Co-Occuring Directions Sketching for Approximate Matrix Multiply

TL;DR

This paper presents a deterministic co-occurring directions sketching algorithm for approximate matrix multiplication that achieves better error bounds and low-rank approximation accuracy than existing methods, validated through empirical experiments.

Contribution

Introduction of a novel deterministic co-occurring directions algorithm for AMM with improved error bounds and empirical performance.

Findings

Achieves a $1 + \\epsilon$ approximation of the optimal low-rank matrix product.

Outperforms existing randomized and deterministic methods in experiments.

Validated theoretical error bounds with empirical results.

Abstract

We introduce co-occurring directions sketching, a deterministic algorithm for approximate matrix product (AMM), in the streaming model. We show that co-occuring directions achieves a better error bound for AMM than other randomized and deterministic approaches for AMM. Co-occurring directions gives a $1 + \epsilon$ -approximation of the optimal low rank approximation of a matrix product. Empirically our algorithm outperforms competing methods for AMM, for a small sketch size. We validate empirically our theoretical findings and algorithms