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 and M. Purificación Galindo-Villardón
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Carlos Martin-Barreiro: Department of Statistics, Universidad de Salamanca, 37008 Salamanca, Spain
John A. Ramirez-Figueroa: Department of Statistics, Universidad de Salamanca, 37008 Salamanca, Spain
Ana B. Nieto-Librero: Department of Statistics, Universidad de Salamanca, 37008 Salamanca, Spain
Víctor Leiva: School of Industrial Engineering, Pontificia Universidad Católica de Valparaíso, Valparaíso 2362807, Chile
Ana Martin-Casado: Department of Statistics, Universidad de Salamanca, 37008 Salamanca, Spain
M. Purificación Galindo-Villardón: Department of Statistics, Universidad de Salamanca, 37008 Salamanca, Spain

Mathematics, 2021, vol. 9, issue 3, 1-22

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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