Dirichlet and Liouville-based normality scores for deep anomaly detection using transformations: applications to images and beyond images

We address the problem of anomaly detection in data by learning a normality score function through the use of data transformations. Applying transformations to a dataset is essential for enhancing its representation and revealing underlying patterns. First, we propose geometric transformations for image data. The core idea of our approach is to train a multi-class deep classifier to distinguish between various geometric transformations. At test time, we construct the normality score function by approximating the softmax output predictions vector using generalized forms of Dirichlet distributions, including the generalized Dirichlet (GD), scaled Dirichlet (SD), shifted scaled Dirichlet (SSD), and Beta-Liouville (BL) distributions. These generalized forms of the Dirichlet distribution are more robust in real-world applications compared to the standard Dirichlet distribution. They offer a more flexible covariance structure, making them suitable for approximating both symmetric and asymmetric distributions. For parameter estimation, we use the maximum likelihood method based on the transformed forms of the original data. In the second step, we extend our approach to non-image data by selecting appropriate transformations. This transformation procedure involves building several neural networks, training them on the original data to obtain its transformed form, and then passing the transformed data through an auto-encoder. Experiments conducted on both image and non-image data demonstrate the effectiveness of our proposed strategy. The results show that our anomaly detection models, based on generalized Dirichlet distributions, outperform baseline techniques and achieve high Area Under the Receiver Operating Characteristic (AUROC) scores.