Geometry of Data

Parvaneh Joharinad; Jürgen Jost

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arXiv · 2203.07208

Geometry of Data

Parvaneh Joharinad·Jürgen Jost

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Abstract

Topological data analysis asks when balls in a metric space $(X,d)$ 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.

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math.MG cs.LG math.DG

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Parvaneh Joharinad, Jürgen Jost. 2022-03-14. Geometry of Data. https://arxiv.org/abs/2203.07208

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