Related papers: A Riemannian rank-adaptive method for higher-order…
Low-rank matrix approximation (LRMA) has been arisen in many applications, such as dynamic MRI, recommendation system and so on. The alternating direction method of multipliers (ADMM) has been designed for the nuclear norm regularized least…
Low-rank matrix estimation under heavy-tailed noise is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs, especially since robust loss…
The low rank tensor completion (LRTC) problem has attracted great attention in computer vision and signal processing. How to acquire high quality image recovery effect is still an urgent task to be solved at present. This paper proposes a…
The Symmetric Tensor Approximation problem (STA) consists of approximating a symmetric tensor or a homogeneous polynomial by a linear combination of symmetric rank-1 tensors or powers of linear forms of low symmetric rank. We present two…
Low-rank matrix completion (LRMC) has demonstrated remarkable success in a wide range of applications. To address the NP-hard nature of the rank minimization problem, the nuclear norm is commonly used as a convex and computationally…
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…
In this paper, we consider finding a low-rank approximation to the solution of a large-scale generalized Lyapunov matrix equation in the form of $A X M + M X A = C$, where $A$ and $M$ are symmetric positive definite matrices. An algorithm…
Low-rank approximation is a technique to approximate a tensor or a matrix with a reduced rank to reduce the memory required and computational cost for simulation. Its broad applications include dimension reduction, signal processing,…
We consider the problem of learning low-rank tensors from partial observations with structural constraints, and propose a novel factorization of such tensors, which leads to a simpler optimization problem. The resulting problem is an…
Low rank tensor representation underpins much of recent progress in tensor completion. In real applications, however, this approach is confronted with two challenging problems, namely (1) tensor rank determination; (2) handling real tensor…
Recently, a tensor-on-tensor (ToT) regression model has been proposed to generalize tensor recovery, encompassing scenarios like scalar-on-tensor regression and tensor-on-vector regression. However, the exponential growth in tensor…
Adaptive stochastic gradient algorithms in the Euclidean space have attracted much attention lately. Such explorations on Riemannian manifolds, on the other hand, are relatively new, limited, and challenging. This is because of the…
We consider a Canonical Polyadic (CP) decomposition approach to low-rank tensor completion (LRTC) by incorporating external pairwise similarity relations through graph Laplacian regularization on the CP factor matrices. The usage of graph…
Tensor completion is a challenging problem with various applications. Many related models based on the low-rank prior of the tensor have been proposed. However, the low-rank prior may not be enough to recover the original tensor from the…
Multi-dimensional data completion is a critical problem in computational sciences, particularly in domains such as computer vision, signal processing, and scientific computing. Existing methods typically leverage either global low-rank…
In recent years, there have been an increasing number of applications of tensor completion based on the tensor train (TT) format because of its efficiency and effectiveness in dealing with higher-order tensor data. However, existing tensor…
Within the tensor singular value decomposition (T-SVD) framework, existing robust low-rank tensor completion approaches have made great achievements in various areas of science and engineering. Nevertheless, these methods involve the T-SVD…
In this paper, we propose a method for the approximation of the solution of high-dimensional weakly coercive problems formulated in tensor spaces using low-rank approximation formats. The method can be seen as a perturbation of a minimal…
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,…
Low-rank tensor completion (LRTC) is an important problem in computer vision and machine learning. The minimax-concave penalty (MCP) function as a non-convex relaxation has achieved good results in the LRTC problem. To makes all the…