Rethinking Structural Anomaly Detection: From Decision Boundaries to Projection Operators

• URL: http://arxiv.org/abs/2606.15280v1
• Date: Sat, 13 Jun 2026 12:37:20 GMT
• Title: Rethinking Structural Anomaly Detection: From Decision Boundaries to Projection Operators
• Abstract summary: We introduce a geometric perspective to address the mismatch between the inductive bias of existing methods and the structure of the data.<n>Specifically, we learn a projection operator onto the manifold of normal samples and define a sample as anomalous if it is altered by this projection.<n> Notably, it provides a unifying interpretation of reconstruction-based methods by explaining their success and failure in terms of projection quality.
• Score: 51.771100367755544
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Most existing anomaly detection methods rely on estimating a probability density or learning an enclosing decision boundary, implicitly assuming that normal data occupies a region of non-zero volume in the ambient space. In contrast, structural anomaly detection considers data that lies near a low-dimensional manifold, creating a mismatch between the inductive bias of existing methods and the structure of the data, often resulting in degraded performance. To address this mismatch, we introduce a geometric perspective. Specifically, we learn a projection operator onto the manifold of normal samples and define a sample as anomalous if it is altered by this projection. This formulation naturally integrates the inductive bias of manifold-supported data and reframes anomaly detection in terms of a projection residual, thereby resolving issues arising from modeling degenerate distributions. Notably, it provides a unifying interpretation of reconstruction-based methods by explaining their success and failure in terms of projection quality. In particular, it explains the strong generalization ability of projection-aligned models as a consequence of contraction behavior toward the manifold. Moreover, by decoupling anomaly detection from probabilistic modeling, it reduces the tendency to misclassify rare but normal samples, a widely recognized limitation of existing approaches. Empirically, we demonstrate that projection-aligned methods achieve strong performance, outperforming boundary-based methods while improving upon existing reconstruction-based approaches.

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