Tensor networks for dimensionality reduction and large-scale optimization: Part 1 low-rank tensor decompositions

A Cichocki, N Lee, I Oseledets, AH Phan… - … and Trends® in …, 2016 - nowpublishers.com
Modern applications in engineering and data science are increasingly based on
multidimensional data of exceedingly high volume, variety, and structural richness …

Low-rank tensor networks for dimensionality reduction and large-scale optimization problems: Perspectives and challenges part 1

A Cichocki, N Lee, IV Oseledets, AH Phan… - arXiv preprint arXiv …, 2016 - arxiv.org
Machine learning and data mining algorithms are becoming increasingly important in
analyzing large volume, multi-relational and multi--modal datasets, which are often …

A survey on tensor techniques and applications in machine learning

Y Ji, Q Wang, X Li, J Liu - IEEE Access, 2019 - ieeexplore.ieee.org
This survey gives a comprehensive overview of tensor techniques and applications in
machine learning. Tensor represents higher order statistics. Nowadays, many applications …

Tensor computation: A new framework for high-dimensional problems in EDA

Z Zhang, K Batselier, H Liu, L Daniel… - IEEE Transactions on …, 2016 - ieeexplore.ieee.org
Many critical electronic design automation (EDA) problems suffer from the curse of
dimensionality, ie, the very fast-scaling computational burden produced by large number of …

SVD-based algorithms for the best rank-1 approximation of a symmetric tensor

Y Guan, MT Chu, D Chu - SIAM Journal on Matrix Analysis and Applications, 2018 - SIAM
This paper revisits the problem of finding the best rank-1 approximation to a symmetric
tensor and makes three contributions. First, in contrast to the many long and lingering …

Orthogonal and unitary tensor decomposition from an algebraic perspective

A Boralevi, J Draisma, E Horobeţ, E Robeva - Israel journal of …, 2017 - Springer
While every matrix admits a singular value decomposition, in which the terms are pairwise
orthogonal in a strong sense, higher-order tensors typically do not admit such an orthogonal …

A constructive arbitrary‐degree Kronecker product decomposition of tensors

K Batselier, N Wong - Numerical Linear Algebra with …, 2017 - Wiley Online Library
We generalize the matrix Kronecker product to tensors and propose the tensor Kronecker
product singular value decomposition that decomposes a real k‐way tensor into a linear …

Application of tensor decomposition to reduce the complexity of neural min-sum channel decoding algorithm

Q Wu, BK Ng, Y Liang, CT Lam, Y Ma - Applied Sciences, 2023 - mdpi.com
Channel neural decoding is very promising as it outperforms the traditional channel
decoding algorithms. Unfortunately, it still faces the disadvantage of high computational …

Tensor Decomposition-based Feature Extraction and Classification to Detect Natural Selection from Genomic Data

MR Amin, M Hasan, SP Arnab… - Molecular Biology and …, 2023 - academic.oup.com
Inferences of adaptive events are important for learning about traits, such as human
digestion of lactose after infancy and the rapid spread of viral variants. Early efforts toward …

Low‐rank tensor completion for visual data recovery via the tensor train rank‐1 decomposition

X Liu, XY Jing, G Tang, F Wu, X Dong - IET Image Processing, 2020 - Wiley Online Library
In this study, the authors study the problem of tensor completion, in particular for three‐
dimensional arrays such as visual data. Previous works have shown that the low‐rank …