arXiv subjects

Audun Myers

Publications and source records attributed to Audun Myers.

At least 19 recordsLinked to original sources

arXiv2025

The Wigner-Ville Transform as an Information Theoretic Tool in Radio-frequency Signal Analysis

This paper presents novel interpretations to the field of classical signal processing of the Wigner-Ville transform as an information measurement tool. The transform's utility in detecting and localizing information-laden signals amidst noisy and cluttered backgrounds, and further providing measure of their information volumes, are detailed herein using Tsallis' entropy and information and related functionals. Example use cases in radio frequency communications are given, where Wigner-Ville-based detection measures can be seen to provide significant sensitivity advantage, for some shown contexts greater than 15~dB advantage, over energy-based measures and without extensive training routines. Such an advantage is particularly significant for applications which have limitations on observation resources including time/space integration pressures and transient and/or feeble signals, where Wigner-Ville-based methods would improve sensing effectiveness by multiple orders of magnitude. The potential for advancement of several such applications is discussed.

eess.SP↗

arXiv2025

HIF: The hypergraph interchange format for higher-order networks

Many empirical systems contain complex interactions of arbitrary size, representing, for example, chemical reactions, social groups, co-authorship relationships, and ecological dependencies. These interactions are known as higher-order interactions and the collection of these interactions comprise a higher-order network, or hypergraph. Hypergraphs have established themselves as a popular and versatile mathematical representation of such systems and a number of software packages written in various programming languages have been designed to analyze these networks. However, the ecosystem of higher-order network analysis software is fragmented due to specialization of each software's programming interface and compatible data representations. To enable seamless data exchange between higher-order network analysis software packages, we introduce the Hypergraph Interchange Format (HIF), a standardized format for storing higher-order network data. HIF supports multiple types of higher-order networks, including undirected hypergraphs, directed hypergraphs, and abstract simplicial complexes, while actively exploring extensions to represent multiplex hypergraphs, temporal hypergraphs, and ordered hypergraphs. To accommodate the wide variety of metadata used in different contexts, HIF also includes support for attributes associated with nodes, edges, and incidences. This initiative is a collaborative effort involving authors, maintainers, and contributors from prominent hypergraph software packages. This project introduces a JSON schema with corresponding documentation and unit tests, example HIF-compliant datasets, and tutorials demonstrating the use of HIF with several popular higher-order network analysis software packages.

physics.soc-ph↗

arXiv2025

Talking to GDELT Through Knowledge Graphs

In this work we study various Retrieval Augmented Regeneration (RAG) approaches to gain an understanding of the strengths and weaknesses of each approach in a question-answering analysis. To gain this understanding we use a case-study subset of the Global Database of Events, Language, and Tone (GDELT) dataset as well as a corpus of raw text scraped from the online news articles. To retrieve information from the text corpus we implement a traditional vector store RAG as well as state-of-the-art large language model (LLM) based approaches for automatically constructing KGs and retrieving the relevant subgraphs. In addition to these corpus approaches, we develop a novel ontology-based framework for constructing knowledge graphs (KGs) from GDELT directly which leverages the underlying schema of GDELT to create structured representations of global events. For retrieving relevant information from the ontology-based KGs we implement both direct graph queries and state-of-the-art graph retrieval approaches. We compare the performance of each method in a question-answering task. We find that while our ontology-based KGs are valuable for question-answering, automated extraction of the relevant subgraphs is challenging. Conversely, LLM-generated KGs, while capturing event summaries, often lack consistency and interpretability. Our findings suggest benefits of a synergistic approach between ontology and LLM-based KG construction, with proposed avenues toward that end.

cs.IR↗

arXiv2025

The Topological Structures of the Orders of Hypergraphs

We provide first a categorical exploration of, and then completion of the mapping of the relationships among, three fundamental perspectives on binary relations: as the incidence matrices of hypergraphs, as the formal contexts of concept lattices, and as specifying topological cosheaves of simplicial (Dowker) complexes on simplicial (Dowker) complexes. We provide an integrative, functorial framework combining previously known with three new results: 1) given a binary relation, there are order isomorphisms among the bounded edge order of the intersection complexes of its dual hypergraphs and its concept lattice; 2) the concept lattice of a context is an isomorphism invariant of the Dowker cosheaf (of abstract simplicial complexes) of that context; and 3) a novel Dowker cosheaf (of chain complexes) of a relation is an isomorphism invariant of the concept lattice of the context that generalizes Dowker's original homological result. We illustrate these concepts throughout with a running example, and demonstrate relationships to past results.

