Related papers: Low Rank Tensor Completion via Adaptive ADMM

In this paper, we propose three approaches for the estimation of the Tucker decomposition of multi-way arrays (tensors) from partial observations. All approaches are formulated as convex minimization problems. Therefore, the minimum is…

This paper investigates the low-rank tensor completion problem, which is about recovering a tensor from partially observed entries. We consider this problem in the tensor train format and extend the preconditioned metric from the matrix…

Tensor factorization has proven useful in a wide range of applications, from sensor array processing to communications, speech and audio signal processing, and machine learning. With few recent exceptions, all tensor factorization…

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 ring (TR) decomposition has been successfully used to obtain the state-of-the-art performance in the visual data completion problem. However, the existing TR-based completion methods are severely non-convex and computationally…

We consider the problem of low-rank decomposition of incomplete multiway tensors. Since many real-world data lie on an intrinsically low dimensional subspace, tensor low-rank decomposition with missing entries has applications in many data…

The problem of low-tubal-rank tensor estimation is a fundamental task with wide applications across high-dimensional signal processing, machine learning, and image science. Traditional approaches tackle such a problem by performing tensor…

We present an efficient low-rank approximation algorithm for non-negative tensors. The algorithm is derived from our two findings: First, we show that rank-1 approximation for tensors can be viewed as a mean-field approximation by treating…

One of the popular approaches for low-rank tensor completion is to use the latent trace norm regularization. However, most existing works in this direction learn a sparse combination of tensors. In this work, we fill this gap by proposing a…

Low-rank tensor completion aims to recover a tensor from partially observed entries, and it is widely applicable in fields such as quantum computing and image processing. Due to the significant advantages of the tensor train (TT) format in…

We consider convex relaxations for recovering low-rank tensors based on constrained minimization over a ball induced by the tensor nuclear norm, recently introduced in \cite{tensor_tSVD}. We build on a recent line of results that considered…

In this paper, we show that the low rank matrix completion problem can be reduced to the problem of finding the rank of a certain 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 article, we develop methods for estimating a low rank tensor from noisy observations on a subset of its entries to achieve both statistical and computational efficiencies. There have been a lot of recent interests in this problem of…

The Nystr\"om method offers an effective way to obtain low-rank approximation of SPD matrices, and has been recently extended and analyzed to nonsymmetric matrices (leading to the generalized Nystr\"om method). It is a randomized,…

Low rank tensor ring model is powerful for image completion which recovers missing entries in data acquisition and transformation. The recently proposed tensor ring (TR) based completion algorithms generally solve the low rank optimization…

Similarity matrix serves as a fundamental tool at the core of numerous downstream machine-learning tasks. However, missing data is inevitable and often results in an inaccurate similarity matrix. To address this issue, Similarity Matrix…

In the realm of tensor optimization, the low-rank Tucker decomposition is crucial for reducing the number of parameters and for saving storage. We explore the geometry of Tucker tensor varieties -- the set of tensors with bounded Tucker…

Recent studies have demonstrated the great potential of reduced order modeling for parametric dynamical systems using low-rank tensor decompositions (LRTD). In particular, within the framework of interpolatory tensorial reduced order models…

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…