A sequential multilinear Nystr\"om algorithm for streaming low-rank approximation of tensors in Tucker format

TL;DR

This paper introduces a sequential multilinear Nyström algorithm designed for efficient low-rank Tucker tensor approximation in streaming data scenarios, leveraging random sketches and demonstrating superior speed in practical applications.

Contribution

It proposes a novel sequential algorithm for streaming low-rank tensor approximation in Tucker format using random sketches, with a deterministic analysis and practical efficiency.

Findings

Algorithm effectively leverages low-rank structures and linear combinations.

Demonstrates superior speed and efficiency in numerical experiments.

Applicable to real-world streaming data like video processing.

Abstract

We present a sequential version of the multilinear Nystr\"om algorithm which is suitable for the low-rank Tucker approximation of tensors given in a streaming format. Accessing the tensor $\mathcal{A}$ exclusively through random sketches of the original data, the algorithm effectively leverages structures in $\mathcal{A}$, such as low-rankness, and linear combinations. We present a deterministic analysis of the algorithm and demonstrate its superior speed and efficiency in numerical experiments including an application in video processing.