Single Pass PCA of Matrix Products
Abstract
In this paper we present a new algorithm for computing a low rank approximation of the product $A^TB$ by taking only a single pass of the two matrices $A$ and $B$. The straightforward way to do this is to (a) first sketch $A$ and $B$ individually, and then (b) find the top components using PCA on the sketch. Our algorithm in contrast retains additional summary information about $A,B$ (e.g. row and column norms etc.) and uses this additional information to obtain an improved approximation from the sketches. Our main analytical result establishes a comparable spectral norm guarantee to existing two-pass methods; in addition we also provide results from an Apache Spark implementation that shows better computational and statistical performance on real-world and synthetic evaluation datasets.
Cite
Text
Wu et al. "Single Pass PCA of Matrix Products." Neural Information Processing Systems, 2016.Markdown
[Wu et al. "Single Pass PCA of Matrix Products." Neural Information Processing Systems, 2016.](https://mlanthology.org/neurips/2016/wu2016neurips-single/)BibTeX
@inproceedings{wu2016neurips-single,
title = {{Single Pass PCA of Matrix Products}},
author = {Wu, Shanshan and Bhojanapalli, Srinadh and Sanghavi, Sujay and Dimakis, Alexandros G},
booktitle = {Neural Information Processing Systems},
year = {2016},
pages = {2585-2593},
url = {https://mlanthology.org/neurips/2016/wu2016neurips-single/}
}