Mathematical Modeling and Clustering Framework for Cyber Threat Analysis Across Industries

Fahim Sufi () and Musleh Alsulami
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Fahim Sufi: School of Public Health and Preventive Medicine, Monash University, Melbourne, VIC 3004, Australia
Musleh Alsulami: Department of Software Engineering, College of Computing, Umm Al-Qura University, Makkah 21961, Saudi Arabia

Mathematics, 2025, vol. 13, issue 4, 1-27

Abstract: The escalating prevalence of cyber threats across industries underscores the urgent need for robust analytical frameworks to understand their clustering, prevalence, and distribution. This study addresses the challenge of quantifying and analyzing relationships between 95 distinct cyberattack types and 29 industry sectors, leveraging a dataset of 9261 entries filtered from over 1 million news articles. Existing approaches often fail to capture nuanced patterns across such complex datasets, justifying the need for innovative methodologies. We present a rigorous mathematical framework integrating chi-square tests, Bayesian inference, Gaussian Mixture Models (GMMs), and Spectral Clustering. This framework identifies key patterns, such as 1150 Zero-Day Exploits clustered in the IT and Telecommunications sector, 732 Advanced Persistent Threats (APTs) in Government and Public Administration, and Malware with a posterior probability of 0.287 dominating the Healthcare sector. Temporal analyses reveal periodic spikes, such as in Zero-Day Exploits, and a persistent presence of Social Engineering Attacks, with 1397 occurrences across industries. These findings are quantified using significance scores (mean: 3.25 ± 0.7) and posterior probabilities, providing evidence for industry-specific vulnerabilities. This research offers actionable insights for policymakers, cybersecurity professionals, and organizational decision makers by equipping them with a data-driven understanding of sector-specific risks. The mathematical formulations are replicable and scalable, enabling organizations to allocate resources effectively and develop proactive defenses against emerging threats. By bridging mathematical theory to real-world cybersecurity challenges, this study delivers impactful contributions toward safeguarding critical infrastructure and digital assets.

Keywords: cybersecurity; mathematical modeling; clustering techniques; Gaussian Mixture Models (GMMs); Spectral Clustering; Bayesian inference; industry-specific cyber threats; temporal analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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