相关论文: Tensor Completion via Tensor QR Decomposition and …

The Tucker tensor decomposition is a natural extension of the singular value decomposition (SVD) to multiway data. We propose to accelerate Tucker tensor decomposition algorithms by using randomization and parallelization. We present two…

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…

Tucker decomposition is a common method for the analysis of multi-way/tensor data. Standard Tucker has been shown to be sensitive against heavy corruptions, due to its L2-norm-based formulation which places squared emphasis to peripheral…

In this paper, we propose a novel model to recover a low-rank tensor by simultaneously performing double nuclear norm regularized low-rank matrix factorizations to the all-mode matricizations of the underlying tensor. An block successive…

Tensor ring (TR) decomposition has recently received increased attention due to its superior expressive performance for high-order tensors. However, the applicability of traditional TR decomposition algorithms to real-world applications is…

The factorization of three-dimensional data continues to gain attention due to its relevance in representing and compressing large-scale datasets. The linear-map-based tensor-tensor multiplication is a matrix-mimetic operation that extends…

In this paper, we investigate tensor recovery problems within the tensor singular value decomposition (t-SVD) framework. We propose the partial sum of the tubal nuclear norm (PSTNN) of a tensor. The PSTNN is a surrogate of the tensor tubal…

Large language models (LLMs) demonstrate outstanding performance in various tasks in machine learning and have thus become one of the most important workloads in today's computing landscape. However, deploying LLM inference poses challenges…

A fast algorithm for solving the under-determined 3-D linear gravity inverse problem based on the randomized singular value decomposition (RSVD) is developed. The algorithm combines an iteratively reweighted approach for $L_1$-norm…

In this paper, we present a fast implementation of the Singular Value Thresholding (SVT) algorithm for matrix completion. A rank-revealing randomized singular value decomposition (R3SVD) algorithm is used to adaptively carry out partial…

From linear classifiers to neural networks, image classification has been a widely explored topic in mathematics, and many algorithms have proven to be effective classifiers. However, the most accurate classifiers typically have…

This paper proposes a general framework to use the cross tensor approximation or tensor ColUmn-Row (CUR) approximation for reconstructing incomplete images and videos. The key importance of the new algorithms is their simplicity and ease of…

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,…

One of the key problems in tensor completion is the number of uniformly random sample entries required for recovery guarantee. The main aim of this paper is to study $n_1 \times n_2 \times n_3$ third-order tensor completion based on…

The fully-connected tensor network (FCTN) decomposition has gained prominence in the field of tensor completion owing to its powerful capacity to capture the low-rank characteristics of tensors. Nevertheless, the recovery of local details…

The big data era is swamping areas including data analysis, machine/deep learning, signal processing, statistics, scientific computing, and cloud computing. The multidimensional feature and huge volume of big data put urgent requirements to…

Tensor decomposition has proven to be a strong tool in various 3D image processing tasks such as denoising and super-resolution. In this context, we recently proposed a canonical polyadic decomposition (CPD) based algorithm for single image…

Matrix completion focuses on recovering a matrix from a small subset of its observed elements, and has already gained cumulative attention in computer vision. Many previous approaches formulate this issue as a low-rank matrix approximation…

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 t-SVD based Tensor Robust Principal Component Analysis (TRPCA) decomposes low rank multi-linear signal corrupted by gross errors into low multi-rank and sparse component by simultaneously minimizing tensor nuclear norm and l 1 norm. But…