Populations of Unlabelled Networks: Graph Space Geometry and Generalized Geodesic Principal Components

Autor:	Anna Calissano, Aasa Feragen, Simone Vantini
Rok vydání:	2023
Předmět:	Statistics and Probability Applied Mathematics General Mathematics Statistics Probability and Uncertainty General Agricultural and Biological Sciences Agricultural and Biological Sciences (miscellaneous)
Zdroj:	Biometrika.
ISSN:	1464-3510 0006-3444
DOI:	10.1093/biomet/asad024
Popis:	Summary Statistical analysis for populations of networks is widely applicable but challenging as networks have strongly non-Euclidean behaviour. Graph space is an exhaustive framework for studying populations of unlabelled networks which are weighted or unweighted, uni- or multi-layered, directed or undirected. Viewing graph space as the quotient of a Euclidean space with respect to a finite group action, we show that it is not a manifold, and that its curvature is unbounded from above. Within this geometrical framework we define generalized geodesic principal components, and we introduce the align all and compute algorithms, all of which allow for the computation of statistics on graph space. The statistics and algorithms are compared with existing methods and empirically validated on three real datasets, showcasing the framework potential utility. The whole framework is implemented within the geomstats Python package.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::734587947cfbf15e673e3ed86be3240d https://doi.org/10.1093/biomet/asad024 Zobrazit plný text záznamu