Anomaly Detection in Trajectory Data with Normalizing Flows

The task of detecting anomalous data patterns is as important in practical applications as challenging. In the context of spatial data, recognition of unexpected trajectories brings additional difficulties, such as high dimensionality and varying pattern lengths. We aim to tackle such a problem from a probability density estimation point of view, since it provides an unsupervised procedure to identify out of distribution samples. More specifically, we pursue an approach based on normalizing flows, a recent framework that enables complex density estimation from data with neural networks. Our proposal computes exact model likelihood values, an important feature of normalizing flows, for each segment of the trajectory. Then, we aggregate the segments' likelihoods into a single coherent trajectory anomaly score. Such a strategy enables handling possibly large sequences with different lengths. We evaluate our methodology, named aggregated anomaly detection with normalizing flows (GRADINGS), using real world trajectory data and compare it with more traditional anomaly detection techniques. The promising results obtained in the performed computational experiments indicate the feasibility of the GRADINGS, specially the variant that considers autoregressive normalizing flows.