LSI dimensions follows the Zipf-distribution, indicating that LSI dimensions represent the latent concepts. Document frequency of words follow the Zipf distribution, and the number of distinct words follows log-normal distribution. Experiments on five standard document collections confirm and illustrate the analysis.