Solving total least-squares problems in information retrieval

Abstract

The singular value decomposition (SVD) is a well-known theoretical and numerical tool used in numerous scientific and engineering applications. Recently, an interesting nonlinear generalization of the SVD, referred to as the Riemannian SVD (R-SVD), has been proposed by De Moor for applications in systems and control. This decomposition can be modified and used to formulate an enhanced implementation of latent semantic indexing (LSI) for conceptual information retrieval. LSI is an SVD-based conceptual retrieval technique and employs a rank-reduced model of the original (sparse) term-by-document matrix. Updating LSI models based on user feedback can be accomplished using constraints modeled by the R-SVD of a low-rank approximation to the original term-by-document matrix. In this work, a new algorithm for computing the R-SVD is described. When used to update an LSI model, this R-SVD algorithm can be a highly effective information filtering technique. Experiments demonstrate that a 20% improvement (in retrieval) over the current LSI model is possible.