Search Results - Tensor Decompositions and Applications in Multilinear Algebra

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

Get full text

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

Get full text

Solving Multilinear Systems via Tensor Inversion by 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…”
Get full text

Tensor Decomposition for Signal Processing and Machine Learning by 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…”
Get full text

A Practical Randomized CP Tensor Decomposition by Battaglino, Casey, Ballard, Grey, Kolda, Tamara G.

Get full text

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

“…Operations with tensors, or multiway arrays, are increasingly prevalent in many applications involving multiway data analysis…”
Get full text

Extension of PCA to Higher Order Data Structures: An Introduction to Tensors, Tensor Decompositions, and Tensor PCA by 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…”
Get full text

Randomized CP tensor decomposition by 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…”
Get full text

Factorization strategies for third-order tensors by 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…”
Get full text

Tensor based geology preserving reservoir parameterization with Higher Order Singular Value Decomposition (HOSVD) by Afra, Sardar, Gildin, Eduardo

“…Parameter estimation through robust parameterization techniques has been addressed in many works associated with history matching and inverse problems…”
Get full text

A Multilinear Nyström Algorithm for Low-Rank Approximation of Tensors in Tucker Format by Bucci, Alberto, Robol, Leonardo

Get full text

Symmetric tensor decomposition by 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…”
Get full text

Decompositions of a Higher-Order Tensor in Block Terms—Part II: Definitions and Uniqueness by 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…”
Get full text

Hierarchical Singular Value Decomposition of Tensors by Grasedyck, Lars

“…The authors define the hierarchical singular value decomposition (SVD) for tensors of order d ≥ 2…”
Get full text

Multilinear time-invariant descriptor systems: Multilinear time-invariant descriptor systems by 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…”
Get full text

A sequential multilinear Nyström algorithm for streaming low-rank approximation of tensors in Tucker format by 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…”
Get full text

A Link between the Canonical Decomposition in Multilinear Algebra and Simultaneous Matrix Diagonalization by 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…”
Get full text

A Multilinear Singular Value Decomposition by 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…”
Get full text

Generating Polynomials and Symmetric Tensor Decompositions by Nie, Jiawang

“…This paper studies symmetric tensor decompositions. For symmetric tensors, there exist linear relations of recursive patterns among their entries…”
Get full text

Blind Separation of Exponential Polynomials and the Decomposition of a Tensor in Rank-$(L_r,L_r,1)$ Terms by 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…”
Get full text