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Spectral tensor-train decomposition [PDF]
SIAM Journal on Scientific Computing, 2015 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.
Bigoni, Daniele +2 more
core +6 more sources
Exploring the feasibility of tensor decomposition for analysis of fNIRS signals: a comparative study with grand averaging method [PDF]
Frontiers in Neuroscience, 2023 The analysis of functional near-infrared spectroscopy (fNIRS) signals has not kept pace with the increased use of fNIRS in the behavioral and brain sciences.
Jasmine Y. Chan +4 more
doaj +2 more sources
Time-aware tensor decomposition for sparse tensors
2021 IEEE 8th International Conference on Data Science and Advanced Analytics (DSAA), 2021 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dawon Ahn, Jun-Gi Jang, U. Kang
semanticscholar +3 more sources
Random Tensor Theory for Tensor Decomposition
Proceedings of the AAAI Conference on Artificial Intelligence, 2022 We propose a new framework for tensor decomposition based on trace invariants, which are particular cases of tensor networks. In general, tensor networks are diagrams/graphs that specify a way to "multiply" a collection of tensors together to produce ...
M. Ouerfelli +2 more
semanticscholar +3 more sources
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
Anandkumar A. +12 more
core +4 more sources
L1-Norm Tucker Tensor Decomposition [PDF]
IEEE Access, 2019 Tucker decomposition is a standard multi-way generalization of Principal-Component Analysis (PCA), appropriate for processing tensor data. Similar to PCA, Tucker decomposition has been shown to be sensitive against faulty data, due to its L2-norm-based ...
Dimitris G. Chachlakis +2 more
doaj +3 more sources
Tensor Decomposition for Model Reduction in Neural Networks: A Review [Feature] [PDF]
IEEE Circuits and Systems Magazine, 2023 Modern neural networks have revolutionized the fields of computer vision (CV) and Natural Language Processing (NLP). They are widely used for solving complex CV tasks and NLP tasks such as image classification, image generation, and machine translation ...
Xingyi Liu, Keshab K. Parhi
semanticscholar +1 more source
Hermitian Tensor Decompositions [PDF]
SIAM Journal on Matrix Analysis and Applications, 2020 Hermitian tensors are generalizations of Hermitian matrices, but they have very different properties. Every complex Hermitian tensor is a sum of complex Hermitian rank-1 tensors. However, this is not true for the real case. We study basic properties for Hermitian tensors such as Hermitian decompositions and Hermitian ranks. For canonical basis tensors,
Nie, Jiawang, Yang, Zi
openaire +2 more sources
Towards Efficient Tensor Decomposition-Based DNN Model Compression with Optimization Framework [PDF]
Computer Vision and Pattern Recognition, 2021 Advanced tensor decomposition, such as tensor train (TT) and tensor ring (TR), has been widely studied for deep neural network (DNN) model compression, especially for recurrent neural networks (RNNs).
Miao Yin, Yang Sui, Siyu Liao, Bo Yuan
semanticscholar +1 more source
Counting Tensor Rank Decompositions [PDF]
Universe, 2021 Tensor rank decomposition is a useful tool for geometric interpretation of the tensors in the canonical tensor model (CTM) of quantum gravity. In order to understand the stability of this interpretation, it is important to be able to estimate how many tensor rank decompositions can approximate a given tensor.
Dennis Obster, Naoki Sasakura
openaire +3 more sources