Bilateral Random Projections

TL;DR

This paper introduces a fast low-rank approximation method for dense matrices using bilateral random projections, with theoretical bounds and empirical validation demonstrating its effectiveness and efficiency.

Contribution

It proposes a novel bilateral random projection technique for low-rank approximation, including a power scheme for improved accuracy, with theoretical analysis and empirical results.

Findings

Method achieves rapid low-rank approximation of dense matrices.

Power scheme enhances approximation precision.

Empirical tests confirm effectiveness and efficiency.

Abstract

Low-rank structure have been profoundly studied in data mining and machine learning. In this paper, we show a dense matrix $X$'s low-rank approximation can be rapidly built from its left and right random projections $Y_1=XA_1$ and $Y_2=X^TA_2$, or bilateral random projection (BRP). We then show power scheme can further improve the precision. The deterministic, average and deviation bounds of the proposed method and its power scheme modification are proved theoretically. The effectiveness and the efficiency of BRP based low-rank approximation is empirically verified on both artificial and real datasets.