Applied Multiway Data Analysis

By P. Kroonenberg. 2008

549 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Control and Systems Engineering

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Citations in the corpus

A literature survey of low‐rank tensor approximation techniques (2013, neutral): “ired solution can be represented by a tensor. In this survey, we will focus on tensors that are induced by the discretization of a multivariate function; we refer to the survey [168] and to the books [174, 239] for the treatment of tensors containing observed data. The simplest way a given multivari”
Best Low Multilinear Rank Approximation of Higher-Order Tensors, Based on the Riemannian Trust-Region Scheme (2011, methodology): “The HOOI [13, 27, 28] is an alternating least-squares algorithm for finding the best rank-(R1, R2, R3) approximation of a tensor.”
Subtracting a best rank-1 approximation may increase tensor rank (2009, background): “In some applications, tensors may be symmetric only in some modes [7], or may not be symmetric nor have equal dimensions [3] [22] [19].”
On uniqueness conditions for Candecomp/Parafac and Indscal with full column rank in one mode (2009, methodology): “The real-valued CP model is used in a majority of applications in psychology and chemistry; see Kroonenberg [10], Kiers and Van Mechelen [7] and Smilde et al. [16].”
Differential-geometric Newton method for the best rank-(R1, R2, R3) approximation of tensors (2008, background): “It has been shown in [15, 33, 34] that problem (1) is equivalent to the problem of maximizing the function”
missMDA: A Package for Handling Missing Values in Multivariate Data Analysis (2016, methodology): “Different multi-blocks methods are available in the literature (Kroonenberg 2008) to answer”
Zur Theorie der Niedrigrangapproximation in Tensorprodukten von Hilberträumen (2013, background): “Zur Geschichte aus dieser Perspektive verweisen wir auf das schöne Buch von Kroonenberg [56], sowie den Übersichtsartikel von Kolda u.”
Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 1 Low-Rank Tensor Decompositions (2016, unknown): “…, 2015b; de Almeida et al. , 2015; Sidiropoulos et al. , 2016; Papalexakis et al. , 2016; Bachmayr et al. , 2016) and books (Smilde et al. , 2004; Kroonenberg, 2008; Cichocki et al. , 2009; Hackbusch, 2012) dealing with TDs and TNs already exist, however, they typically focus on standard models,…”
Tensor decomposition of EEG signals: a brief review. (2015, unknown): “It was ﬁrst deﬁned in the ﬁeld of mathematics (Hitchcock, 1927), and has been glorious in the ﬁelds of psychometrics and chemometrices for multi-way data analysis (Kroonenberg, 2008; Smilde et al., 2004).”
Tensor Decomposition for Signal Processing and Machine Learning (2016, methodology): “The first variant of Tucker-ALS goes back to the work of Kroonenberg and De Leeuw; see [39] and references therein.”
Tensor Decompositions for Signal Processing Applications: From two-way to multiway component analysis (2014, methodology): “Tensors were subsequently adopted in diverse branches of data analysis such as chemometrics, food industry and social sciences [7, 8].”
On the typical rank of real binary forms (2009, background): “Motivation The decomposition of tensors into a minimal sum of rank-1 terms, sometimes referred to as the canonical polyadic (CP) decomposition, has raised a great interest in several quite different branches of engineering [3,8,13,22,25,28,29] as well as in mathematics [4,6,7,20,21,23,24].”
Decompositions of a Higher-Order Tensor in Block Terms - Part II: Definitions and Uniqueness (2008, background): “PARAFAC has found important applications in signal processing and data analysis [37].”
Jacobi Algorithm for the Best Low Multilinear Rank Approximation of Symmetric Tensors (2013, methodology): “The most widely used algorithm is still the one based on alternating least squares [16, 34, 35, 3, 48] because of its simplicity and its satisfying performance.”
Tensor Decompositions and Applications (2009, background): “In section 3, we discuss the CP decomposition, its connection to tensor rank and tensor border rank, conditions for uniqueness, algorithms and computational issues, and applications.”
MACH: Fast Randomized Tensor Decompositions (2009, background): “, SVD on different 2-way slices of the tensor as observed by [24].”