  Many well-known and effective anomaly detection methods assume that a
reasonable decision boundary has a hypersphere shape, which however is
difficult to obtain in practice and is not sufficiently compact, especially
when the data are in high-dimensional spaces. In this paper, we first propose a
novel deep anomaly detection model that improves the original hypersphere
learning through an orthogonal projection layer, which ensures that the
training data distribution is consistent with the hypersphere hypothesis,
thereby increasing the true positive rate and decreasing the false negative
rate. Moreover, we propose a bi-hypersphere compression method to obtain a
hyperspherical shell that yields a more compact decision region than a
hyperball, which is demonstrated theoretically and numerically. The proposed
methods are not confined to common datasets such as image and tabular data, but
are also extended to a more challenging but promising scenario, graph-level
anomaly detection, which learns graph representation with maximum mutual
information between the substructure and global structure features while
exploring orthogonal single- or bi-hypersphere anomaly decision boundaries. The
numerical and visualization results on benchmark datasets demonstrate the
superiority of our methods in comparison to many baselines and state-of-the-art
methods.
