The Riemannian SVD (or R-SVD) is a recent nonlinear generalization of the SVD which has been used for specific applications in systems and control. This decomposition can be modified and used to formulate a filtering-based implementation of Latent Semantic Indexing (LSI) for conceptual information retrieval. With LSI, the underlying semantic structure of a collection is represented in k-dimensional space using a rank-k approximation to the corresponding (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.
Jiang, E. P., & Berry, M. W. (1998). Information filtering using the Riemannian SVD (R-SVD). In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1457 LNCS, pp. 386–395). Springer Verlag. https://doi.org/10.1007/bfb0018555