Desarrollo de una librería de software de código abierto para el análisis de datos de tres vías mediante los modelos Disjoint-PARAFAC y Disjoint-Tucker3

Abstract

CONDITION FOR PROJECT PUBLICATION. This project aims to develop and implement a computational library for three-way data analysis using Tucker3 and PARAFAC models with orthogonal disjoint components, based on the hypothesis that enforcing disjointness improves interpretability without significantly compromising the explanatory power of the model. The motivation for this study lies in the need for analytical tools that facilitate the understanding of latent structures in complex multivariate data, reducing issues such as cross-loadings and degeneracy commonly observed in traditional approaches. The project was developed through the implementation of multilinear decomposition algorithms in the Python and R programming languages, employing linear algebra techniques, singular value decomposition, and iterative optimization schemes. Both simulated datasets and a real dataset consisting of socioeconomic indicators from several countries over multiple years were used, organized in the form of a three-dimensional tensor. The results demonstrated that the disjoint models produced clearer and more structured loading matrices, allowing a unique assignment of each entity to a specific component. In addition, a reduction in component overlap and improved solution stability were observed. It is concluded that the incorporation of disjoint components into Tucker3 and PARAFAC models represents an effective alternative for three-way data analysis, providing enhanced interpretability, robustness, and reproducibility for future multivariate applications. Keywords: three-way analysis, Tucker3, PARAFAC, disjoint components, multivariate