Applications of linear algebra in information retrieval and hypertext analysis

Information retrieval is concerned with representing content in a form that can be easily accessed by users with information needs [61, 651. A definition at this level of generality applies equally well to any index-based retrieval system or database application; so let us focus the topic a little more carefully. Information retrieval, as a field, works primarily with highly unstructured content, such as text documents written in natural language; it deals with information needs that are generally not formulated according to precise specifications; and its criteria for success are based in large part on the demands of a diverse set of human users. Our purpose in this short article is not to provide a survey of the field of information retrieval for this we refer the reader to texts and surveys such as [25, 29, 51, 60, 61, 62, 63, 65, 701. Rather, we wish to discuss some specific applications of techniques from linear algebra to information retrieval and hypertext analysis. In particular, we focus on spectral methods the use of eigenvectors and singular vectors of matrices and their role in these areas. After briefly introducing the use of vector-space models in information retrieval [52, 651, we describe the application of the singular value decomposition to dimensionreduction, through the Latent Semantic Indexing technique [14]. We contrast this with several other approaches to clustering and dimension-reduction based on vector-space models.