Comparative analysis of the global innovation index combining the graph visualization and topological data analysis approaches - Rolando Ismael Yépez; Maricela Fernanda Ormaza (Revista de Investigación, Desarrollo e Innovación)
This study analyzes the Global Innovation Index (GII) of the 100 most innovative countries in 2022 and 2023, applying the Fruchterman-Reingold algorithm to obtain a spatial distribution of the data and utilizing persistent homology with Vietoris-Rips complexes at three scales (ε = 0.3, 1.0, and 1.5) to form connected components or structures. The results reveal evolutionary patterns in the global innovation ecosystem. With ε = 0.3, connected components increase from 13 to 14 between 2022 and 2023, reflecting fragmentation that captures heterogeneity in innovation levels, with innovation islands such as Switzerland, United States, and Sweden appearing isolated from developing economies. At ε = 1.5, complete unification into a single connected component is observed, revealing an underlying continuity in the global innovation spectrum. This methodology complements traditional approaches by revealing structural transitions and topological distances between countries, providing a foundation for strategic interventions that could reduce persistent inequalities between innovation leaders and followers.