research
∙
07/27/2023
Bounding the Interleaving Distance for Geometric Graphs with a Loss Function
A geometric graph is an abstract graph along with an embedding of the gr...
share
research
∙
06/23/2023
Using persistent homology to understand dimensionality reduction in resting-state fMRI
Evaluating the success of a manifold learning method remains a challengi...
research
∙
05/10/2023
NervePool: A Simplicial Pooling Layer
For deep learning problems on graph-structured data, pooling layers are ...
research
∙
01/18/2023
Robust Zero-crossings Detection in Noisy Signals using Topological Signal Processing
We explore a novel application of zero-dimensional persistent homology f...
research
∙
10/18/2022
Comparing Embedded Graphs Using Average Branching Distance
Graphs drawn in the plane are ubiquitous, arising from data sets through...
research
∙
05/23/2022
Temporal Network Analysis Using Zigzag Persistence
This work presents a framework for studying temporal networks using zigz...
research
∙
04/27/2022
Topological Signal Processing using the Weighted Ordinal Partition Network
One of the most important problems arising in time series analysis is th...
research
∙
10/11/2021
Reeb Graph Metrics from the Ground Up
The Reeb graph has been utilized in various applications including the a...
research
∙
07/09/2021
Realizable piecewise linear paths of persistence diagrams with Reeb graphs
Reeb graphs are widely used in a range of fields for the purposes of ana...
research
∙
10/17/2020
Automatic Tree Ring Detection using Jacobi Sets
Tree ring widths are an important source of climatic and historical data...
research
∙
09/18/2020
Using Zigzag Persistent Homology to Detect Hopf Bifurcations in Dynamical Systems
Bifurcations in dynamical systems characterize qualitative changes in th...
research
∙
07/15/2020
A family of metrics from the truncated smoothing of Reeb graphs
In this paper, we introduce an extension of smoothing on Reeb graphs, wh...
research
∙
04/29/2020
A Relative Theory of Interleavings
The interleaving distance, although originally developed for persistent ...
research
∙
02/12/2020
Graph Similarity Using PageRank and Persistent Homology
The PageRank of a graph is a scalar function defined on the node set of ...
research
∙
10/27/2019
Chatter Diagnosis in Milling Using Supervised Learning and Topological Features Vector
Chatter detection has become a prominent subject of interest due to its ...
research
∙
10/18/2019
Adaptive Partitioning for Template Functions on Persistence Diagrams
As the field of Topological Data Analysis continues to show success in t...
research
∙
09/08/2019
Probabilistic Convergence and Stability of Random Mapper Graphs
We study the probabilistic convergence between the mapper graph and the ...
research
∙
07/31/2019
A Structural Average of Labeled Merge Trees for Uncertainty Visualization
Physical phenomena in science and engineering are frequently modeled usi...
research
∙
07/31/2019
Intrinsic Interleaving Distance for Merge Trees
Merge trees are a type of graph-based topological summary that tracks th...
research
∙
04/16/2019
Persistent Homology of Complex Networks for Dynamic State Detection
In this paper we develop a novel Topological Data Analysis (TDA) approac...
research
∙
02/19/2019
Approximating Continuous Functions on Persistence Diagrams Using Template Functions
The persistence diagram is an increasingly useful tool arising from the ...
research
∙
02/17/2019
Using Persistent Homology to Quantify a Diurnal Cycle in Hurricane Felix
The diurnal cycle of tropical cyclones (TCs) is a daily cycle in clouds ...
research
∙
09/17/2018
Computing Wasserstein Distance for Persistence Diagrams on a Quantum Computer
Persistence diagrams are a useful tool from topological data analysis wh...
research
∙
05/01/2018
Topological Data Analysis for True Step Detection in Piecewise Constant Signals
This paper introduces a simple yet powerful approach based on topologica...
research
∙
03/23/2018
Chatter Classification in Turning Using Machine Learning and Topological Data Analysis
Chatter identification and detection in machining processes has been an ...
research
∙
02/28/2018