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A New Algorithm for Computing Disjoint Orthogonal Components in the Parallel Factor Analysis Model with Simulations and Applications to Real-World Data

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)

  • Xavier Cabezas

    (Faculty of Natural Sciences and Mathematics, Universidad Politécnica ESPOL, Guayaquil 090902, Ecuador)

  • Victor 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)

Abstract

In this paper, we extend the use of disjoint orthogonal components to three-way table analysis with the parallel factor analysis model. Traditional methods, such as scaling, orthogonality constraints, non-negativity constraints, and sparse techniques, do not guarantee that interpretable loading matrices are obtained in this model. We propose a novel heuristic algorithm that allows simple structure loading matrices to be obtained by calculating disjoint orthogonal components. This algorithm is also an alternative approach for solving the well-known degeneracy problem. We carry out computational experiments by utilizing simulated and real-world data to illustrate the benefits of the proposed algorithm.

Suggested Citation

  • Carlos Martin-Barreiro & John A. Ramirez-Figueroa & Xavier Cabezas & Victor Leiva & Ana Martin-Casado & M. Purificación Galindo-Villardón, 2021. "A New Algorithm for Computing Disjoint Orthogonal Components in the Parallel Factor Analysis Model with Simulations and Applications to Real-World Data," Mathematics, MDPI, vol. 9(17), pages 1-22, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2058-:d:622331
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    References listed on IDEAS

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    1. Giordani, Paolo & Kiers, Henk A. L. & Del Ferraro, Maria Antonietta, 2014. "Three-Way Component Analysis Using the R Package ThreeWay," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 57(i07).
    2. J. Carroll & Jih-Jie Chang, 1970. "Analysis of individual differences in multidimensional scaling via an n-way generalization of “Eckart-Young” decomposition," Psychometrika, Springer;The Psychometric Society, vol. 35(3), pages 283-319, September.
    3. Caro-Lopera, Francisco J. & Leiva, Víctor & Balakrishnan, N., 2012. "Connection between the Hadamard and matrix products with an application to matrix-variate Birnbaum-Saunders distributions," Journal of Multivariate Analysis, Elsevier, vol. 104(1), pages 126-139, February.
    4. Vichi, Maurizio & Saporta, Gilbert, 2009. "Clustering and disjoint principal component analysis," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 3194-3208, June.
    5. Tomasi, Giorgio & Bro, Rasmus, 2006. "A comparison of algorithms for fitting the PARAFAC model," Computational Statistics & Data Analysis, Elsevier, vol. 50(7), pages 1700-1734, April.
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    Cited by:

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    3. Alma Y. Alanis, 2022. "Bioinspired Intelligent Algorithms for Optimization, Modeling and Control: Theory and Applications," Mathematics, MDPI, vol. 10(13), pages 1-2, July.

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