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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…
This paper derives the CS decomposition for orthogonal tensors (T-CSD) and the generalized singular value decomposition for two tensors (T-GSVD) via the T-product. The structures of the two decompositions are analyzed in detail and are…
In the present paper we propose two new algorithms of tensor completion for three-order tensors. The proposed methods consist in minimizing the average rank of the underlying tensor using its approximate function namely the tensor nuclear…
In recent years, the application of tensors has become more widespread in fields that involve data analytics and numerical computation. Due to the explosive growth of data, low-rank tensor decompositions have become a powerful tool to…
There are several factorizations of multi-dimensional tensors into lower-dimensional components, known as `tensor networks'. We consider the popular `tensor-train' (TT) format and ask: How efficiently can we compute a low-rank approximation…
We study tensor completion (TC) through the lens of low-rank tensor decomposition (TD). Many TD algorithms use fast alternating minimization methods to solve highly structured linear regression problems at each step (e.g., for CP, Tucker,…
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…
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…
Tensors provide a robust framework for managing high-dimensional data. Consequently, tensor analysis has emerged as an active research area in various domains, including machine learning, signal processing, computer vision, graph analysis,…
In this paper, we address the multi-view subspace clustering problem. Our method utilizes the circulant algebra for tensor, which is constructed by stacking the subspace representation matrices of different views and then rotating, to…
We propose a new algorithm for the computation of a singular value decomposition (SVD) low-rank approximation of a matrix in the Matrix Product Operator (MPO) format, also called the Tensor Train Matrix format. Our tensor network randomized…
This paper introduces the functional tensor singular value decomposition (FTSVD), a novel dimension reduction framework for tensors with one functional mode and several tabular modes. The problem is motivated by high-order longitudinal data…
An efficient, accurate and reliable approximation of a matrix by one of lower rank is a fundamental task in numerical linear algebra and signal processing applications. In this paper, we introduce a new matrix decomposition approach termed…
This paper develops fast and efficient algorithms for computing Tucker decomposition with a given multilinear rank. By combining random projection and the power scheme, we propose two efficient randomized versions for the truncated…
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 this paper, we mainly develop the well-known vector and matrix polynomial extrapolation methods in tensor framework. To this end, some new products between tensors are defined and the concept of positive definitiveness is extended for…
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…
Tensor singular value decomposition (t-SVD) is a promising tool for multi-dimensional image representation, which decomposes a multi-dimensional image into a latent tensor and an accompanying transform matrix. However, two critical…
Recently, there has been a lot of research into tensor singular value decomposition (t-SVD) by using discrete Fourier transform (DFT) matrix. The main aims of this paper are to propose and study tensor singular value decomposition based on…
By representing documents as mixtures of topics, topic modeling has allowed the successful analysis of datasets across a wide spectrum of applications ranging from ecology to genetics. An important body of recent work has demonstrated the…