Tensor-Based Sketching Method for the Low-Rank Approximation of Data Streams

TL;DR

This paper introduces a tensor-based sketching method for low-rank approximation of data streams that leverages data structure for improved accuracy and speed, outperforming existing algorithms.

Contribution

The paper proposes a novel tensor-based sketching approach that exploits data stream structure and uses tensor decomposition for quasi-optimal sketching matrices.

Findings

More accurate than previous methods

Significantly faster in experiments

Achieves quasi-optimal approximation

Abstract

Low-rank approximation in data streams is a fundamental and significant task in computing science, machine learning and statistics. Multiple streaming algorithms have emerged over years and most of them are inspired by randomized algorithms, more specifically, sketching methods. However, many algorithms are not able to leverage information of data streams and consequently suffer from low accuracy. Existing data-driven methods improve accuracy but the training cost is expensive in practice. In this paper, from a subspace perspective, we propose a tensor-based sketching method for low-rank approximation of data streams. The proposed algorithm fully exploits the structure of data streams and obtains quasi-optimal sketching matrices by performing tensor decomposition on training data. A series of experiments are carried out and show that the proposed tensor-based method can be more accurate and much faster than the previous work.