Results 31 to 40 of about 23,770 (308)
CoRR, 2016 Tensor networks have in recent years emerged as the powerful tools for solving the large-scale optimization problems. One of the most popular tensor network is tensor train (TT) decomposition that acts as the building blocks for the complicated tensor networks.
Qibin Zhao +4 more
openaire +2 more sources
Spectral Tensor-Train Decomposition [PDF]
SIAM Journal on Scientific Computing, 2016 The accurate approximation of high-dimensional functions is an essential task in uncertainty quantification and many other fields. We propose a new function approximation scheme based on a spectral extension of the tensor-train (TT) decomposition. We first define a functional version of the TT decomposition and analyze its properties. We obtain results
Daniele Bigoni +2 more
openaire +4 more sources
IEEE Access, 2018 Reliable detection and recovery of a microseismic event in large volume of passive monitoring data is usually a challenging task due to the low signal-to-noise ratio environment.
Naveed Iqbal +5 more
doaj +1 more source
Robust Tensor Decomposition for Image Representation Based on Generalized Correntropy
, 2020 Traditional tensor decomposition methods, e.g., two dimensional principal component analysis and two dimensional singular value decomposition, that minimize mean square errors, are sensitive to outliers. To overcome this problem, in this paper we propose
Sun, Changming +3 more
core +1 more source
Tensor Completion Using Kronecker Rank-1 Tensor Train With Application to Visual Data Inpainting
IEEE Access, 2018 The problem of data reconstruction with partly sampled elements under a tensor structure, which is referred to as tensor completion, is addressed in this paper.
Weize Sun, Yuan Chen, Hing Cheung So
doaj +1 more source
Hankel Tensor Decompositions and Ranks [PDF]
SIAM Journal on Matrix Analysis and Applications, 2019 Hankel tensors are generalizations of Hankel matrices. This article studies the relations among various ranks of Hankel tensors. We give an algorithm that can compute the Vandermonde ranks and decompositions for all Hankel tensors. For a generic $n$-dimensional Hankel tensor of even order or order three, we prove that the the cp rank, symmetric rank ...
Jiawang Nie, Ke Ye
openaire +3 more sources
On the Decomposition of Tensors by Contraction [PDF]
Reviews of Modern Physics, 1949 The decomposition of tensors into irreducible representations of the orthogonal groups is calculated for three and four dimensions. The connection is shown with the problem of the allowed values of ordinary and isotopic spin for a given symmetry of the spacial eigenfunction of a nuclear system.
openaire +1 more source
Low Tensor Rank Constrained Image Inpainting Using a Novel Arrangement Scheme
Applied SciencesEmploying low tensor rank decomposition in image inpainting has attracted increasing attention. This study exploited novel tensor arrangement schemes to transform an image (a low-order tensor) to a higher-order tensor without changing the total number of
Shuli Ma +4 more
doaj +1 more source
Graph Regularized Tensor Decomposition for Recommender Systems
, 2022 Humans make decisions when presented with choices based on influences. The Internet today presents people with abundant choices to choose from. Recommending choices with an emphasis on people's preferences has become increasingly sought.
Chandrashekar, Rohan (author)
core
Efficient Tensor Decompositions
, 2020 This chapter studies the problem of decomposing a tensor into a sum of constituent rank one tensors. While tensor decompositions are very useful in designing learning algorithms and data analysis, they are NP-hard in the worst-case. We will see how to design efficient algorithms with provable guarantees under mild assumptions, and using beyond worst ...
openaire +2 more sources