1 code implementation • 14 Jun 2021 • Alexander Wagner, Elchanan Solomon, Paul Bendich
We propose a novel approach to dimensionality reduction combining techniques of metric geometry and distributed persistent homology, in the form of a gradient-descent based method called DIPOLE.
no code implementations • 28 Jan 2021 • Elchanan Solomon, Alexander Wagner, Paul Bendich
Moreover, the quasi-isometry bounds depend on the size of the subsets taken, so that as the size of these subsets goes from small to large, the invariant interpolates between a purely geometric one and a topological one.
no code implementations • 17 Sep 2020 • Elchanan Solomon, Alexander Wagner, Paul Bendich
Topological statistics, in the form of persistence diagrams, are a class of shape descriptors that capture global structural information in data.
no code implementations • 30 Oct 2019 • Alexander Wagner
Persistence diagrams do not admit an inner product structure compatible with any Wasserstein metric.
no code implementations • 11 May 2019 • Peter Bubenik, Alexander Wagner
We show that persistence diagrams with the bottleneck distance do not even admit a coarse embedding into a Hilbert space.