Fixed-Rank Approximation of a Positive-Semidefinite Matrix from Streaming Data
Abstract
Several important applications, such as streaming PCA and semidefinite programming, involve a large-scale positive-semidefinite (psd) matrix that is presented as a sequence of linear updates. Because of storage limitations, it may only be possible to retain a sketch of the psd matrix. This paper develops a new algorithm for fixed-rank psd approximation from a sketch. The approach combines the Nystrom approximation with a novel mechanism for rank truncation. Theoretical analysis establishes that the proposed method can achieve any prescribed relative error in the Schatten 1-norm and that it exploits the spectral decay of the input matrix. Computer experiments show that the proposed method dominates alternative techniques for fixed-rank psd matrix approximation across a wide range of examples.
Cite
@article{arxiv.1706.05736,
title = {Fixed-Rank Approximation of a Positive-Semidefinite Matrix from Streaming Data},
author = {Joel A. Tropp and Alp Yurtsever and Madeleine Udell and Volkan Cevher},
journal= {arXiv preprint arXiv:1706.05736},
year = {2017}
}