Robust Low-rank Tensor Recovery: Models and Algorithms
This work addresses robust tensor decomposition for applications like data analysis, but it is incremental, building on existing robust PCA and tensor completion methods.
The paper tackles robust low-rank tensor recovery to handle outliers and missing data in multilinear analysis, proposing convex and nonconvex models with tailored algorithms that show global convergence and practical effectiveness in real applications.
Robust tensor recovery plays an instrumental role in robustifying tensor decompositions for multilinear data analysis against outliers, gross corruptions and missing values and has a diverse array of applications. In this paper, we study the problem of robust low-rank tensor recovery in a convex optimization framework, drawing upon recent advances in robust Principal Component Analysis and tensor completion. We propose tailored optimization algorithms with global convergence guarantees for solving both the constrained and the Lagrangian formulations of the problem. These algorithms are based on the highly efficient alternating direction augmented Lagrangian and accelerated proximal gradient methods. We also propose a nonconvex model that can often improve the recovery results from the convex models. We investigate the empirical recoverability properties of the convex and nonconvex formulations and compare the computational performance of the algorithms on simulated data. We demonstrate through a number of real applications the practical effectiveness of this convex optimization framework for robust low-rank tensor recovery.