A new algorithm for computing disjoint orthogonal components in the three-way tucker model

Carlos Martin-Barreiro; John A. Ramirez-Figueroa; Ana B. Nieto-Librero; Víctor Leiva; Ana Martin-Casado; M. Purificación Galindo-Villardón

doi:10.3390/math9030203

A new algorithm for computing disjoint orthogonal components in the three-way tucker model

Carlos Martin-Barreiro, John A. Ramirez-Figueroa, Ana B. Nieto-Librero, Víctor Leiva, Ana Martin-Casado, M. Purificación Galindo-Villardón

SCHOOL OF INDUSTRIAL ENGINEERING

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11 Scopus citations

Abstract

One of the main drawbacks of the traditional methods for computing components in the three-way Tucker model is the complex structure of the final loading matrices preventing an easy interpretation of the obtained results. In this paper, we propose a heuristic algorithm for computing disjoint orthogonal components facilitating the analysis of three-way data and the interpretation of results. We observe in the computational experiments carried out that our novel algorithm ameliorates this drawback, generating final loading matrices with a simple structure and then easier to interpret. Illustrations with real data are provided to show potential applications of the algorithm.

Original language	English
Article number	203
Pages (from-to)	1-22
Number of pages	22
Journal	Mathematics
Volume	9
Issue number	3
DOIs	https://doi.org/10.3390/math9030203
State	Published - Jan 2021

Keywords

Greedy algorithms
Heuristic algorithms
PCA
R software
Singular value decomposition
Three-way tables
Tucker3 model

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10.3390/math9030203

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title = "A new algorithm for computing disjoint orthogonal components in the three-way tucker model",

abstract = "One of the main drawbacks of the traditional methods for computing components in the three-way Tucker model is the complex structure of the final loading matrices preventing an easy interpretation of the obtained results. In this paper, we propose a heuristic algorithm for computing disjoint orthogonal components facilitating the analysis of three-way data and the interpretation of results. We observe in the computational experiments carried out that our novel algorithm ameliorates this drawback, generating final loading matrices with a simple structure and then easier to interpret. Illustrations with real data are provided to show potential applications of the algorithm.",

keywords = "Greedy algorithms, Heuristic algorithms, PCA, R software, Singular value decomposition, Three-way tables, Tucker3 model",

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AU - Ramirez-Figueroa, John A.

AU - Nieto-Librero, Ana B.

AU - Leiva, Víctor

AU - Martin-Casado, Ana

AU - Purificación Galindo-Villardón, M.

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N2 - One of the main drawbacks of the traditional methods for computing components in the three-way Tucker model is the complex structure of the final loading matrices preventing an easy interpretation of the obtained results. In this paper, we propose a heuristic algorithm for computing disjoint orthogonal components facilitating the analysis of three-way data and the interpretation of results. We observe in the computational experiments carried out that our novel algorithm ameliorates this drawback, generating final loading matrices with a simple structure and then easier to interpret. Illustrations with real data are provided to show potential applications of the algorithm.

AB - One of the main drawbacks of the traditional methods for computing components in the three-way Tucker model is the complex structure of the final loading matrices preventing an easy interpretation of the obtained results. In this paper, we propose a heuristic algorithm for computing disjoint orthogonal components facilitating the analysis of three-way data and the interpretation of results. We observe in the computational experiments carried out that our novel algorithm ameliorates this drawback, generating final loading matrices with a simple structure and then easier to interpret. Illustrations with real data are provided to show potential applications of the algorithm.

KW - Greedy algorithms

KW - Heuristic algorithms

KW - PCA

KW - R software

KW - Singular value decomposition

KW - Three-way tables

KW - Tucker3 model

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JF - Mathematics

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ER -

A new algorithm for computing disjoint orthogonal components in the three-way tucker model

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