32 citations · 69 across the 25 of their papers we have counts for
29 papers
TAGTorch: A PyTorch Library for Geometry, Topology, and Symmetry-Aware Machine Learning
Brendan Kennedy, Tegan Emerson, Gregory Roek +2
Over the last decade, neural networks have been applied to an increasingly diverse range of applications, including data with rich geometric, topological, or symmetry-related struc…
Large Language Model-Based Reward Design for Deep Reinforcement Learning-Driven Autonomous Cyber Defense
Sayak Mukherjee, Samrat Chatterjee, Emilie Purvine +2
Designing rewards for autonomous cyber attack and defense learning agents in a complex, dynamic environment is a challenging task for subject matter experts. We propose a large lan…
Hypergraph Topological Features for Autoencoder-Based Intrusion Detection for Cybersecurity Data
Bill Kay, Sinan G. Aksoy, Molly Baird +8
In this position paper, we argue that when hypergraphs are used to capture multi-way local relations of data, their resulting topological features describe global behaviour. Conseq…
Stepping out of Flatland: Discovering Behavior Patterns as Topological Structures in Cyber Hypergraphs
Helen Jenne, Sinan G. Aksoy, Daniel Best +9
Data breaches and ransomware attacks occur so often that they have become part of our daily news cycle. This is due to a myriad of factors, including the increasing number of inter…
HyperNetX: A Python package for modeling complex network data as hypergraphs
Brenda Praggastis, Sinan Aksoy, Dustin Arendt +5
HyperNetX (HNX) is an open source Python library for the analysis and visualization of complex network data modeled as hypergraphs. Initially released in 2019, HNX facilitates expl…
Malicious Cyber Activity Detection Using Zigzag Persistence
Audun Myers, Alyson Bittner, Sinan Aksoy +8
In this study we synthesize zigzag persistence from topological data analysis with autoencoder-based approaches to detect malicious cyber activity and derive analytic insights. Cyb…
Topological Analysis of Temporal Hypergraphs
Audun Myers, Cliff Joslyn, Bill Kay +3
In this work we study the topological properties of temporal hypergraphs. Hypergraphs provide a higher dimensional generalization of a graph that is capable of capturing multi-way…
Experimental Observations of the Topology of Convolutional Neural Network Activations
Emilie Purvine, Davis Brown, Brett Jefferson +6
Topological data analysis (TDA) is a branch of computational mathematics, bridging algebraic topology and data science, that provides compact, noise-robust representations of compl…
The SVD of Convolutional Weights: A CNN Interpretability Framework
Brenda Praggastis, Davis Brown, Carlos Ortiz Marrero +3
Deep neural networks used for image classification often use convolutional filters to extract distinguishing features before passing them to a linear classifier. Most interpretabil…
Proceedings of TDA: Applications of Topological Data Analysis to Data Science, Artificial Intelligence, and Machine Learning Workshop at SDM 2022
R. W. R. Darling, John A. Emanuello, Emilie Purvine +1
Topological Data Analysis (TDA) is a rigorous framework that borrows techniques from geometric and algebraic topology, category theory, and combinatorics in order to study the "sha…
Sheaves as a Framework for Understanding and Interpreting Model Fit
Henry Kvinge, Brett Jefferson, Cliff Joslyn +1
As data grows in size and complexity, finding frameworks which aid in interpretation and analysis has become critical. This is particularly true when data comes from complex system…
Topological Simplifications of Hypergraphs
Youjia Zhou, Archit Rathore, Emilie Purvine +1
We study hypergraph visualization via its topological simplification. We explore both vertex simplification and hyperedge simplification of hypergraphs using tools from topological…
Argumentative Topology: Finding Loop(holes) in Logic
Sarah Tymochko, Zachary New, Lucius Bynum +4
Advances in natural language processing have resulted in increased capabilities with respect to multiple tasks. One of the possible causes of the observed performance gains is the…
Hypergraph Models of Biological Networks to Identify Genes Critical to Pathogenic Viral Response
Song Feng, Emily Heath, Brett Jefferson +25
Background: Representing biological networks as graphs is a powerful approach to reveal underlying patterns, signatures, and critical components from high-throughput biomolecular d…
Directional Laplacian Centrality for Cyber Situational Awareness
Sinan G. Aksoy, Emilie Purvine, Stephen J. Young
Cyber operations is drowning in diverse, high-volume, multi-source data. In order to get a full picture of current operations and identify malicious events and actors analysts must…
Hypernetwork Science: From Multidimensional Networks to Computational Topology
Cliff A. Joslyn, Sinan Aksoy, Tiffany J. Callahan +5
As data structures and mathematical objects used for complex systems modeling, hypergraphs sit nicely poised between on the one hand the world of network models, and on the other t…
A Sheaf Theoretical Approach to Uncertainty Quantification of Heterogeneous Geolocation Information
Cliff Joslyn, Lauren Charles, Chris DePerno +7
Integration of heterogeneous sensors is a challenging problem across a range of applications. Prominent among these are multi-target tracking, where one must combine observations f…
Relative Hausdorff Distance for Network Analysis
Sinan G. Aksoy, Kathleen E. Nowak, Emilie Purvine +1
Similarity measures are used extensively in machine learning and data science algorithms. The newly proposed graph Relative Hausdorff (RH) distance is a lightweight yet nuanced sim…
Hypernetwork Science via High-Order Hypergraph Walks
Sinan G. Aksoy, Cliff Joslyn, Carlos Ortiz Marrero +2
We propose high-order hypergraph walks as a framework to generalize graph-based network science techniques to hypergraphs. Edge incidence in hypergraphs is quantitative, yielding h…
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…
Local homology of abstract simplicial complexes
Michael Robinson, Chris Capraro, Cliff Joslyn +4
This survey describes some useful properties of the local homology of abstract simplicial complexes. Although the existing literature on local homology is somewhat dispersed, it is…
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…
A generative graph model for electrical infrastructure networks
Sinan G. Aksoy, Emilie Purvine, Eduardo Cotilla-Sanchez +1
We propose a generative graph model for electrical infrastructure networks that accounts for heterogeneity in both node and edge type. To inform the model design, we analyze the pr…