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Multiscale tensor decomposition
2016 50th Asilomar Conference on Signals, Systems and Computers, 2016Large datasets usually contain redundant information and summarizing these datasets is important for better data interpretation. Higher-order data reduction is usually achieved through low-rank tensor approximation which assumes that the data lies near a linear subspace across each mode.
Alp Ozdemir +2 more
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Sensitivity in Tensor Decomposition
IEEE Signal Processing Letters, 2019Canonical polyadic (CP) tensor decomposition is an important task in many applications. Many times, the true tensor rank is not known, or noise is present, and in such situations, different existing CP decomposition algorithms provide very different results.
Petr Tichavský +2 more
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Tensor Decomposition Via Core Tensor Networks
ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2021Tensor decomposition (TD) has shown promising performance in image completion and denoising. Existing methods always aim to decompose one tensor into latent factors or core tensors by optimizing a particular cost function based on a specific tensor model.
Jianfu Zhang 0003 +3 more
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SIAM Journal on Scientific Computing, 2011
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.
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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.
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Randomized Tensor Wheel Decomposition
SIAM Journal on Scientific ComputingzbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mengyu Wang, Yajie Yu, Hanyu Li
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Facial Recognition Using Tensor-Tensor Decompositions
SIAM Journal on Imaging Sciences, 2013A tensor is a multidimensional array. First-order tensors and second-order tensors can be viewed as vectors and matrices, respectively. Tensors of higher order, with the ability to include more information, appear more frequently nowadays in image and signal processing, data mining, biomedical engineering, and so on.
Ning Hao +3 more
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Probabilistic Streaming Tensor Decomposition
2018 IEEE International Conference on Data Mining (ICDM), 2018Tensor decomposition is a fundamental tool for multiway data analysis. While most decomposition algorithms operate a collection of static data and perform batch processes, many applications produce data in a streaming manner — every time a subset of entries are generated, and previously seen entries cannot be revisited.
Yishuai Du +3 more
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On the Decomposition of Modular Tensors (I)
The Annals of Mathematics, 1942The present paper is the second part of [8] (brackets refer to bibliography) referred to below as Part I. We number sections, formulae, theorems, etc. consecutively from those in Part I, and use the same notation. For instance, f is a field of characteristic p with q (?_ cc ) elements; Zi is a t-vector space of dimension n; (5 = 65(n, f) is the full ...
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Decomposition of Tensors of the Classical Groups
Journal of Mathematical Physics, 1967A tensor symmetrization procedure obtained in a recent publication [Phys. Rev. Letters 16, 1058 (1966)] is shown to support rather than disprove Weyl's tensor symmetrization theorem. This ``extended'' symmetrization procedure differs from Weyl's approach in that to construct a subspace irreducible under GL(n, c) one starts with a set of formal states ...
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Computing tensor product decompositions
ACM Transactions on Mathematical Software, 1993An algorithm is presented for computing the decomposition of a tensor product of two irreducible representations of a semisimple complex Lie group into its irreducible components. The algorithm uses a known formula which expresses the multiplicities of the highest weight vectors in the decomposition as an alternating sum indexed by the Weyl group. This
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