SVD update methods for large matrices and applications

We consider the problem of updating the SVD when augmenting a tall thin matrix, i.e., a rectangular matrix A is an element of R-m x n with m >> n. Supposing that an SVD of A is already known, and given a matrix B is an element of R-m x n', we derive an efficient method to compute and efficiently store the SVD of the augmented matrix [AB] is an element of Rm x (n+n').This is an important tool for two types of applications: in the context of principal component analysis, the dominant left singular vectors provided by this decomposition form an orthonormal basis for the best linear subspace of a given dimension, while from the right singular vectors one can extract an orthonormal basis of the kernel of the matrix. We also describe two concrete applications of these concepts which motivated the development of our method and to which it is very well adapted. (C) 2018 Elsevier Inc. All rights reserved.