Efficient Sparse Low-Rank Tensor Completion Using the Frank-Wolfe Algorithm
نویسندگان
چکیده
Most tensor problems are NP-hard, and low-rank tensor completion is much more difficult than low-rank matrix completion. In this paper, we propose a time and spaceefficient low-rank tensor completion algorithm by using the scaled latent nuclear norm for regularization and the FrankWolfe (FW) algorithm for optimization. We show that all the steps can be performed efficiently. In particular, FW’s linear subproblem has a closed-form solution which can be obtained from rank-one SVD. By utilizing sparsity of the observed tensor, we only need to maintain sparse tensors and a set of small basis matrices. Experimental results show that the proposed algorithm is more accurate, much faster and more scalable than the state-of-the-art.
منابع مشابه
An Extended Frank-Wolfe Method with "In-Face" Directions, and Its Application to Low-Rank Matrix Completion
Motivated principally by the low-rank matrix completion problem, we present an extension of the Frank-Wolfe Method that is designed to induce near-optimal solutions on low-dimensional faces of the feasible region. This is accomplished by a new approach to generating “in-face” directions at each iteration, as well as through new choice rules for selecting between in-face and “regular” Frank-Wolf...
متن کاملReweighted Low-Rank Tensor Completion and its Applications in Video Recovery
This paper focus on recovering multi-dimensional data called tensor from randomly corrupted incomplete observation. Inspired by reweighted l1 norm minimization for sparsity enhancement, this paper proposes a reweighted singular value enhancement scheme to improve tensor low tubular rank in the tensor completion process. An efficient iterative decomposition scheme based on t-SVD is proposed whic...
متن کاملTensor completion and low-n-rank tensor recovery via convex optimization
In this paper we consider sparsity on a tensor level, as given by the n-rank of a tensor. In the important sparse-vector approximation problem (compressed sensing) and the low-rank matrix recovery problem, using a convex relaxation technique proved to be a valuable solution strategy. Here, we will adapt these techniques to the tensor setting. We use the n-rank of a tensor as sparsity measure an...
متن کاملAccelerated and Inexact Soft-Impute for Large-Scale Matrix and Tensor Completion
Matrix and tensor completion aim to recover a low-rank matrix / tensor from limited observations and have been commonly used in applications such as recommender systems and multi-relational data mining. A state-of-the-art matrix completion algorithm is Soft-Impute, which exploits the special “sparse plus low-rank” structure of the matrix iterates to allow efficient SVD in each iteration. Though...
متن کاملScalable Robust Matrix Recovery: Frank-Wolfe Meets Proximal Methods
Recovering matrices from compressive and grossly corrupted observations is a fundamental problem in robust statistics, with rich applications in computer vision and machine learning. In theory, under certain conditions, this problem can be solved in polynomial time via a natural convex relaxation, known as Compressive Principal Component Pursuit (CPCP). However, all existing provable algorithms...
متن کامل