Tuning the Performance of a Computational Persistent Homology Package

In recent years, persistent homology has become an attractive method for data analysis. It captures topological features, such as connected components, holes, and voids from point cloud data and summarizes the way in which these features appear and disappear in a filtration sequence. In this project, we focus on improving the performanceof Eirene, a computational package for persistent homology. Eirene is a 5000-line open-source software library implemented in the dynamic programming language Julia. We use the Julia profiling tools to identify performance bottlenecks and develop novel methods to manage them, including the parallelization of some time-consuming functions on multicore/manycore hardware. Empirical results show that performance can be greatly improved

Hypergraph Topological Features for Autoencoder-Based Intrusion Detection for Cybersecurity Data

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. Consequently, these features capture complex correlations that can then serve as high fidelity inputs to autoencoder-driven anomaly detection pipelines. We propose two such potential pipelines for cybersecurity data, one that uses an autoencoder directly to determine network intrusions, and one that de-noises input data for a persistent homology system, PHANTOM. We provide heuristic justification for the use of the methods described therein for an intrusion detection pipeline for cyber data. We conclude by showing a small example over synthetic cyber attack data

Stepping out of Flatland: Discovering Behavior Patterns as Topological Structures in Cyber Hypergraphs

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 internet-of-things devices, shift to remote work during the pandemic, and advancement in adversarial techniques, which all contribute to the increase in both the complexity of data captured and the challenge of protecting our networks. At the same time, cyber research has made strides, leveraging advances in machine learning and natural language processing to focus on identifying sophisticated attacks that are known to evade conventional measures. While successful, the shortcomings of these methods, particularly the lack of interpretability, are inherent and difficult to overcome. Consequently, there is an ever-increasing need to develop new tools for analyzing cyber data to enable more effective attack detection. In this paper, we present a novel framework based in the theory of hypergraphs and topology to understand data from cyber networks through topological signatures, which are both flexible and can be traced back to the log data. While our approach's mathematical grounding requires some technical development, this pays off in interpretability, which we will demonstrate with concrete examples in a large-scale cyber network dataset. These examples are an introduction to the broader possibilities that lie ahead; our goal is to demonstrate the value of applying methods from the burgeoning fields of hypernetwork science and applied topology to understand relationships among behaviors in cyber data.Comment: 18 pages, 11 figures. This paper is written for a general audienc