Related papers: Nonconvex Robust High-Order Tensor Completion Usin…
In this paper we focus on the problem of completion of multidimensional arrays (also referred to as tensors) from limited sampling. Our approach is based on a recently proposed tensor-Singular Value Decomposition (t-SVD) [1]. Using this…
In tensor completion tasks, the traditional low-rank tensor decomposition models suffer from the laborious model selection problem due to their high model sensitivity. In particular, for tensor ring (TR) decomposition, the number of model…
Tensor completion and robust principal component analysis have been widely used in machine learning while the key problem relies on the minimization of a tensor rank that is very challenging. A common way to tackle this difficulty is to…
Tensor completion can estimate missing values of a high-order data from its partially observed entries. Recent works show that low rank tensor ring approximation is one of the most powerful tools to solve tensor completion problem. However,…
In this paper, we focus on the fixed TT-rank and precision problems of finding an approximation of the tensor train (TT) decomposition of a tensor. Note that the TT-SVD and TT-cross are two well-known algorithms for these two problems.…
In low-rank tensor completion tasks, due to the underlying multiple large-scale singular value decomposition (SVD) operations and rank selection problem of the traditional methods, they suffer from high computational cost and high…
In this paper we propose efficient randomized fixed-precision techniques for low tubal rank approximation of tensors. The proposed methods are faster and more efficient than the existing fixed-precision algorithms for approximating the…
Unlike the matrix case, computing low-rank approximations of tensors is NP-hard and numerically ill-posed in general. Even the best rank-1 approximation of a tensor is NP-hard. In this paper, we use convex optimization to develop…
Matrix completion, the problem of completing missing entries in a data matrix with low dimensional structure (such as rank), has seen many fruitful approaches and analyses. Tensor completion is the tensor analog, that attempts to impute…
Randomized numerical linear algebra is proved to bridge theoretical advancements to offer scalable solutions for approximating tensor decomposition. This paper introduces fast randomized algorithms for solving the fixed Tucker-rank problem…
This study aims to solve the over-reliance on the rank estimation strategy in the standard tensor factorization-based tensor recovery and the problem of a large computational cost in the standard t-SVD-based tensor recovery. To this end, we…
This paper conducts a rigorous analysis for provable estimation of multidimensional arrays, in particular third-order tensors, from a random subset of its corrupted entries. Our study rests heavily on a recently proposed tensor algebraic…
Currently, existing tensor recovery methods fail to recognize the impact of tensor scale variations on their structural characteristics. Furthermore, existing studies face prohibitive computational costs when dealing with large-scale…
Low-rank tensor completion recovers missing entries based on different tensor decompositions. Due to its outstanding performance in exploiting some higher-order data structure, low rank tensor ring has been applied in tensor completion. To…
The recently proposed tensor robust principal component analysis (TRPCA) methods based on tensor singular value decomposition (t-SVD) have achieved numerous successes in many fields. However, most of these methods are only applicable to…
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…
Low rank tensor learning, such as tensor completion and multilinear multitask learning, has received much attention in recent years. In this paper, we propose higher order matching pursuit for low rank tensor learning problems with a convex…
This paper considers the completion problem for a tensor (also referred to as a multidimensional array) from limited sampling. Our greedy method is based on extending the low-rank approximation pursuit (LRAP) method for matrix completions…
Higher-order low-rank tensor arises in many data processing applications and has attracted great interests. Inspired by low-rank approximation theory, researchers have proposed a series of effective tensor completion methods. However, most…
In recent studies, the tensor ring (TR) rank has shown high effectiveness in tensor completion due to its ability of capturing the intrinsic structure within high-order tensors. A recently proposed TR rank minimization method is based on…