Suchergebnisse - Tensor Decompositions and Applications in Multilinear Algebra

Decomposition of a Tensor into Multilinear Rank-\({(M_{{r}},N_{{r}},\cdot )}\) Terms von Domanov, Ignat, Vervliet, Nico, Evert, Eric, De Lathauwer, Lieven

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On Uniqueness and Computation of the Decomposition of a Tensor into Multilinear Rank-$(1,L_r,L_r)$ Terms von Domanov, Ignat, Lathauwer, Lieven De

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Solving Multilinear Systems via Tensor Inversion von Brazell, M., Li, N., Navasca, C., Tamon, C.

“… $. With these isomorphic group structures, we derive a tensor SVD which we have shown to be equivalent to well-known canonical polyadic decomposition and multilinear SVD provided that some constraints are satisfied …”
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Tensor Decomposition for Signal Processing and Machine Learning von Sidiropoulos, Nicholas D., De Lathauwer, Lieven, Xiao Fu, Kejun Huang, Papalexakis, Evangelos E., Faloutsos, Christos

“… Tensors or multiway arrays are functions of three or more indices (i, j, k, . . . )-similar to matrices (two-way arrays …”
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A Practical Randomized CP Tensor Decomposition von Battaglino, Casey, Ballard, Grey, Kolda, Tamara G.

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An Order-$p$ Tensor Factorization with Applications in Imaging von Martin, Carla D., Shafer, Richard, LaRue, Betsy

“… Operations with tensors, or multiway arrays, are increasingly prevalent in many applications involving multiway data analysis …”
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Extension of PCA to Higher Order Data Structures: An Introduction to Tensors, Tensor Decompositions, and Tensor PCA von Zare, Ali, Ozdemir, Alp, Iwen, Mark A., Aviyente, Selin

“… Data in the form of multidimensional arrays, also referred to as tensors, arise in a variety of applications including chemometrics, hyperspectral imaging, high-resolution videos, neuroimaging …”
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Randomized CP tensor decomposition von Erichson, N Benjamin, Manohar, Krithika, Brunton, Steven L, Kutz, J Nathan

“… The CANDECOMP/PARAFAC (CP) tensor decomposition is a popular dimensionality-reduction method for multiway data …”
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Factorization strategies for third-order tensors von Kilmer, Misha E., Martin, Carla D.

“… ) or the Tucker models, or some variation thereof. Such decompositions are motivated by specific applications where the goal is to find an approximate such representation for a given multiway array …”
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Tensor based geology preserving reservoir parameterization with Higher Order Singular Value Decomposition (HOSVD) von Afra, Sardar, Gildin, Eduardo

“… Parameter estimation through robust parameterization techniques has been addressed in many works associated with history matching and inverse problems …”
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A Multilinear Nyström Algorithm for Low-Rank Approximation of Tensors in Tucker Format von Bucci, Alberto, Robol, Leonardo

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Symmetric tensor decomposition von Brachat, Jerome, Comon, Pierre, Mourrain, Bernard, Tsigaridas, Elias

“… We present an algorithm for decomposing a symmetric tensor, of dimension n and order d, as a sum of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for binary forms …”
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Decompositions of a Higher-Order Tensor in Block Terms—Part II: Definitions and Uniqueness von De Lathauwer, Lieven

“… In this paper we introduce a new class of tensor decompositions. Intuitively, we decompose a given tensor block into blocks of smaller size, where the size is characterized by a set of mode-$n$ ranks …”
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Hierarchical Singular Value Decomposition of Tensors von Grasedyck, Lars

“… The authors define the hierarchical singular value decomposition (SVD) for tensors of order d ≥ 2 …”
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Multilinear time-invariant descriptor systems: Multilinear time-invariant descriptor systems von Ma, Wanli, Liu, Chengdong, Wei, Yimin

“… In this paper, we develop a framework for multilinear time-invariant (MLTI) description systems based on tensor M-product and establish fundamental theoretical results …”
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A sequential multilinear Nyström algorithm for streaming low-rank approximation of tensors in Tucker format von Bucci, Alberto, Hashemi, Behnam

“… We present a sequential version of the multilinear Nyström algorithm which is suitable for low-rank Tucker approximation of tensors given in a streaming format …”
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A Link between the Canonical Decomposition in Multilinear Algebra and Simultaneous Matrix Diagonalization von De Lathauwer, Lieven

“… Canonical decomposition is a key concept in multilinear algebra. In this paper we consider the decomposition of higher-order tensors which have the property that the rank is smaller than the greatest dimension …”
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A Multilinear Singular Value Decomposition von De Lathauwer, Lieven, De Moor, Bart, Vandewalle, Joos

“… We discuss a multilinear generalization of the singular value decomposition. There is a strong analogy between several properties of the matrix and the higher-order tensor decomposition …”
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Generating Polynomials and Symmetric Tensor Decompositions von Nie, Jiawang

“… This paper studies symmetric tensor decompositions. For symmetric tensors, there exist linear relations of recursive patterns among their entries …”
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Blind Separation of Exponential Polynomials and the Decomposition of a Tensor in Rank-$(L_r,L_r,1)$ Terms von De Lathauwer, Lieven

“… We present a new necessary and sufficient condition for essential uniqueness of the decomposition of a third-order tensor in rank-$(L_r,L_r,1)$ terms …”
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