Abstract:

This paper develops an identity for additive modivations of a singular value decomposition (SVD) to reflect updates, downdates, shifts, and edits of the data matrix. This sets the stage for fast and ememory-efficient sequential algorithms for tracking singular values and subspaces. In conjunction with a fast solution for the pseudo-inverse of a submatrix of an orthogonal matrix, we develop a scheme for computing a thin SVD of streaming data in a single pass with linear time complexity: A rank-r think SVD of a p x q matrix can be computed in O(pqr) time for r less-than-or-equal sqroot(min(p,q)).