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 Nyström 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
Text
Tropp et al. "Fixed-Rank Approximation of a Positive-Semidefinite Matrix from Streaming Data." Neural Information Processing Systems, 2017.Markdown
[Tropp et al. "Fixed-Rank Approximation of a Positive-Semidefinite Matrix from Streaming Data." Neural Information Processing Systems, 2017.](https://mlanthology.org/neurips/2017/tropp2017neurips-fixedrank/)BibTeX
@inproceedings{tropp2017neurips-fixedrank,
title = {{Fixed-Rank Approximation of a Positive-Semidefinite Matrix from Streaming Data}},
author = {Tropp, Joel A and Yurtsever, Alp and Udell, Madeleine and Cevher, Volkan},
booktitle = {Neural Information Processing Systems},
year = {2017},
pages = {1225-1234},
url = {https://mlanthology.org/neurips/2017/tropp2017neurips-fixedrank/}
}