Approximate Rank-Detecting Factorization of Low-Rank Tensors

TL;DR

This paper introduces AROFAC2, an algorithm that accurately detects the rank and computes the factorization of degree 3 tensors, outperforming traditional methods like PARAFAC in robustness and reliability.

Contribution

The paper presents AROFAC2, a novel tensor factorization algorithm that detects true tensor rank and improves stability over existing methods.

Findings

AROFAC2 accurately detects tensor rank in synthetic and real data.

It outperforms PARAFAC in robustness to noise and outliers.

The algorithm is stable under non-Gaussian noise conditions.

Abstract

We present an algorithm, AROFAC2, which detects the (CP-)rank of a degree 3 tensor and calculates its factorization into rank-one components. We provide generative conditions for the algorithm to work and demonstrate on both synthetic and real world data that AROFAC2 is a potentially outperforming alternative to the gold standard PARAFAC over which it has the advantages that it can intrinsically detect the true rank, avoids spurious components, and is stable with respect to outliers and non-Gaussian noise.