200 citations · 471 across the 22 of their papers we have counts for
22 papers
Topological summaries of fingerprint ridge patterns carry identity information
Chad M. Topaz, Niny Arcila-Maya, Elizabeth Munch +2
Fingerprints are the most widely deployed biometric. Verifying whether two impressions come from the same finger typically relies on minutiae, small landmarks such as skin ridge en…
A U-match Algorithm for Persistent Relative Homology
Christian Lentz, Gregory Henselman-Petrusek, Lori Ziegelmeier
A central problem in data-driven scientific inquiry is how to interpret structure in noisy, high-dimensional data. Topological data analysis (TDA) provides a solution via persisten…
Higher-Order Network Structure Inference: A Topological Approach to Network Selection
Adam Schroeder, Russell Funk, Jingyi Guan +2
Thresholding---the pruning of nodes or edges based on their properties or weights---is an essential preprocessing tool for extracting interpretable structure from complex network d…
Understanding U.S. Racial Segregation Through Persistent Homology
Ori Friesen, Lori Ziegelmeier
Racial segregation is a widespread social and physical phenomenon present in every city across the United States. Although prevalent nationwide, each city has a unique history of r…
A survey of simplicial, relative, and chain complex homology theories for hypergraphs
Ellen Gasparovic, Emilie Purvine, Radmila Sazdanovic +3
Hypergraphs have seen widespread application in network and data science communities in recent years. We present a survey of recent work to construct auxiliary structures from hype…
Image Triangulation Using the Sobel Operator for Vertex Selection
Olivia Laske, Lori Ziegelmeier
Image triangulation, the practice of decomposing images into triangles, deliberately employs simplification to create an abstracted representation. While triangulating an image is…
A Topology Scavenger Hunt to Introduce Topological Data Analysis
Lori Ziegelmeier
Topology at the undergraduate level is often a theoretical mathematics course, introducing concepts from point-set topology or possibly algebraic topology. However, the last two de…
U-match factorization: sparse homological algebra, lazy cycle representatives, and dualities in persistent (co)homology
Haibin Hang, Chad Giusti, Lori Ziegelmeier +1
Persistent homology is a leading tool in topological data analysis (TDA). Many problems in TDA can be solved via homological -- and indeed, linear -- algebra. However, matrices in…
Minimal Cycle Representatives in Persistent Homology using Linear Programming: an Empirical Study with User's Guide
Lu Li, Connor Thompson, Gregory Henselman-Petrusek +2
Cycle representatives of persistent homology classes can be used to provide descriptions of topological features in data. However, the non-uniqueness of these representatives creat…
Capturing Dynamics of Time-Varying Data via Topology
Lu Xian, Henry Adams, Chad M. Topaz +1
One approach to understanding complex data is to study its shape through the lens of algebraic topology. While the early development of topological data analysis focused primarily…
Analyzing Collective Motion with Machine Learning and Topology
Dhananjay Bhaskar, Angelika Manhart, Jesse Milzman +4
We use topological data analysis and machine learning to study a seminal model of collective motion in biology [D'Orsogna et al., Phys. Rev. Lett. 96 (2006)]. This model describes…
Local Versus Global Distances for Zigzag Persistence Modules
Ellen Gasparovic, Maria Gommel, Emilie Purvine +4
This short note establishes explicit and broadly applicable relationships between persistence-based distances computed locally and globally. In particular, we show that the bottlen…
The Relationship Between the Intrinsic Cech and Persistence Distortion Distances for Metric Graphs
Ellen Gasparovic, Maria Gommel, Emilie Purvine +4
Metric graphs are meaningful objects for modeling complex structures that arise in many real-world applications, such as road networks, river systems, earthquake faults, blood vess…
Assessing biological models using topological data analysis
M. Ulmer, Lori Ziegelmeier, Chad M. Topaz
We use topological data analysis as a tool to analyze the fit of mathematical models to experimental data. This study is built on data obtained from motion tracking groups of aphid…
On Homotopy Types of Vietoris-Rips Complexes of Metric Gluings
Michal Adamaszek, Henry Adams, Ellen Gasparovic +6
We study Vietoris-Rips complexes of metric wedge sums and metric gluings. We show that the Vietoris-Rips complex of a wedge sum, equipped with a natural metric, is homotopy equival…
Mind the Gap: A Study in Global Development through Persistent Homology
Andrew Banman, Lori Ziegelmeier
The Gapminder project set out to use statistics to dispel simplistic notions about global development. In the same spirit, we use persistent homology, a technique from computationa…
A Complete Characterization of the 1-Dimensional Intrinsic Cech Persistence Diagrams for Metric Graphs
Ellen Gasparovic, Maria Gommel, Emilie Purvine +4
Metric graphs are special types of metric spaces used to model and represent simple, ubiquitous, geometric relations in data such as biological networks, social networks, and road…
Stratifying High Dimensional Data Based on Proximity to the Convex Hull Boundary
Lori Ziegelmeier, Michael Kirby, Chris Peterson
The convex hull of a set of points, , serves to expose extremal properties of and can help identify elements in of high interest. For many problems, particularly in the…
Persistent Homology on Grassmann Manifolds for Analysis of Hyperspectral Movies
Sofya Chepushtanova, Michael Kirby, Chris Peterson +1
The existence of characteristic structure, or shape, in complex data sets has been recognized as increasingly important for mathematical data analysis. This realization has motivat…
Persistence Images: A Stable Vector Representation of Persistent Homology
Henry Adams, Sofya Chepushtanova, Tegan Emerson +7
Many datasets can be viewed as a noisy sampling of an underlying space, and tools from topological data analysis can characterize this structure for the purpose of knowledge discov…
Topological Data Analysis of Biological Aggregation Models
Chad M. Topaz, Lori Ziegelmeier, Tom Halverson
We apply tools from topological data analysis to two mathematical models inspired by biological aggregations such as bird flocks, fish schools, and insect swarms. Our data consists…
Locally Linear Embedding Clustering Algorithm for Natural Imagery
Lori Ziegelmeier, Michael Kirby, Chris Peterson
The ability to characterize the color content of natural imagery is an important application of image processing. The pixel by pixel coloring of images may be viewed naturally as p…