Outlier scoring algorithm using hypervolume-ratio-variance for non-dense data

Abstract

Anomaly detection is critical in domains such as financial fraud detection, network security, and healthcare, where identifying rare deviations from expected behavior has high practical stakes. Conventional methods, including Local Outlier Factor (LOF), suffer degraded performance on high-dimensional and non-dense datasets where defining "normal" behavior is inherently difficult. This thesis proposes the Hypervolume-Ratio-Variance Outlier Factor (HVOF), a novel unsupervised, modeless-AI anomaly-scoring algorithm. Building on the Mass-ratio-variance Outlier Factor (MOF), HVOF replaces point-count-based mass ratios with hypervolume ratios derived from each point's nearest-neighbor spatial extent, computed via a d-root transformation of d-dimensional hyperspheres. Each point's anomaly score is the variance of its hypervolume-ratio distribution across all other points: dense-region points yield low variance, while geometrically isolated points yield high variance. Experimental results confirm that HVOF is computationally efficient, interpretable, and training-free, with promising applications to data stream analysis and ECG signal monitoring.