Deep Orthogonal Hypersphere Compression for Anomaly Detection

TL;DR

This paper introduces a novel deep anomaly detection approach using orthogonal projections and bi-hypersphere compression to create more compact and accurate decision boundaries, applicable to various data types including graphs.

Contribution

It proposes a new deep hypersphere learning model with orthogonal projection and bi-hypersphere compression, extending anomaly detection to graph data with improved accuracy.

Findings

Enhanced true positive rates and reduced false negatives.

More compact decision regions than traditional hyperballs.

Superior performance on benchmark datasets.

Abstract

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.