Block classical Gram–Schmidt-based block updating in low-rank matrix approximation

Abstract

Low-rank matrix approximations have recently gained broad popularity in scientific computing areas. Theyare used to extract correlations and remove noise from matrix-structured data with limited loss of information. Truncatedsingular value decomposition (SVD) is the main tool for computing low-rank approximation. However, in applicationssuch as latent semantic indexing where document collections are dynamic over time, i.e. the term document matrixis subject to repeated updates, SVD becomes prohibitive due to the high computational expense. Alternative decompositions have been proposed for these applications such as low-rank ULV/URV decompositions and truncated ULVdecomposition. Herein, we propose a BLAS-3 compatible block updating truncated ULV decomposition algorithm basedon the block classical Gram–Schmidt process. The simulation results presented show that the block update algorithm ispromising