146 citations · 344 across the 20 of their papers we have counts for
4 papers · 1 filter
Principal Component Analysis of Persistent Homology Rank Functions with case studies of Spatial Point Patterns, Sphere Packing and Colloids
Vanessa Robins, Katharine Turner
Persistent homology, while ostensibly measuring changes in topology, captures multiscale geometrical information. It is a natural tool for the analysis of point patterns. In this p…
Persistent Homology Transform for Modeling Shapes and Surfaces
Katharine Turner, Sayan Mukherjee, Doug M Boyer
In this paper we introduce a statistic, the persistent homology transform (PHT), to model surfaces in and shapes in . This statistic is a collection of…
Medians of populations of persistence diagrams
Katharine Turner
Persistence diagrams are common objects in the field of Topological Data Analysis. They are topological summaries that capture both topological and geometric structure within data.…
Fréchet Means for Distributions of Persistence diagrams
Katharine Turner, Yuriy Mileyko, Sayan Mukherjee +1
Given a distribution on persistence diagrams and observations we introduce an algorithm in this paper that estimates a Fréchet mean from the…