A sequential multilinear Nyström algorithm for streaming low-rank approximation of tensors in Tucker format

TL;DR

The paper introduces a sequential multilinear Nyström algorithm for streaming, low-rank Tucker approximation of tensors. The tensor $\mathcal{A}$ is accessed only via random sketches, enabling exploitation of low-rank structure and linear combinations. A deterministic analysis is provided, and numerical experiments demonstrate faster performance and efficiency, including an application to video processing. The method offers a scalable, memory-efficient framework for online tensor completion and approximation in Tucker format.

Abstract

We present a sequential version of the multilinear Nyström 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.