math.CO↗

arXiv2025

Entropic Analysis of Time Series through Kernel Density Estimation

This work presents a novel framework for time series analysis using entropic measures based on the kernel density estimate (KDE) of the time series' Takens' embeddings. Using this framework we introduce two distinct analytical tools: (1) a multi-scale KDE entropy metric, denoted as $\Delta\text{KE}$, which quantifies the evolution of time series complexity across different scales by measuring certain entropy changes, and (2) a sliding baseline method that employs the Kullback-Leibler (KL) divergence to detect changes in time series dynamics through changes in KDEs. The $\Delta{\rm KE}$ metric offers insights into the information content and ``unfolding'' properties of the time series' embedding related to dynamical systems, while the KL divergence-based approach provides a noise and outlier robust approach for identifying time series change points (injections in RF signals, e.g.). We demonstrate the versatility and effectiveness of these tools through a set of experiments encompassing diverse domains. In the space of radio frequency (RF) signal processing, we achieve accurate detection of signal injections under varying noise and interference conditions. Furthermore, we apply our methodology to electrocardiography (ECG) data, successfully identifying instances of ventricular fibrillation with high accuracy. Finally, we demonstrate the potential of our tools for dynamic state detection by accurately identifying chaotic regimes within an intermittent signal. These results show the broad applicability of our framework for extracting meaningful insights from complex time series data across various scientific disciplines.

cs.IT↗

arXiv2024

ICML Topological Deep Learning Challenge 2024: Beyond the Graph Domain

This paper describes the 2nd edition of the ICML Topological Deep Learning Challenge that was hosted within the ICML 2024 ELLIS Workshop on Geometry-grounded Representation Learning and Generative Modeling (GRaM). The challenge focused on the problem of representing data in different discrete topological domains in order to bridge the gap between Topological Deep Learning (TDL) and other types of structured datasets (e.g. point clouds, graphs). Specifically, participants were asked to design and implement topological liftings, i.e. mappings between different data structures and topological domains --like hypergraphs, or simplicial/cell/combinatorial complexes. The challenge received 52 submissions satisfying all the requirements. This paper introduces the main scope of the challenge, and summarizes the main results and findings.

cs.LG↗

arXiv2024

Permutation Entropy for Signal Analysis

Shannon Entropy is the preeminent tool for measuring the level of uncertainty (and conversely, information content) in a random variable. In the field of communications, entropy can be used to express the information content of given signals (represented as time series) by considering random variables which sample from specified subsequences. In this paper, we will discuss how an entropy variant, the \textit{permutation entropy} can be used to study and classify radio frequency signals in a noisy environment. The permutation entropy is the entropy of the random variable which samples occurrences of permutation patterns from time series given a fixed window length, making it a function of the distribution of permutation patterns. Since the permutation entropy is a function of the relative order of data, it is (global) amplitude agnostic and thus allows for comparison between signals at different scales. This article is intended to describe a permutation patterns approach to a data driven problem in radio frequency communications research, and includes a primer on all non-permutation pattern specific background. An empirical analysis of the methods herein on radio frequency data is included. No prior knowledge of signals analysis is assumed, and permutation pattern specific notation will be included. This article serves as a self-contained introduction to the relationship between permutation patterns, entropy, and signals analysis for studying radio frequency signals and includes results on a classification task.

cs.IT↗

arXiv2024

Understanding High-Order Network Structure using Permissible Walks on Attributed Hypergraphs

Hypergraphs have been a recent focus of study in mathematical data science as a tool to understand complex networks with high-order connections. One question of particular relevance is how to leverage information carried in hypergraph attributions when doing walk-based techniques. In this work, we focus on a new generalization of a walk in a network that recovers previous approaches and allows for a description of permissible walks in hypergraphs. Permissible walk graphs are constructed by intersecting the attributed $s$-line graph of a hypergraph with a relation respecting graph. The attribution of the hypergraph's line graph commonly carries over information from categorical and temporal attributions of the original hypergraph. To demonstrate this approach on a temporally attributed example, we apply our framework to a Reddit data set composed of hyperedges as threads and authors as nodes where post times are tracked.

cs.SI↗

arXiv2024

ICML 2023 Topological Deep Learning Challenge : Design and Results

This paper presents the computational challenge on topological deep learning that was hosted within the ICML 2023 Workshop on Topology and Geometry in Machine Learning. The competition asked participants to provide open-source implementations of topological neural networks from the literature by contributing to the python packages TopoNetX (data processing) and TopoModelX (deep learning). The challenge attracted twenty-eight qualifying submissions in its two-month duration. This paper describes the design of the challenge and summarizes its main findings.

