146 citations · 344 across the 20 of their papers we have counts for
26 papers
The Reeb Transform
Erin Chambers, Shankha Shubhra Mukherjee, Katharine Turner
Reeb Transforms offer a compact representation of how shapes in change when sliced along varying directions. We define the Reeb Transform as the family of Reeb graph…
When lookout sees crackle: Anomaly detection via kernel density estimation
Rob J Hyndman, Sevvandi Kandanaarachchi, Katharine Turner
We present an updated version of lookout -- an algorithm for detecting anomalies using kernel density estimates with bandwidth based on Rips death diameters -- with theoretical gua…
Planar Symmetry Detection and Quantification using the Extended Persistent Homology Transform
Nicholas Bermingham, Vanessa Robins, Katharine Turner
Symmetry is ubiquitous throughout nature and can often give great insights into the formation, structure and stability of objects studied by mathematicians, physicists, chemists an…
Representing Vineyard Modules
Katharine Turner
Time-series of persistence diagrams, more commonly known as vineyards, are a useful way to capture how multi-scale topological features vary over time. However, we do lose signific…
Computation of degree-1 persistent homology on larger point-clouds using the Reduced Vietoris-Rips filtration
Musashi Ayrton Koyama, Facundo Mémoli, Vanessa Robins +1
Computing Persistent Homology for large point clouds remains a bottleneck for the wider adoption of persistent homology by the scientific community. We present an algorithm which c…
The Extended Persistent Homology Transform of manifolds with boundary
Katharine Turner, Vanessa Robins, James Morgan
The Extended Persistent Homology Transform (XPHT) is a topological transform which takes as input a shape embedded in Euclidean space, and to each unit vector assigns the extended…
Graph Pseudometrics from a Topological Point of View
Ana Lucia Garcia-Pulido, Kathryn Hess, Jane Tan +3
We explore pseudometrics for directed graphs in order to better understand their topological properties. The directed flag complex associated to a directed graph provides a useful…
Notes on an Elementary Proof for the Stability of Persistence Diagrams
Primoz Skraba, Katharine Turner
These notes are a self-contained short proof of the stability of persistence diagrams.
Towards Stratified Space Learning: Linearly Embedded Graphs
Yossi Bokor, Katharine Turner, Christopher Williams
In this paper, we consider the simplest class of stratified spaces -- linearly embedded graphs. We present an algorithm that learns the abstract structure of an embedded graph and…
Wasserstein Stability for Persistence Diagrams
Primoz Skraba, Katharine Turner
The stability of persistence diagrams is among the most important results in applied and computational topology. Most results in the literature phrase stability in terms of the bot…
Stratified Space Learning: Reconstructing Embedded Graphs
Yossi Bokor, Daniel Grixti-Cheng, Markus Hegland +2
Many data-rich industries are interested in the efficient discovery and modelling of structures underlying large data sets, as it allows for the fast triage and dimension reduction…
Intrinsic Interleaving Distance for Merge Trees
Ellen Gasparovic, Elizabeth Munch, Steve Oudot +3
Merge trees are a type of graph-based topological summary that tracks the evolution of connected components in the sublevel sets of scalar functions. They enjoy widespread applicat…
Same But Different: Distance Correlations Between Topological Summaries
Katharine Turner, Gard Spreemann
Persistent homology allows us to create topological summaries of complex data. In order to analyse these statistically, we need to choose a topological summary and a relevant metri…
How Many Directions Determine a Shape and other Sufficiency Results for Two Topological Transforms
Justin Curry, Sayan Mukherjee, Katharine Turner
In this paper we consider two topological transforms that are popular in applied topology: the Persistent Homology Transform (PHT) and the Euler Characteristic Transform (ECT). Bot…
Fitting Markovian binary trees using global and individual demographic data
Sophie Hautphenne, Melanie Massaro, Katharine Turner
We consider a class of branching processes called Markovian binary trees, in which the individuals lifetime and reproduction epochs are modeled using a transient Markovian arrival…
Rips filtrations for quasi-metric spaces and asymmetric functions with stability results
Katharine Turner
The Rips filtration over a finite metric space and its corresponding persistent homology are prominent methods in TDA to summarise the shape of data. Crucial to their use is the bo…
Topological analysis of the connectome of digital reconstructions of neural microcircuits
Pawe Dotko, Kathryn Hess, Ran Levi +6
A recent publication provides the network graph for a neocortical microcircuit comprising 8 million connections between 31,000 neurons (H. Markram, et al., Reconstruction and simul…
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…
Hypothesis Testing for Topological Data Analysis
Andrew Robinson, Katharine Turner
Persistent homology is a vital tool for topological data analysis. Previous work has developed some statistical estimators for characteristics of collections of persistence diagram…
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.…
Probabilistic Fréchet Means for Time Varying Persistence Diagrams
Elizabeth Munch, Katharine Turner, Paul Bendich +3
In order to use persistence diagrams as a true statistical tool, it would be very useful to have a good notion of mean and variance for a set of diagrams. In 2011, Mileyko and his…
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…
Harmonic tori in de Sitter spaces
Emma Carberry, Katharine Turner
We show that all superconformal harmonic immersions from genus one surfaces into de Sitter spaces with globally defined harmonic sequence are of finite-type and henc…