Deep learning methods, especially the family of autoencoder architectures, exhibit state-of-the-art detection rates in anomaly detection tasks.
Additionally, recent results show that learning latent spaces with deep architectures on Riemannian manifolds may further improve performances as well as related interpolation tasks. In this paper, we study the use of Riemannian manifolds with variational autoencoders (VAEs) for anomaly detection on data from water providers. Besides traditional embeddings in Euclidean space, we study embeddings in Poincaré disc, spheres, and Stiefel manifolds, where in general, the Poincaré disc is often preferred for data with hierarchical structures, embeddings in spheres suggests itself for cyclical structures and the Stiefel manifold is well suited for time-dependent data. Data from water providers clearly meets all three criteria and we report on empirical results with the different manifolds as latent spaces and compare their detection performance to that of standard Euclidean embeddings.