Related papers: Tensor extrapolation methods with applications

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…

There is a significant expansion in both volume and range of applications along with the concomitant increase in the variety of data sources. These ever-expanding trends have highlighted the necessity for more versatile analysis tools that…

Due to the explosive growth of large-scale data sets, tensors have been a vital tool to analyze and process high-dimensional data. Different from the matrix case, tensor decomposition has been defined in various formats, which can be…

In this paper, we propose a general framework for tensor singular value decomposition (tensor SVD), which focuses on the methodology and theory for extracting the hidden low-rank structure from high-dimensional tensor data. Comprehensive…

The tensor-tensor product (t-product) [M. E. Kilmer and C. D. Martin, 2011] is a natural generalization of matrix multiplication. Based on t-product, many operations on matrix can be extended to tensor cases, including tensor SVD, tensor…

While Spectral Methods have long been used for Principal Component Analysis, this survey focusses on work over the last 15 years with three salient features: (i) Spectral methods are useful not only for numerical problems, but also discrete…

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…

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…

We propose a sampling-based method for computing the tensor ring (TR) decomposition of a data tensor. The method uses leverage score sampled alternating least squares to fit the TR cores in an iterative fashion. By taking advantage of the…

In this paper we suggest a new algorithm for the computation of a best rank one approximation of tensors, called alternating singular value decomposition. This method is based on the computation of maximal singular values and the…

This paper introduces an extended tensor decomposition (XTD) method for model reduction. The proposed method is based on a sparse non-separated enrichment to the conventional tensor decomposition, which is expected to improve the…

We propose a constructive algorithm that decomposes an arbitrary real tensor into a finite sum of orthonormal rank-1 outer products. The algorithm, named TTr1SVD, works by converting the tensor into a tensor-train rank-1 (TTr1) series via…

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…

Tensor completion and robust principal component analysis have been widely used in machine learning while the key problem relies on the minimization of a tensor rank that is very challenging. A common way to tackle this difficulty is to…

Higher-order tensor decompositions are analogous to the familiar Singular Value Decomposition (SVD), but they transcend the limitations of matrices (second-order tensors). SVD is a powerful tool that has achieved impressive results in…

We propose a new fast streaming algorithm for the tensor completion problem of imputing missing entries of a low-tubal-rank tensor using the tensor singular value decomposition (t-SVD) algebraic framework. We show the t-SVD is a…

Approximating higher-order tensors by the Tucker format has been applied in many fields such as psychometrics, chemometrics, signal processing, pattern classification, and so on. In this paper, we propose some new Tucker-like approximations…

The tensor decomposition addressed in this paper may be seen as a generalisation of Singular Value Decomposition of matrices. We consider general multilinear and multihomogeneous tensors. We show how to reduce the problem to a truncated…

Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and…

Tensor interpolation is an essential step for tensor data analysis in various fields of application and scientific disciplines. In the present work, novel interpolation schemes for general, i.e., symmetric or non-symmetric, invertible…