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The probabilistic tensor decomposition toolbox
Machine Learning: Science and Technology, 2020 This article introduces the probabilistic tensor decomposition toolbox - a MATLAB toolbox for tensor decomposition using Variational Bayesian inference and Gibbs sampling. An introduction and overview of probabilistic tensor decomposition and its connection with classical tensor decomposition methods based on maximum likelihood is provided.
Jesper Løve Hinrich +2 more
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Decomposition of linear tensor transformations [PDF]
CoRR, 2023 arXiv admin note: text overlap with arXiv:2305 ...
Turchetti, Claudio
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EA-ADMM: noisy tensor PARAFAC decomposition based on element-wise average ADMM
EURASIP Journal on Advances in Signal Processing, 2022 Tensor decomposition is widely used to exploit the internal correlation in multi-way data analysis and process for communications and radar systems.
Gang Yue, Zhuo Sun
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On the optimization landscape of tensor decompositions [PDF]
Mathematical Programming, 2020 Best paper in the NIPS 2016 Workshop on Nonconvex Optimization for Machine Learning: Theory and Practice.
Rong Ge 0001, Tengyu Ma 0001
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Multi-Modal Image Fusion Based on Matrix Product State of Tensor
Frontiers in Neurorobotics, 2021 Multi-modal image fusion integrates different images of the same scene collected by different sensors into one image, making the fused image recognizable by the computer and perceived by human vision easily.
Yixiang Lu +4 more
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Decomposition Algorithms for Tensors and Polynomials
SIAM Journal on Applied Algebra and Geometry, 2023 19 ...
Antonio Laface +2 more
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Design and Implementation of Tucker Decomposition Module Based on CUDA and CUBLAS [PDF]
Jisuanji gongcheng, 2019 Because tensor Tucker decomposition is widely used in image processing,face recognition,signal processing and other fields,Tucker decomposition algorithm becomes a key research object.However,the current popular Tucker decomposition algorithm needs to ...
ZHOU Qi,CHAI Xiaoli,MA Kejie,YU Zeren
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Legendre decomposition for tensors*
Journal of Statistical Mechanics: Theory and Experiment, 2019 Abstract We present a novel nonnegative tensor decomposition method, called Legendre decomposition, which factorizes an input tensor into a multiplicative combination of parameters. Thanks to the well-developed theory of information geometry, the reconstructed tensor is unique and always minimizes the KL divergence from an input tensor ...
Mahito Sugiyama +2 more
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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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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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