cs.LG↗

arXiv2023

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.

cs.CR↗

arXiv2023

Malicious Cyber Activity Detection Using Zigzag Persistence

In this study we synthesize zigzag persistence from topological data analysis with autoencoder-based approaches to detect malicious cyber activity and derive analytic insights. Cybersecurity aims to safeguard computers, networks, and servers from various forms of malicious attacks, including network damage, data theft, and activity monitoring. Here we focus on the detection of malicious activity using log data. To do this we consider the dynamics of the data by exploring the changing topology of a hypergraph representation gaining insights into the underlying activity. Hypergraphs provide a natural representation of cyber log data by capturing complex interactions between processes. To study the changing topology we use zigzag persistence which captures how topological features persist at multiple dimensions over time. We observe that the resulting barcodes represent malicious activity differently than benign activity. To automate this detection we implement an autoencoder trained on a vectorization of the resulting zigzag persistence barcodes. Our experimental results demonstrate the effectiveness of the autoencoder in detecting malicious activity in comparison to standard summary statistics. Overall, this study highlights the potential of zigzag persistence and its combination with temporal hypergraphs for analyzing cybersecurity log data and detecting malicious behavior.

cs.CG↗

arXiv2023

Temporal Network Analysis Using Zigzag Persistence

This work presents a framework for studying temporal networks using zigzag persistence, a tool from the field of Topological Data Analysis (TDA). The resulting approach is general and applicable to a wide variety of time-varying graphs. For example, these graphs may correspond to a system modeled as a network with edges whose weights are functions of time, or they may represent a time series of a complex dynamical system. We use simplicial complexes to represent snapshots of the temporal networks that can then be analyzed using zigzag persistence. We show two applications of our method to dynamic networks: an analysis of commuting trends on multiple temporal scales, e.g., daily and weekly, in the Great Britain transportation network, and the detection of periodic/chaotic transitions due to intermittency in dynamical systems represented by temporal ordinal partition networks. Our findings show that the resulting zero- and one-dimensional zigzag persistence diagrams can detect changes in the networks' shapes that are missed by traditional connectivity and centrality graph statistics.

cs.CG↗

arXiv2023

Formal Concept Lattice Representations and Algorithms for Hypergraphs

There is increasing focus on analyzing data represented as hypergraphs, which are better able to express complex relationships amongst entities than are graphs. Much of the critical information about hypergraph structure is available only in the intersection relationships of the hyperedges, and so forming the "intersection complex" of a hypergraph is quite valuable. This identifies a valuable isomorphism between the intersection complex and the "concept lattice" formed from taking the hypergraph's incidence matrix as a "formal context": hypergraphs also generalize graphs in that their incidence matrices are arbitrary Boolean matrices. This isomorphism allows connecting discrete algorithms for lattices and hypergraphs, in particular s-walks or s-paths on hypergraphs can be mapped to order theoretical operations on the concept lattice. We give new algorithms for formal concept lattices and hypergraph s-walks on concept lattices. We apply this to a large real-world dataset and find deep lattices implying high interconnectivity and complex geometry of hyperedges.

cs.DS↗

arXiv2023

Topological Analysis of Temporal Hypergraphs

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 connections. As such, they have become an integral part of network science. A common use of hypergraphs is to model events as hyperedges in which the event can involve many elements as nodes. This provides a more complete picture of the event, which is not limited by the standard dyadic connections of a graph. However, a common attribution to events is temporal information as an interval for when the event occurred. Consequently, a temporal hypergraph is born, which accurately captures both the temporal information of events and their multi-way connections. Common tools for studying these temporal hypergraphs typically capture changes in the underlying dynamics with summary statistics of snapshots sampled in a sliding window procedure. However, these tools do not characterize the evolution of hypergraph structure over time, nor do they provide insight on persistent components which are influential to the underlying system. To alleviate this need, we leverage zigzag persistence from the field of Topological Data Analysis (TDA) to study the change in topological structure of time-evolving hypergraphs. We apply our pipeline to both a cyber security and social network dataset and show how the topological structure of their temporal hypergraphs change and can be used to understand the underlying dynamics.

