Faculty of Organization and Informatics University of Zagreb
Abstract
Our capabilities for collecting and storing data of all kinds are greater then ever. On the other side analyzing, summarizing and extracting information from this data is harder than ever. That’s why there is a growing need for the fast and efficient algorithms for information retrieval.In this paper we present some mathematical models based on linear algebra used to extract the relevant documents for some subjects out of a large set of text document. This is a typical problem of a search engine on the World Wide Web. We use vector space model, which is based on literal matching of terms in the documents and the queries. The vector space model is implemented by creating the term-document matrix. Literal matching of terms does not necessarily retrieve all relevant documents. Synonymy (multiple words having the same meaning) and polysemy (words having multiple meaning) are two major obstacles for efficient information retrieval. Latent Semantic Indexing represents documents by approximations and tends to cluster documents on similar topics even if their term profiles are somewhat different. This approximate representation is accomplished using a low-rank singular value decomposition (SVD) approximation of the term-document matrix. In this paper we compare the precision of information retrieval for different ranks of SVD representation of term-document matrix
