Latent semantic indexing (LSI) is a tool used by search engines to create relations between different search terms and to correlate them with documents related to these terms. This information is typically manipulated using a term-document matrix, a sparse matrix with rows as terms and columns as documents. In order to make this matrix an effective search tool, a low rank approximation of the original term-document matrix is taken, resulting in a smaller, faster matrix that also removes many extraneous relationships.

Relevance of results to a given search term is further ensured by using a truncated singular value decomposition (SVD) to solve for the documents related to the term as this approximation removes documents with very small relational values. While the truncation is a helpful side effect of the truncated SVD, accurate results would be produced using the full value of the SVD, but it would take longer and be more likely to include results unrelated to the query.

More information at

LSI Keyword Research and Co-Occurrence Theory

LSI How-to Calculations

Singular Value Decomposition (SVD) and Search Engines (SEO)