An anomaly detection method for conformal mechanism

This paper introduces a novel hypersphere-based anomaly detection method enhanced by a conformal mapping transformation to address challenges such as data sparsity, computational complexity, and the scarcity of labeled anomalies in high-dimensional spaces. The core of our approach, termed HS-MT, is the construction of two separate hyperspheres to model normal and anomalous instances, leveraging their efficiency and interpretability. A key contribution is the derivation and theoretical validation of a specific conformal mapping function that projects data into a transformed space, effectively condensing anomalous points into tighter clusters and improving their detectability. Experiments on synthetic and real-world UCI datasets demonstrate that HS-MT consistently outperforms state-of-the-art methods in accuracy, recall, and computational efficiency, particularly in scenarios with high anomaly ratios. The results confirm that the proposed mapping function and dual-hypersphere design together offer a scalable and theoretically grounded solution for identifying subtle anomalies in complex datasets.