Results 171 to 180 of about 196,468 (204)
Uniqueness of Nonnegative Tensor Approximations [PDF]
IEEE Transactions on Information Theory, 2016 We show that for a nonnegative tensor, a best nonnegative rank-r approximation is almost always unique, its best rank-one approximation may always be chosen to be a best nonnegative rank-one approximation, and that the set of nonnegative tensors with non-unique best rank-one approximations form an algebraic hypersurface.
Pierre Comon, Lek-Heng Lim
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Nonnegative Approximations of Nonnegative Tensors [PDF]
Journal of Chemometrics, 2009 AbstractWe study the decomposition of a nonnegative tensor into a minimal sum of outer product of nonnegative vectors and the associated parsimonious naïve Bayes probabilistic model. We show that the corresponding approximation problem, which is central to nonnegative PARAFAC, will always have optimal solutions. The result holds for any choice of norms
Pierre Comon, Lek-Heng Lim
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Finding the Largest Eigenvalue of a Nonnegative Tensor [PDF]
SIAM Journal on Matrix Analysis and Applications, 2010 Starting from a well-known iterative method for calculating the spectral radius of an irreducible nonnegative matrix, proposed by Collatz in 1942, the authors construct an iterative method for calculating the largest eigenvalue of an irreducible nonnegative tensor.
Michael Ng, Liqun Qi, Guanglu Zhou
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Fast Decomposition of Large Nonnegative Tensors [PDF]
IEEE Signal Processing Letters, 2015 In signal processing, tensor decompositions have gained in popularity this last decade. In the meantime, the volume of data to be processed has drastically increased. This calls for novel methods to handle Big Data tensors. Since most of these huge data are issued from physical measurements, which are intrinsically real nonnegative, being able to ...
Jeremy E Cohen, Pierre Comon
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An Always Convergent Algorithm for the Largest Eigenvalue of an Irreducible Nonnegative Tensor
Journal of Computational and Applied Mathematics, 2010 In this paper we propose an iterative method to calculate the largest eigenvalue of a nonnegative tensor. We prove this method converges for any irreducible nonnegative tensor.
Guanglu Zhou, Nur Fadhilah Ibrahim
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On New Classes of Nonnegative Symmetric Tensors [PDF]
SIAM Journal on Optimization, 2017 Summary: In this paper we introduce three new classes of nonnegative forms (or equivalently, symmetric tensors) and their extensions. The newly identified nonnegative symmetric tensors constitute distinctive convex cones in the space of general symmetric tensors (order six or above).
Bilian Chen, Shuzhong Zhang, Zhening Li
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Fast Nonnegative Tensor Factorizations with Tensor Train Model
Lobachevskii Journal of Mathematics, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shcherbakova, E. M., Tyrtyshnikov, E. E.
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Continuation methods for nonnegative rank‐1 approximation of nonnegative tensors
Numerical Linear Algebra with Applications, 2021AbstractIn this article, the rank‐1 approximation of a nonnegative tensor is considered. Mathematically, the approximation problem can be formulated as an optimization problem. The Karush–Kuhn–Tucker (KKT) point of the optimization problem can be obtained by computing the nonnegative Z‐eigenvectoryof enlarged tensor . Therefore, we propose an iterative
Fu-Shin Hsu +2 more
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Convergence of an Algorithm for the Largest Singular Value of a Nonnegative Rectangular Tensor
Linear Algebra and Its Applications, 2013 In this paper, we present an iterative algorithm for computing thelargest singular value of a nonnegative rectangular tensor.We establishthe convergence of this algorithm for any irreducible nonnegativerectangular ...
Liqun Qi, Guanglu Zhou, Louis Caccetta
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Nonlinear Perron--Frobenius Theorems for Nonnegative Tensors
SIAM Review, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Antoine Gautier 0001 +2 more
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