10 citations · 13 across the 5 of their papers we have counts for
8 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…
Geometric Fusion via Joint Delay Embeddings
Elchanan Solomon, Paul Bendich
We introduce geometric and topological methods to develop a new framework for fusing multi-sensor time series. This framework consists of two steps: (1) a joint delay embedding, wh…
Intrinsic Topological Transforms via the Distance Kernel Embedding
Clément Maria, Steve Oudot, Elchanan Solomon
Topological transforms are parametrized families of topological invariants, which, by analogy with transforms in signal processing, are much more discriminative than single measure…
Inverse Problems in Topological Persistence
Steve Oudot, Elchanan Solomon
In this survey, we review the literature on inverse problems in topological persistence theory. The first half of the survey is concerned with the question of surjectivity, i.e. th…
Stability of Extended Functional Persistence in Dimensions Zero and One
Elchanan Solomon
The stability result, as stated, is incorrect. In particular, the 1-dimensional extended persistence diagrams of a finely-triangulated simplicial complex X equipped with a continuo…
Barcode Embeddings for Metric Graphs
Steve Oudot, Elchanan Solomon
Stable topological invariants are a cornerstone of persistence theory and applied topology, but their discriminative properties are often poorly-understood. In this paper we study…