🤖 AI Summary
Existing anomaly detection methods typically assume that normal data occupy a non-zero volume in the ambient space, overlooking their intrinsic geometric structure as lying on a low-dimensional manifold, which limits performance. This work proposes a novel manifold projection paradigm: learning a projection operator that maps inputs onto the manifold of normal samples and using the projection residual as the anomaly criterion. By avoiding explicit modeling of the degenerate data distribution, the approach prevents misclassifying rare yet normal instances and provides a unified explanation for both the effectiveness and failure modes of reconstruction-based methods. Extensive experiments demonstrate that the proposed framework significantly outperforms conventional boundary-learning approaches and achieves state-of-the-art results across multiple benchmarks compared to existing reconstruction-based models.
📝 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.