
TSingular Values and TSketching for Third Order Tensors
Based upon the TSVD (tensor SVD) of third order tensors, introduced by ...
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Higher order Matching Pursuit for Low Rank Tensor Learning
Low rank tensor learning, such as tensor completion and multilinear mult...
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TLib: A Flexible C++ Tensor Framework for Numerical Tensor Calculus
Numerical tensor calculus comprise basic tensor operations such as the e...
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Higherorder ergodicity coefficients for stochastic tensors
Ergodicity coefficients for stochastic matrices provide valuable upper b...
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Higherorder ergodicity coefficients
Ergodicity coefficients for stochastic matrices provide valuable upper b...
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A unifying PerronFrobenius theorem for nonnegative tensors via multihomogeneous maps
Inspired by the definition of symmetric decomposition, we introduce the ...
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KullbackLeibler Principal Component for Tensors is not NPhard
We study the problem of nonnegative rankone approximation of a nonnegat...
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Shifted and extrapolated power methods for tensor ℓ^peigenpairs
This work is concerned with the computation of ℓ^peigenvalues and eigenvectors of square tensors with d modes. In the first part we propose two possible shifted variants of the popular (higherorder) power method computation of ℓ^peigenpairs proving the convergence of both the schemes to the Perron ℓ^peigenvector of the tensor, and the maximal corresponding ℓ^peigenvalue, when the tensor is entrywise nonnegative and p is strictly larger than the number of modes. Then, motivated by the slow rate of convergence that the proposed methods achieve for certain realworld tensors, when p≈ d, the number of modes, in the second part we introduce an extrapolation framework based on the simplified topological εalgorithm to efficiently accelerate the shifted power sequences. Numerical results on synthetic and real world problems show the improvements gained by the introduction of the shifting parameter and the efficiency of the acceleration technique.
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