Non-Euclidean Models for Fraud Detection in Irregular Temporal Data Environments

Traditional anomaly detection methods often assume that data points are independent or exhibit regularly structured relationships, as in Euclidean data such as time series or image grids. However, real-world data frequently involve irregular, interconnected structures, requiring a shift toward non-Euclidean approaches. This study introduces a novel anomaly detection framework designed to handle non-Euclidean data by modeling transactions as graph signals. By leveraging graph convolution filters, we extract meaningful connection strengths that capture relational dependencies often overlooked in traditional methods. Utilizing the Graph Convolutional Networks (GCN) framework, we integrate graph-based embeddings with conventional anomaly detection models, enhancing performance through relational insights. Our method is validated on European credit card transaction data, demonstrating its effectiveness in detecting fraudulent transactions, particularly those with subtle patterns that evade traditional, amount-based detection techniques. The results highlight the advantages of incorporating temporal and structural dependencies into fraud detection, showcasing the robustness and applicability of our approach in complex, real-world scenarios.