相关论文: FasTer: Fast Tensor Completion with Nonconvex Regu…

We consider a novel algorithm, for the completion of partially observed low-rank tensors, as a generalization of matrix completion. The proposed low-rank tensor completion (TC) method builds on the conventional nuclear norm (NN)…

Nonlinear convex problems arise in various areas of applied mathematics and engineering. Classical techniques such as the relaxed proximal point algorithm (PPA) and the prediction correction (PC) method were proposed for linearly…

Matrix factorization is a popular approach for large-scale matrix completion. The optimization formulation based on matrix factorization can be solved very efficiently by standard algorithms in practice. However, due to the non-convexity…

A regularization algorithm using inexact function values and inexact derivatives is proposed and its evaluation complexity analyzed. This algorithm is applicable to unconstrained problems and to problems with inexpensive constraints (that…

This paper proposes a novel formulation of the tensor completion problem to impute missing entries of data represented by tensors. The formulation is introduced in terms of tensor train (TT) rank which can effectively capture global…

In this paper we present a general convex optimization approach for solving high-dimensional multiple response tensor regression problems under low-dimensional structural assumptions. We consider using convex and weakly decomposable…

The low-rank tensor completion (LRTC) problem aims to reconstruct a tensor from partial sample information, which has attracted significant interest in a wide range of practical applications such as image processing and computer vision.…

Currently, low-rank tensor completion has gained cumulative attention in recovering incomplete visual data whose partial elements are missing. By taking a color image or video as a three-dimensional (3D) tensor, previous studies have…

Recovering a large matrix from limited measurements is a challenging task arising in many real applications, such as image inpainting, compressive sensing and medical imaging, and this kind of problems are mostly formulated as low-rank…

The goal of tensor completion is to recover a tensor from a subset of its entries, often by exploiting its low-rank property. Among several useful definitions of tensor rank, the low-tubal-rank was shown to give a valuable characterization…

In this paper we accomplish the development of the fast rank-adaptive solver for tensor-structured symmetric positive definite linear systems in higher dimensions. In [arXiv:1301.6068] this problem is approached by alternating minimization…

Higher-order tensors arise frequently in applications such as neuroimaging, recommendation system, social network analysis, and psychological studies. We consider the problem of low-rank tensor estimation from possibly incomplete,…

The recent low-rank prior based models solve the tensor completion problem efficiently. However, these models fail to exploit the local patterns of tensors, which compromises the performance of tensor completion. In this paper, we propose a…

Low rank regularization, in essence, involves introducing a low rank or approximately low rank assumption for matrix we aim to learn, which has achieved great success in many fields including machine learning, data mining and computer…

Modern decision-making scenarios often involve data that is both high-dimensional and rich in higher-order contextual information, where existing bandits algorithms fail to generate effective policies. In response, we propose in this paper…

Originally developed for imputing missing entries in low rank, or approximately low rank matrices, matrix completion has proven widely effective in many problems where there is no reason to assume low-dimensional linear structure in the…

The use of convex regularizers allows for easy optimization, though they often produce biased estimation and inferior prediction performance. Recently, nonconvex regularizers have attracted a lot of attention and outperformed convex ones.…

The subdifferential of convex functions of the singular spectrum of real matrices has been widely studied in matrix analysis, optimization and automatic control theory. Convex analysis and optimization over spaces of tensors is now gaining…

Low-rank matrix models have been universally useful for numerous applications, from classical system identification to more modern matrix completion in signal processing and statistics. The nuclear norm has been employed as a convex…

In this paper, we propose a new algorithm for recovery of low-rank matrices from compressed linear measurements. The underlying idea of this algorithm is to closely approximate the rank function with a smooth function of singular values,…