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Smoothed analysis of tensor decompositions [PDF]
Proceedings of the forty-sixth annual ACM symposium on Theory of computing, 2014 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 tensors analogs of much of the matrix algebra toolkit are unlikely to exist because of hardness results.
Aditya Bhaskara +3 more
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A Survey on Tensor Techniques and Applications in Machine Learning
IEEE Access, 2019 This survey gives a comprehensive overview of tensor techniques and applications in machine learning. Tensor represents higher order statistics. Nowadays, many applications based on machine learning algorithms require a large amount of structured high ...
Yuwang Ji, Qiang Wang, Xuan Li, Jie Liu
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Randomized CP tensor decomposition
Machine Learning: Science and Technology, 2020 Abstract The CANDECOMP/PARAFAC (CP) tensor decomposition is a popular dimensionality-reduction method for multiway data. Dimensionality reduction is often sought after since many high-dimensional tensors have low intrinsic rank relative to the dimension of the ambient measurement space.
N. Benjamin Erichson +3 more
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Tensor-CUR Decompositions for Tensor-Based Data [PDF]
SIAM Journal on Matrix Analysis and Applications, 2006 Motivated by numerous applications in which the data may be modeled by a variable subscripted by three or more indices, we develop a tensor-based extension of the matrix CUR decomposition. The tensor-CUR decomposition is most relevant as a data analysis tool when the data consist of one mode that is qualitatively different from the others. In this case,
Michael W. Mahoney +2 more
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Tensor Decompositions in Deep Learning [PDF]
CoRR, 2020 The paper surveys the topic of tensor decompositions in modern machine learning applications. It focuses on three active research topics of significant relevance for the community. After a brief review of consolidated works on multi-way data analysis, we consider the use of tensor decompositions in compressing the parameter space of deep learning ...
Bacciu D., Mandic D. P.
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DAO-CP: Data-Adaptive Online CP decomposition for tensor stream
PLoS ONE, 2022 How can we accurately and efficiently decompose a tensor stream? Tensor decomposition is a crucial task in a wide range of applications and plays a significant role in latent feature extraction and estimation of unobserved entries of data. The problem of
Sangjun Son +3 more
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, 2022 Early identification of coronary artery disease (CAD) can facilitate timely clinical intervention and save lives. This study aims to develop a machine learning framework that uses tensor analysis on heart rate (HR) signals to automate the CAD detection ...
Acharya, U. Rajendra +3 more
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Skew-symmetric tensor decomposition [PDF]
Communications in Contemporary Mathematics, 2019 We introduce the “skew apolarity lemma” and we use it to give algorithms for the skew-symmetric rank and the decompositions of tensors in [Formula: see text] with [Formula: see text] and [Formula: see text]. New algorithms to compute the rank and a minimal decomposition of a tritensor are also presented.
Enrique Esteban Arrondo +3 more
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Finsler geometry on higher order tensor fields and applications to high angular resolution diffusion imaging. [PDF]
, 2009 We study 3D-multidirectional images, using Finsler geometry. The application considered here is in medical image analysis, specifically in High Angular Resolution Diffusion Imaging (HARDI) (Tuch et al. in Magn. Reson. Med.
Florack, L.M.J. +9 more
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Spline- and tensor-based signal reconstruction : from structure analysis to high-performance algorithms to multiplatform implementations and medical applications [PDF]
, 2015 The problem of signal reconstruction is of fundamental practical value for many applications associated with the field of signal and image processing.
Morozov, Oleksii
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