73 citations · 141 across the 26 of their papers we have counts for
33 papers
Query Complexity of Densest Sub(hyper)graph Problems
Sinan G. Aksoy, Eli Friedman, Nate Veldt +1
Rubinstein et al. introduce the study of connectivity and minimum cut problems in the cut query model, where an algorithm can only access the edges of a graph through CUT queries.…
Re-imagining Spectral Graph Theory
Sinan G. Aksoy, Stephen J. Young
We propose a Laplacian based on general inner product spaces, which we call the inner product Laplacian. We show the combinatorial and normalized graph Laplacians, as well as other…
HyperMagNet: A Magnetic Laplacian based Hypergraph Neural Network
Tatyana Benko, Martin Buck, Ilya Amburg +2
In data science, hypergraphs are natural models for data exhibiting multi-way relations, whereas graphs only capture pairwise. Nonetheless, many proposed hypergraph neural networks…
Randomized Algorithms for Symmetric Nonnegative Matrix Factorization
Koby Hayashi, Sinan G. Aksoy, Grey Ballard +1
Symmetric Nonnegative Matrix Factorization (SymNMF) is a technique in data analysis and machine learning that approximates a symmetric matrix with a product of a nonnegative, low-r…
Fast Parallel Tensor Times Same Vector for Hypergraphs
Shruti Shivakumar, Ilya Amburg, Sinan G. Aksoy +3
Hypergraphs are a popular paradigm to represent complex real-world networks exhibiting multi-way relationships of varying sizes. Mining centrality in hypergraphs via symmetric adja…
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…
Scalable tensor methods for nonuniform hypergraphs
Sinan G. Aksoy, Ilya Amburg, Stephen J. Young
While multilinear algebra appears natural for studying the multiway interactions modeled by hypergraphs, tensor methods for general hypergraphs have been stymied by theoretical and…
Filtering higher-order datasets
Nicholas W. Landry, Ilya Amburg, Mirah Shi +1
Many complex systems often contain interactions between more than two nodes, known as higher-order interactions, which can change the structure of these systems in significant ways…
Seven open problems in applied combinatorics
Sinan G. Aksoy, Ryan Bennink, Yuzhou Chen +10
We present and discuss seven different open problems in applied combinatorics. The application areas relevant to this compilation include quantum computing, algorithmic differentia…
Skew-Symmetric Adjacency Matrices for Clustering Directed Graphs
Koby Hayashi, Sinan G. Aksoy, Haesun Park
Cut-based directed graph (digraph) clustering often focuses on finding dense within-cluster or sparse between-cluster connections, similar to cut-based undirected graph clustering…
High-order Line Graphs of Non-uniform Hypergraphs: Algorithms, Applications, and Experimental Analysis
Xu T. Liu, Jesun Firoz, Sinan Aksoy +5
Hypergraphs offer flexible and robust data representations for many applications, but methods that work directly on hypergraphs are not readily available and tend to be prohibitive…
SpectralFly: Ramanujan Graphs as Flexible and Efficient Interconnection Networks
Stephen Young, Sinan Aksoy, Jesun Firoz +5
In recent years, graph theoretic considerations have become increasingly important in the design of HPC interconnection topologies. One approach is to seek optimal or near-optimal…
Parallel Algorithms and Heuristics for Efficient Computation of High-Order Line Graphs of Hypergraphs
Xu T. Liu, Jesun Firoz, Andrew Lumsdaine +4
This paper considers structures of systems beyond dyadic (pairwise) interactions and investigates mathematical modeling of multi-way interactions and connections as hypergraphs, wh…
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…
Hypergraph Random Walks, Laplacians, and Clustering
Koby Hayashi, Sinan G. Aksoy, Cheong Hee Park +1
We propose a flexible framework for clustering hypergraph-structured data based on recently proposed random walks utilizing edge-dependent vertex weights. When incorporating edge-d…
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…
Spectral Threshold for Extremal Cyclic Edge-Connectivity
Sinan G. Aksoy, Mark Kempton, Stephen J. Young
The cyclic edge-connectivity of a graph is the least such that there exists a set of edges whose removal disconnects into components where every component contains…
Ramanujan Graphs and the Spectral Gap of Supercomputing Topologies
Sinan G. Aksoy, Paul Bruillard, Stephen J. Young +1
Graph eigenvalues play a fundamental role in controlling structural properties, such as bisection bandwidth, diameter, and fault tolerance, which are critical considerations in the…
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…
A linear-time algorithm and analysis of graph Relative Hausdorff distance
Sinan G. Aksoy, Kathleen E. Nowak, Stephen J. Young
Graph similarity metrics serve far-ranging purposes across many domains in data science. As graph datasets grow in size, scientists need comparative tools that capture meaningful d…