35 citations · 52 across the 5 of their papers we have counts for
7 papers
Improving Metric Dimensionality Reduction with Distributed Topology
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…
From Geometry to Topology: Inverse Theorems for Distributed Persistence
Elchanan Solomon, Alexander Wagner, Paul Bendich
What is the "right" topological invariant of a large point cloud X? Prior research has focused on estimating the full persistence diagram of X, a quantity that is very expensive to…
A Fast and Robust Method for Global Topological Functional Optimization
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. The mapping from data structures t…
Portfolio Optimization with Expectile and Omega Functions
Alexander Wagner, Stan Uryasev
This paper proves equivalences of portfolio optimization problems with negative expectile and omega ratio. We derive subgradients for the negative expectile as a function of the po…
Nonembeddability of Persistence Diagrams with Wasserstein Metric
Alexander Wagner
Persistence diagrams do not admit an inner product structure compatible with any Wasserstein metric. Hence, when applying kernel methods to persistence diagrams, the underlying fea…
Embeddings of Persistence Diagrams into Hilbert Spaces
Peter Bubenik, Alexander Wagner
Since persistence diagrams do not admit an inner product structure, a map into a Hilbert space is needed in order to use kernel methods. It is natural to ask if such maps necessari…