Calissano, A., Pereira, L., Lueg, J., Miolane, N.
Abstract
Analysis of non-Euclidean data such as graphs and trees requires (specific) mathematical machinery due to their less-rich structure when compared to Euclidean spaces or smooth Riemannian manifolds. These spaces can still leverage the rich structure of the latter. For example, graph space results from quotienting out matrices endowed with the Frobenius metric by the permutation group, Billera–Holmes–Vogtmann (BHV) space strata are Euclidean, and wald space is embedded in the space of symmetric positive definite (SPD) matrices. We present a Python package for the analysis of data living in geodesic metric spaces – topological spaces equipped with a metric and a geodesic function where the metric is the length of the shortest geodesic joining two points. We describe the package structure, based on a point, a point set, and a metric built using geodesic metric space theory, and we provide three implementation examples. The package is implemented as a plug-in of the Geomstats Python package, allowing users to access and adapt the available geometrical and data analysis tools for strongly non-Euclidean data in a theoretically consistent way. The code is unit-tested and documented.
Citation
Calissano, A., Pereira, L. F., Lueg, J., & Miolane, N. (2024). On the Implementation of Geodesic Metric Spaces.
BibTeX
@article{calissano2024implementation, title={On the Implementation of Geodesic Metric Spaces}, author={Calissano, Anna and Pereira, Lu{\'\i}s F and Lueg, Jonas and Miolane, Nina}, year={2024} }
