Advancing Anomaly Detection with Robust and Graph-Based Learning Methods: From Support Vector Data Description to Graph Neural Networks.

Anomaly detection is crucial across various domains, particularly in handling highly skewed datasets where only normal operating conditions are available for training. To effectively identify abnormal events, specialized one-class classifiers have been developed. This dissertation explores robust and scalable anomaly detection methods, focusing on enhancing support vector techniques to accommodate complex data structures like graphs. The first study introduces the Robust Support Vector Data Description (RSVDD) model, which improves standard SVDD by incorporating a rescaled hinge loss function, making it more resistant to outliers. Using a half-quadratic optimization method, RSVDD dynamically adjusts the influence of each data point, leading to improved anomaly detection in both synthetic and real-world datasets. The second study addresses anomaly detection in graph-structured data, where node dependencies introduce additional challenges. The proposed Least Squares One-Class Graph Neural Network (LS-OCGNN) integrates Graph Neural Networks (GNNs) with a least-squares hypersphere learning approach. This novel framework enhances efficiency by leveraging a closed-form solution for hypersphere radius estimation, reducing Type II errors and improving sensitivity to complex anomalies, as demonstrated on datasets such as the Cora citation network. The final study extends one-class classification by introducing Least Squares Support Vector Machine with Graph Neural Networks (LSOCSVM-GNN), a scalable framework for detecting anomalies in attributed networks. By integrating node features and graph structure, LSOCSVM-GNN overcomes limitations of traditional SVM-based methods in graph-based scenarios. Together, these studies advance one-class classification by combining classical support vector approaches with modern graph-based learning frameworks. The proposed methods offer scalable, high-performance anomaly detection solutions with practical applications in cybersecurity, fraud detection, and social network analysis.