New Anomaly Detection Method Uses Projection Operators for Manifold Data

This paper introduces a novel geometric perspective for structural anomaly detection, challenging the common assumption that normal data occupies a non-zero volume region. Instead, it focuses on data that lies near a low-dimensional manifold, a scenario where existing methods often struggle due to a mismatch in inductive bias. The proposed approach involves learning a projection operator that maps data onto the manifold of normal samples. An anomaly is then identified if it is significantly altered by this projection, effectively measuring the "projection residual." This formulation naturally aligns with the inductive bias of manifold-supported data. This new perspective also offers a unifying interpretation for reconstruction-based methods, explaining their successes and failures based on projection quality. It highlights how projection-aligned models achieve strong generalization through contraction behavior towards the manifold and reduces the misclassification of rare but normal samples, a known limitation of probabilistic modeling approaches. Empirical results confirm that projection-aligned methods outperform boundary-based techniques and enhance existing reconstruction-based methods.