Related papers: Hierarchical Prior Regularized Matrix Factorizatio…

A well-known method for completing low-rank matrices based on convex optimization has been established by Cand{\`e}s and Recht. Although theoretically complete, the method may not entirely solve the low-rank matrix completion problem. This…

Regularized nonnegative low-rank approximations, such as sparse Nonnegative Matrix Factorization or sparse Nonnegative Tucker Decomposition, form an important branch of dimensionality reduction models known for their enhanced…

Tensor completion refers to the problem of recovering the missing, corrupted or unobserved entries in data represented by tensors. In this paper, we tackle the tensor completion problem in the scenario in which multiple tensor acquisitions…

Higher-order tensors are becoming prevalent in many scientific areas such as computer vision, social network analysis, data mining and neuroscience. Traditional tensor decomposition approaches face three major challenges: model selecting,…

The paper addresses the problem of low-rank trace norm minimization. We propose an algorithm that alternates between fixed-rank optimization and rank-one updates. The fixed-rank optimization is characterized by an efficient factorization…

Recent advances in IoT and biometric sensing technologies have led to the generation of massive and high-dimensional tensor data, yet achieving accurate and efficient low-rank approximation remains a major challenge. Most existing tensor…

Low-rank tensor estimation offers a powerful approach to addressing high-dimensional data challenges and can substantially improve solutions to ill-posed inverse problems, such as image reconstruction under noisy or undersampled conditions.…

Low-rank matrix completion has been studied extensively under various type of categories. The problem could be categorized as noisy completion or exact completion, also active or passive completion algorithms. In this paper we focus on…

Convolutional neural networks excel in image recognition tasks, but this comes at the cost of high computational and memory complexity. To tackle this problem, [1] developed a tensor factorization framework to compress fully-connected…

This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…

We propose an isogeometric solver for Poisson problems that combines i)low-rank tensor techniques to approximate the unknown solution and the system matrix, as a sum of a few terms having Kronecker product structure, ii) a Truncated…

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…

CANDECOMP/PARAFAC (CP) tensor factorization of incomplete data is a powerful technique for tensor completion through explicitly capturing the multilinear latent factors. The existing CP algorithms require the tensor rank to be manually…

We consider tensor factorizations based on sparse measurements of the components of relatively high rank tensors. The measurements are designed in a way that the underlying graph of interactions is a random graph. The setup will be useful…

Existing methods of vector autoregressive model for multivariate time series analysis make use of low-rank matrix approximation or Tucker decomposition to reduce the dimension of the over-parameterization issue. In this paper, we propose a…

Modern technological advances have enabled an unprecedented amount of structured data with complex temporal dependence, urging the need for new methods to efficiently model and forecast high-dimensional tensor-valued time series. This paper…

Low-rank matrix completion has achieved great success in many real-world data applications. A matrix factorization model that learns latent features is usually employed and, to improve prediction performance, the similarities between latent…

We propose new Riemannian preconditioned algorithms for low-rank tensor completion via the polyadic decomposition of a tensor. These algorithms exploit a non-Euclidean metric on the product space of the factor matrices of the low-rank…

Matrix completion aims to recover an unknown low-rank matrix from a small subset of its entries. In many applications, the rank of the unknown target matrix is known in advance. In this paper, first we revisit a recently proposed rank-based…

Nonconvex regularization has been popularly used in low-rank matrix learning. However, extending it for low-rank tensor learning is still computationally expensive. To address this problem, we develop an efficient solver for use with a…