Search Results for author: Alexander Wagner

Found 5 papers, 1 papers with code

Improving Metric Dimensionality Reduction with Distributed Topology

1 code implementation14 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.

Dimensionality Reduction

From Geometry to Topology: Inverse Theorems for Distributed Persistence

no code implementations28 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.

A Fast and Robust Method for Global Topological Functional Optimization

no code implementations17 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.

Nonembeddability of Persistence Diagrams with $p>2$ Wasserstein Metric

no code implementations30 Oct 2019 Alexander Wagner

Persistence diagrams do not admit an inner product structure compatible with any Wasserstein metric.

Embeddings of Persistence Diagrams into Hilbert Spaces

no code implementations11 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.

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