cs.CG↗

arXiv2022

Topological Signal Processing using the Weighted Ordinal Partition Network

One of the most important problems arising in time series analysis is that of bifurcation, or change point detection. That is, given a collection of time series over a varying parameter, when has the structure of the underlying dynamical system changed? For this task, we turn to the field of topological data analysis (TDA), which encodes information about the shape and structure of data. The idea of utilizing tools from TDA for signal processing tasks, known as topological signal processing (TSP), has gained much attention in recent years, largely through a standard pipeline that computes the persistent homology of the point cloud generated by the Takens' embedding. However, this procedure is limited by computation time since the simplicial complex generated in this case is large, but also has a great deal of redundant data. For this reason, we turn to a more recent method for encoding the structure of the attractor, which constructs an ordinal partition network (OPN) representing information about when the dynamical system has passed between certain regions of state space. The result is a weighted graph whose structure encodes information about the underlying attractor. Our previous work began to find ways to package the information of the OPN in a manner that is amenable to TDA; however, that work only used the network structure and did nothing to encode the additional weighting information. In this paper, we take the next step: building a pipeline to analyze the weighted OPN with TDA and showing that this framework provides more resilience to noise or perturbations in the system and improves the accuracy of the dynamic state detection.

stat.ML↗

arXiv2020

Dynamic State Analysis of a Driven Magnetic Pendulum using Ordinal Partition Networks and Topological Data Analysis

The use of complex networks for time series analysis has recently shown to be useful as a tool for detecting dynamic state changes for a wide variety of applications. In this work, we implement the commonly used ordinal partition network to transform a time series into a network for detecting these state changes for the simple magnetic pendulum. The time series that we used are obtained experimentally from a base-excited magnetic pendulum apparatus, and numerically from the corresponding governing equations.The magnetic pendulum provides a relatively simple, non-linear example demonstrating transitions from periodic to chaotic motion with the variation of system parameters. For our method, we implement persistent homology, a shape measuring tool from Topological Data Analysis (TDA), to summarize the shape of the resulting ordinal partition networks as a tool for detecting state changes. We show that this network analysis tool provides a clear distinction between periodic and chaotic time series. Another contribution of this work is the successful application of the networks-TDA pipeline, for the first time, to signals from non-autonomous nonlinear systems. This opens the door for our approach to be used as an automatic design tool for studying the effect of design parameters on the resulting system response. Other uses of this approach include fault detection from sensor signals in a wide variety of engineering operations.

physics.data-an↗

arXiv2020

Effects of Correlated Noise on the Performance of Persistence Based Dynamic State Detection Methods

The ability to characterize the state of dynamic systems has been a pertinent task in the time series analysis community. Traditional measures such as Lyapunov exponents are often times difficult to recover from noisy data, especially if the dimensionality of the system is not known. More recent binary and network based testing methods have delivered promising results for unknown deterministic systems, however noise injected into a periodic signal leads to false positives. Recently, we showed the advantage of using persistent homology as a tool for achieving dynamic state detection for systems with no known model and showed its robustness to white Gaussian noise. In this work, we explore the robustness of the persistence based methods to the influence of colored noise and show that colored noise processes of the form $1/f^α$ lead to false positive diagnostic at lower signal to noise ratios for $α<0$.

eess.SP↗

arXiv2020

On the Automatic Parameter Selection for Permutation Entropy

Permutation Entropy (PE) has been shown to be a useful tool for time series analysis due to its low computational cost and noise robustness. This has drawn for its successful application in many fields. Some of these include damage detection, disease forecasting, and financial volatility analysis. However, to successfully use PE, an accurate selection of two parameters is needed: the permutation dimension $n$ and embedding delay $τ$. These parameters are often suggested by experts based on a heuristic or by a trial and error approach. unfortunately, both of these methods can be time-consuming and lead to inaccurate results. To help combat this issue, in this paper we investigate multiple schemes for automatically selecting these parameters with only the corresponding time series as the input. Specifically, we develop a frequency-domain approach based on the least median of squares and the Fourier spectrum, as well as extend two existing methods: Permutation Auto-Mutual Information (PAMI) and Multi-scale Permutation Entropy (MPE) for determining $τ$. We then compare our methods as well as current methods in the literature for obtaining both $τ$ and $n$ against expert-suggested values in published works. We show that the success of any method in automatically generating the correct PE parameters depends on the category of the studied system. Specifically, for the delay parameter $τ$, we show that our frequency approach provides accurate suggestions for periodic systems, nonlinear difference equations, and ECG/EEG data, while the mutual information function computed using adaptive partitions provides the most accurate results for chaotic differential equations. For the permutation dimension $n$, both False Nearest Neighbors and MPE provide accurate values for $n$ for most of the systems with $n = 5$ being suitable in most cases.

physics.data-an↗