In the LSI model, queries are formed into pseudo-documents that specify
the location of the query in the reduced term-document space. Given
q, a vector whose non-zero elements contain the weighted (using
the same local and global weighting schemes applied to the document
collection being searched; see Section 2.2.2) term-frequency
counts of the terms that appear in the query, the pseudo-document,
, can be represented by
Thus, the pseudo-document consists of the sum of the term vectors
(
) corresponding to the terms specified in the query scaled
by the inverse of the singular values (
). The
singular values are used
to individually weight each dimension of the term-document space [5].
Once the query is projected into the term-document space, one of several similarity measures can be applied to compare the position of the pseudo-document to the positions of the terms or documents in the reduced term-document space. One popular similarity measure, the cosine similarity measure, is often used because, by only finding the angle between the pseudo-document and the terms or documents in the reduced space, the lengths of the documents, which can affect the distance between the pseudo-document and the documents in the space, are normalized. Once the similarities between the pseudo-document and all the terms and documents in the space have been computed, the terms or documents are ranked according to the results of the similarity measure, and the highest-ranking terms or documents, or all the terms and documents exceeding some threshold value, are returned to the user [5].