Journal ArticleDOI
Tensor-Train Decomposition
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TLDR
The new form gives a clear and convenient way to implement all basic operations efficiently, and the efficiency is demonstrated by the computation of the smallest eigenvalue of a 19-dimensional operator.Abstract:
A simple nonrecursive form of the tensor decomposition in $d$ dimensions is presented. It does not inherently suffer from the curse of dimensionality, it has asymptotically the same number of parameters as the canonical decomposition, but it is stable and its computation is based on low-rank approximation of auxiliary unfolding matrices. The new form gives a clear and convenient way to implement all basic operations efficiently. A fast rounding procedure is presented, as well as basic linear algebra operations. Examples showing the benefits of the decomposition are given, and the efficiency is demonstrated by the computation of the smallest eigenvalue of a 19-dimensional operator.read more
Citations
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Journal ArticleDOI
Recent advances in convolutional neural networks
Jiuxiang Gu,Zhenhua Wang,Jason Kuen,Lianyang Ma,Amir Shahroudy,Bing Shuai,Ting Liu,Xingxing Wang,Gang Wang,Jianfei Cai,Tsuhan Chen +10 more
TL;DR: A broad survey of the recent advances in convolutional neural networks can be found in this article, where the authors discuss the improvements of CNN on different aspects, namely, layer design, activation function, loss function, regularization, optimization and fast computation.
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Deep convolutional neural networks for image classification: A comprehensive review
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Machine learning and the physical sciences
Giuseppe Carleo,J. Ignacio Cirac,Kyle Cranmer,Laurent Daudet,Maria Schuld,Naftali Tishby,Leslie Vogt-Maranto,Lenka Zdeborová +7 more
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Recent Advances in Convolutional Neural Networks
Jiuxiang Gu,Zhenhua Wang,Jason Kuen,Lianyang Ma,Amir Shahroudy,Bing Shuai,Ting Liu,Xingxing Wang,Li Wang,Gang Wang,Jianfei Cai,Tsuhan Chen +11 more
TL;DR: This paper details the improvements of CNN on different aspects, including layer design, activation function, loss function, regularization, optimization and fast computation, and introduces various applications of convolutional neural networks in computer vision, speech and natural language processing.
Journal ArticleDOI
Tensor Decomposition for Signal Processing and Machine Learning
Nicholas D. Sidiropoulos,Lieven De Lathauwer,Xiao Fu,Kejun Huang,Evangelos E. Papalexakis,Christos Faloutsos +5 more
TL;DR: The material covered includes tensor rank and rank decomposition; basic tensor factorization models and their relationships and properties; broad coverage of algorithms ranging from alternating optimization to stochastic gradient; statistical performance analysis; and applications ranging from source separation to collaborative filtering, mixture and topic modeling, classification, and multilinear subspace learning.
References
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Journal ArticleDOI
Tensor Decompositions and Applications
Tamara G. Kolda,Brett W. Bader +1 more
TL;DR: This survey provides an overview of higher-order tensor decompositions, their applications, and available software.
Journal ArticleDOI
Analysis of individual differences in multidimensional scaling via an n-way generalization of 'eckart-young' decomposition
J. Douglas Carroll,Jih-Jie Chang +1 more
TL;DR: In this paper, an individual differences model for multidimensional scaling is outlined in which individuals are assumed differentially to weight the several dimensions of a common "psychological space" and a corresponding method of analyzing similarities data is proposed, involving a generalization of Eckart-Young analysis to decomposition of three-way (or higher-way) tables.
Journal ArticleDOI
A Multilinear Singular Value Decomposition
TL;DR: There is a strong analogy between several properties of the matrix and the higher-order tensor decomposition; uniqueness, link with the matrix eigenvalue decomposition, first-order perturbation effects, etc., are analyzed.
Journal ArticleDOI
Some mathematical notes on three-mode factor analysis
TL;DR: The model for three-mode factor analysis is discussed in terms of newer applications of mathematical processes including a type of matrix process termed the Kronecker product and the definition of combination variables.
Foundations of the PARAFAC procedure: Models and conditions for an "explanatory" multi-model factor analysis
TL;DR: It is shown that an extension of Cattell's principle of rotation to Proportional Profiles (PP) offers a basis for determining explanatory factors for three-way or higher order multi-mode data.