Abstract. PCA is a classical statistical technique whose simplicity and maturity has seen it find widespread use for anomaly detection. However, it is limited in this regard by being sensitive to gross perturbations of the input, and by seeking a linear subspace that captures normal behaviour. The first issue has been dealt with by robust PCA, a variant of PCA that explicitly allows for some data points to be arbitrarily corrupted; however, this does not resolve the second issue, and indeed introduces the new issue that one can no longer inductively find anomalies on a test set. This paper addresses both issues in a single model, the robust autoencoder. This method learns a nonlinear subspace that captures the majority of data points, while allowing for some data to have arbitrary corruption. The model is simple to train and leverages recent advances in the optimisation of deep neural networks. Experiments on a range of real-world datasets highlight the model's effectiveness.

Unlike conventional anomaly detection research that focuses on point anomalies, our goal is to detect anomalous collections of individual data points. In particular, we perform group anomaly detection (GAD) with an emphasis on irregular group distributions (e.g. irregular mixtures of image pixels). GAD is an important task in detecting unusual and anomalous phenomena in real-world applications such as high energy particle physics, social media and medical imaging. In this paper, we take a generative approach by proposing deep generative models: Adversarial autoencoder (AAE) and variational autoencoder (VAE) for group anomaly detection. Both AAE and VAE detect group anomalies using point-wise input data where group memberships are known a priori. We conduct extensive experiments to evaluate our models on real world datasets. The empirical results demonstrate that our approach is effective and robust in detecting group anomalies.

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