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arXiv · 2203.08306

Data, geometry and homology

Jens Agerberg·Wojciech Chacholski·Ryan Ramanujam
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Abstract

Homology-based invariants can be used to characterize the geometry of datasets and thereby gain some understanding of the processes generating those datasets. In this work we investigate how the geometry of a dataset changes when it is subsampled in various ways. In our framework the dataset serves as a reference object; we then consider different points in the ambient space and endow them with a geometry defined in relation to the reference object, for instance by subsampling the dataset proportionally to the distance between its elements and the point under consideration. We illustrate how this process can be used to extract rich geometrical information, allowing for example to classify points coming from different data distributions.

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Jens Agerberg, Wojciech Chacholski, Ryan Ramanujam. 2022-03-15. Data, geometry and homology. https://arxiv.org/abs/2203.08306

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