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Peter Bubenik: Distances for Topological Data Analysis

Time: Tue 2021-02-02 16.15

Location: Zoom, meeting ID: 625 8662 8413

Participating: Peter Bubenik, University of Florida

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Abstract

Topological data analysis starts with encoding data as a diagram of topological spaces. To this diagram we apply standard topological, algebraic, and combinatorial tools to produce a summary of our data. Now we would like to be able perform a quantitative analysis. I will show how a family of distances, called Wasserstein distances, arise in a natural way, and how an extension of these ideas produces a summary for which we have not only distances but also angles (in fact, a Hilbert space) allowing us to apply statistics and machine learning.