AN APPLIED MATHEMATICAL FRAMEWORK FOR PRIVACY-PRESERVING INTRUSION DETECTION USING FEATURE SELECTION AND FUSION MODELS.

The widespread deployment of Internet of Things (IoT) and cloud-driven networks has raised the threat level of digital infrastructures to that of advanced cyberattacks. However, Atrad has to be distinguished from some previous work; many IDSs find it difficult to detect attacks and maintain a high detection rate while protecting sensitive user data at the same time. To help alleviate this situation, we present an applied mathematics framework for privacy-preserving intrusion detection that combines optimal feature selection with fusion classification models. The approach reduces feature space sizes using strong mathematical methods, such as the L1 Regularisation Technique, for those features that are most discriminant and non-cost-sensitive, enabling limited computational overhead in threat detection. Meanwhile, privacy-preserving mechanisms are incorporated to avoid the unauthorised exposure of sensitive traffic patterns during the detection procedure. A multi-level fusion approach, comprising both statistical, information-theoretic, and learning models, increases the robustness of detection in the presence of diverse attack families. Experimental evaluation using standard intrusion datasets demonstrates that the proposed framework outperforms the state-of-the-art in terms of accuracy, precision, and recall, and notably reduces false alarms. Additionally, the proposed mathematical optimisation of feature subsets and fusion weights will ensure scalability and applicability in practical network environments. This work paves the way for secure, efficient, and privacy-aware IDS design by bridging the gap between theoretical soundness and practical relevance in contemporary cyber defence systems.