An Efficient Randomized Fixed-Precision Algorithm for Tensor Singular Value Decomposition

TL;DR

This paper introduces a new randomized fixed-precision algorithm for tensor singular value decomposition that automatically determines the optimal tubal rank and achieves high accuracy efficiently.

Contribution

It presents a novel fixed-precision tensor SVD algorithm that does not require prior rank estimation and improves accuracy with power iteration.

Findings

Efficiently computes low tubal rank approximations

Automatically finds optimal tubal rank for a given error bound

Demonstrates superior performance on synthetic and real datasets

Abstract

The existing randomized algorithms need an initial estimation of the tubal rank to compute a tensor singular value decomposition. This paper proposes a new randomized fixedprecision algorithm which for a given third-order tensor and a prescribed approximation error bound, automatically finds an optimal tubal rank and the corresponding low tubal rank approximation. The algorithm is based on the random projection technique and equipped with the power iteration method for achieving a better accuracy. We conduct simulations on synthetic and real-world datasets to show the efficiency and performance of the proposed algorithm.