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A New Algorithm for Computing Disjoint Orthogonal Components in the Three-Way Tucker Model

Author

Listed:
  • Carlos Martin-Barreiro

    (Department of Statistics, Universidad de Salamanca, 37008 Salamanca, Spain
    Faculty of Natural Sciences and Mathematics, Universidad Politécnica ESPOL, Guayaquil 090902, Ecuador)

  • John A. Ramirez-Figueroa

    (Department of Statistics, Universidad de Salamanca, 37008 Salamanca, Spain
    Faculty of Natural Sciences and Mathematics, Universidad Politécnica ESPOL, Guayaquil 090902, Ecuador)

  • Ana B. Nieto-Librero

    (Department of Statistics, Universidad de Salamanca, 37008 Salamanca, Spain
    Institute of Biomedical Research of 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
    Institute of Biomedical Research of Salamanca, 37008 Salamanca, Spain)

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.

Suggested Citation

  • Carlos Martin-Barreiro & John A. Ramirez-Figueroa & Ana B. Nieto-Librero & Víctor Leiva & Ana Martin-Casado & M. Purificación Galindo-Villardón, 2021. "A New Algorithm for Computing Disjoint Orthogonal Components in the Three-Way Tucker Model," Mathematics, MDPI, vol. 9(3), pages 1-22, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:3:p:203-:d:483453
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    References listed on IDEAS

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    7. Will Wei Sun & Junwei Lu & Han Liu & Guang Cheng, 2017. "Provable sparse tensor decomposition," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(3), pages 899-916, June.
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