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.

翻译：大多数现有的异常检测方法依赖于估计概率密度或学习一个包围性决策边界，隐含假设正常数据占据环境空间中非零体积的区域。相反，结构异常检测考虑位于低维流形附近的数据，这导致了现有方法的归纳偏置与数据结构之间的不匹配，常常导致性能下降。为了解决这种不匹配，我们引入了一个几何视角。具体来说，我们学习一个投影算子，将数据投影到正常样本的流形上，并将样本定义为异常如果它被该投影改变。这种公式自然地整合了流形支撑数据的归纳偏置，并将异常检测重新定义为投影残差问题，从而解决了由建模退化分布引起的问题。值得注意的是，它通过从投影质量的角度解释重建方法的成功与失败，为基于重建的方法提供了统一的解释。特别是，它解释了投影对齐模型强大泛化能力的原因，即对向流形收缩的行为。此外，通过将异常检测与概率建模解耦，它减少了将罕见但正常的样本误分类的倾向，这是现有方法广泛认可的局限性。实验上，我们证明了投影对齐方法实现了强劲性能，超越了基于边界的方法，同时改进了现有的基于重建的方法。