A new algorithm for computing disjoint orthogonal components in the parallel factor analysis model with simulations and applications to real-world data

Carlos Martin-Barreiro, John A. Ramirez-Figueroa, Xavier Cabezas, Victor Leiva, Ana Martin-Casado, M. Purificación Galindo-Villardón

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Article number2058
JournalMathematics
Volume9
Issue number17
DOIs
StatePublished - 1 Sep 2021
Externally publishedYes

Keywords

  • Degeneracy
  • Disjoint components
  • Heuristic algorithms
  • Parafac model
  • PCA
  • R software
  • Three-way tables

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