Metric geometry of spaces of persistence diagrams

Persistent homology and applications, topological data analysis (55N31) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Dimension theory in general topology (54F45)

Cites Work

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Using persistent homology and dynamical distances to analyze protein binding
A rigidity theorem in Alexandrov spaces with lower curvature bound
Gromov-Hausdorff distance for pointed metric spaces
Large scale geometry
Fréchet means for distributions of persistence diagrams
A splitting theorem for infinite dimensional Alexandrov spaces with nonnegative curvature and its applications
Stability of persistence diagrams
Asymptotic dimension
Lipschitz functions have $L_{p}$-stable persistence
On tangent cones of Alexandrov spaces with curvature bounded below
Generalized persistence diagrams
Numeric invariants from multidimensional persistence
Computing persistent homology
On the stability of interval decomposable persistence modules
Generalized persistence diagrams for persistence modules over posets
Virtual persistence diagrams, signed measures, Wasserstein distances, and Banach spaces
Universality of persistence diagrams and the bottleneck and Wasserstein distances
Embeddings of persistence diagrams into Hilbert spaces
Understanding the topology and the geometry of the space of persistence diagrams via optimal partial transport
On the spread of positively curved Alexandrov spaces
Medians of populations of persistence diagrams
Decomposition of exact pfd persistence bimodules
Optimal transport for applied mathematicians. Calculus of variations, PDEs, and modeling
The asymptotic dimension of quotients by finite groups
Riemannian $L^{p}$ center of mass: Existence, uniqueness, and convexity
Probability measures on the space of persistence diagrams
A.D. Alexandrov spaces with curvature bounded below
Kernel method for persistence diagrams via kernel embedding and weight factor
Barycenters in Alexandrov spaces of curvature bounded below
Nonembeddability of persistence diagrams with $p>2$ Wasserstein metric
The space of persistence diagrams on $n$ points coarsely embeds into Hilbert space
Asymptotic Dimension
Statistical topological data analysis using persistence landscapes
Gromov-Hausdorff convergence of metric pairs and metric tuples
Basic metric geometry of the bottleneck distance
Topological and metric properties of spaces of generalized persistence diagrams
Bi-Lipschitz embeddings of the space of unordered $m$-tuples with a partial transportation metric

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