Efficient Computation of the Riemannian SVD in Total Least Squares Problems in Information Retrieval

Recently, a nonlinear generalization of the singular value decomposition (SVD), called the Riemannian-SVD (R-SVD), for solving full rank total least squares problems was extended to low rank matrices within the context of latent semantic indexing (LSI) in information retrieval. This new approach, called RSVD-LSI, is based on the full SVD of an m x n term-by-document matrix A and requires the dense m x m left singular matrix U and the n x n right singular matrix V. Here, m corresponds to the size of the dictionary and n corresponds to the number of documents. We dicuss this method along with an efficient implementation of the method that takes into account the sparsity of A.