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; VICTOR ELISEO LEIVA SANCHEZ; 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, VICTOR ELISEO LEIVA SANCHEZ, Ana Martin-Casado, M. Purificación Galindo-Villardón

Research output: Contribution to journal › Article › peer-review

5 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
Externally published	Yes

Keywords

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

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10.3390/math9030203

Cite this

@article{53d47fae10884f5e9512edeaf0d584fe,

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",

author = "Carlos Martin-Barreiro and Ramirez-Figueroa, {John A.} and Nieto-Librero, {Ana B.} and {LEIVA SANCHEZ}, {VICTOR ELISEO} and Ana Martin-Casado and {Purificaci{\'o}n Galindo-Villard{\'o}n}, M.",

year = "2021",

month = jan,

doi = "10.3390/math9030203",

language = "English",

volume = "9",

pages = "1--22",

journal = "Mathematics",

issn = "2227-7390",

number = "3",

}

A new algorithm for computing disjoint orthogonal components in the three-way tucker model. / Martin-Barreiro, Carlos; Ramirez-Figueroa, John A.; Nieto-Librero, Ana B.; LEIVA SANCHEZ, VICTOR ELISEO; Martin-Casado, Ana; Purificación Galindo-Villardón, M.

In: Mathematics, Vol. 9, No. 3, 203, 01.2021, p. 1-22.

Research output: Contribution to journal › Article › peer-review

TY - JOUR

T1 - A new algorithm for computing disjoint orthogonal components in the three-way tucker model

AU - Martin-Barreiro, Carlos

AU - Ramirez-Figueroa, John A.

AU - Nieto-Librero, Ana B.

AU - LEIVA SANCHEZ, VICTOR ELISEO

AU - Martin-Casado, Ana

AU - Purificación Galindo-Villardón, M.

PY - 2021/1

Y1 - 2021/1

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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DO - 10.3390/math9030203

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JO - Mathematics

JF - Mathematics

SN - 2227-7390

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ER -

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

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