Towards a standardized notation and terminology in multiway analysis

By Henk A. L. Kiers. 2000

756 citations recorded by the source corpus.

Subfields: Computational Mathematics, Radiology, Nuclear Medicine and Imaging

View Paper: https://www.semanticscholar.org/paper/6179b2232c635008fed0f5ea0c8c5c82ccd1bdda

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In Computational Mathematics

In Radiology, Nuclear Medicine and Imaging

Citations in the corpus

A Link between the Canonical Decomposition in Multilinear Algebra and Simultaneous Matrix Diagonalization (2006, methodology): “In-dimensional vector obtained from A by varying the index in and keeping the other indices fixed [ 27 ].”
A scalable optimization approach for fitting canonical tensor decompositions (2011, methodology): “We generally use the notation of [31], which was adapted from [29].”
A randomized algorithm for a tensor-based generalization of the singular value decomposition (2007, background): “We refer to the (usually implicit) construction of A [ α ] as matricizing [27] or unfolding [34] A along mode α and deﬁne the α -rank of the tensor A to be the rank of the matrix A [ α ] .”
Factorization strategies for third-order tensors (2011, methodology): “We use the accepted notation where an order-p tensor is indexed by p indices and can be represented as a multidimensional array of data [17].”
Unsupervised Multiway Data Analysis: A Literature Survey (2009, methodology): “We denote higher-order arrays using underlined boldface letters, e.g., X, following the standard notation in [11].”
Parallel matrix factorization for low-rank tensor completion (2013, neutral): “Introducing one common variable Z to relate these matrix factorizations, we solve the following model to recover M (2) min where X = ( X 1 , . . . , X N ) and Y = ( Y 1 , . . . , Y N ).”
Shifted factor analysis—Part I: Models and properties (2003, methodology): “For example, see Reference [28] and references cited therein.”
Multilinear operators for higher-order decompositions (2006, background): “, [14] versus [24].”
A closed‐form expression for computing the sensitivity in second‐order bilinear calibration (2005, methodology): “Relevant second-order methodologies are based on: (1) the use of latent variables, such as unfolded partial leastsquares (PLS) [24], where ‘unfolded’ refers to working with previously vectorized data matrices [25], multi-way PLS (nPLS) [26] and PLS combined with residual bilinearization (RBL) [27,28”
Tensor Factorization for Low-Rank Tensor Completion (2018, methodology): “For fairness, in our method, we also set the initialized rank r0 = [30, 30, 30] for all testing images.”
Efficient MATLAB Computations with Sparse and Factored Tensors (2007, neutral): “The CANDECOMP/PARAFAC decomposition was simultaneously developed as the canonical decomposition of Carroll and Chang [9] and the parallel factors model of Harshman [19]; it is henceforth referred to as CP per Kiers [23].”