Parallel Active Subspace Decomposition for Scalable and Efficient Tensor Robust Principal Component Analysis

TL;DR

This paper introduces PASD, a scalable tensor RPCA method that reduces computational costs by dividing tensor unfoldings into smaller parts, leading to faster and more accurate results.

Contribution

The paper presents a novel parallel active subspace decomposition approach that significantly improves efficiency and accuracy in tensor RPCA over existing methods.

Findings

More accurate than state-of-the-art approaches

Orders of magnitude faster computational speed

Effective on synthetic and real-world data

Abstract

Tensor robust principal component analysis (TRPCA) has received a substantial amount of attention in various fields. Most existing methods, normally relying on tensor nuclear norm minimization, need to pay an expensive computational cost due to multiple singular value decompositions (SVDs) at each iteration. To overcome the drawback, we propose a scalable and efficient method, named Parallel Active Subspace Decomposition (PASD), which divides the unfolding along each mode of the tensor into a columnwise orthonormal matrix (active subspace) and another small-size matrix in parallel. Such a transformation leads to a nonconvex optimization problem in which the scale of nulcear norm minimization is generally much smaller than that in the original problem. Furthermore, we introduce an alternating direction method of multipliers (ADMM) method to solve the reformulated problem and provide rigorous analyses for its convergence and suboptimality. Experimental results on synthetic and real-world data show that our algorithm is more accurate than the state-of-the-art approaches, and is orders of magnitude faster.