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Hierarchical Gaussian Mixture Normalizing Flow Modeling for Unified Anomaly Detection

Unified anomaly detection (AD) is one of the most challenges for anomaly detection, where one unified model is trained with normal samples from multiple classes with the objective to detect anomalies in these classes. For such a challenging task, popular normalizing flow (NF) based AD methods may fall into a "homogeneous mapping" issue,where the NF-based AD models are biased to generate similar latent representations for both normal and abnormal features, and thereby lead to a high missing rate of anomalies. In this paper, we propose a novel Hierarchical Gaussian mixture normalizing flow modeling method for accomplishing unified Anomaly Detection, which we call HGAD. Our HGAD consists of two key components: inter-class Gaussian mixture modeling and intra-class mixed class centers learning. Compared to the previous NF-based AD methods, the hierarchical Gaussian mixture modeling approach can bring stronger representation capability to the latent space of normalizing flows, so that even complex multi-class distribution can be well represented and learned in the latent space. In this way, we can avoid mapping different class distributions into the same single Gaussian prior, thus effectively avoiding or mitigating the "homogeneous mapping" issue. We further indicate that the more distinguishable different class centers, the more conducive to avoiding the bias issue. Thus, we further propose a mutual information maximization loss for better structuring the latent feature space. We evaluate our method on four real-world AD benchmarks, where we can significantly improve the previous NF-based AD methods and also outperform the SOTA unified AD methods.

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