Projection techniques to update the truncated SVD of evolving matrices with applications

Updating the rank-k truncated Singular Value Decomposition (SVD) of a matrix subject to the periodic addition of new rows (and/or columns) is a major computational kernel in important real-world applications such as latent semantic indexing and recommender systems. In this work we propose a new algorithm to update the truncated SVD of evolving matrices, i.e., matrices which are periodically augmented with a new set of rows (and/or columns). The proposed algorithm undertakes a projection viewpoint and builds a pair of subspaces which approximate the linear span of the sought singular vectors of the evolving matrix. We discuss and analyze two different choices to form the projection subspace, with the second approach being slower but leading to higher accuracy. Experiments on matrices from different applications suggest that the proposed algorithm can lead to higher qualitative accuracy than previous state-of-the-art approaches, as well as more accurate approximations of the truncated SVD. Moreover, the new algorithm is generally faster than other competitive approaches.