Geometry of Data
Metric Geometry
2022-03-15 v1 Machine Learning
Differential Geometry
Abstract
Topological data analysis asks when balls in a metric space intersect. Geometric data analysis asks how much balls have to be enlarged to intersect. We connect this principle to the traditional core geometric concept of curvature. This enables us, on one hand, to reconceptualize curvature and link it to the geometric notion of hyperconvexity. On the other hand, we can then also understand methods of topological data analysis from a geometric perspective.
Cite
@article{arxiv.2203.07208,
title = {Geometry of Data},
author = {Parvaneh Joharinad and Jürgen Jost},
journal= {arXiv preprint arXiv:2203.07208},
year = {2022}
}