# Anomaly Detection in Trajectory Data with Normalizing Flows

arXiv: https://arxiv.org/abs/2004.05958 · HTML: https://mlsanity.com/paper/2004.05958/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Apr 2020.

## Built on by (most cited first, 11 of 11)

- [Fully Convolutional Cross-Scale-Flows for Image-based Defect Detection](https://mlsanity.com/paper/2110.02855/) (2021)
- [Asymmetric Student-Teacher Networks for Industrial Anomaly Detection](https://mlsanity.com/paper/2210.07829/) (2022)
- [Improved Techniques for Maximum Likelihood Estimation for Diffusion ODEs](https://mlsanity.com/paper/2305.03935/) (2023)
- [Neural Flow Diffusion Models: Learnable Forward Process for Improved Diffusion Modelling](https://mlsanity.com/paper/2404.12940/) (2024)
- [Flow-based Self-supervised Density Estimation for Anomalous Sound Detection](https://mlsanity.com/paper/2103.08801/) (2021)
- [The voraus-AD Dataset for Anomaly Detection in Robot Applications](https://mlsanity.com/paper/2311.04765/) (2023)
- [An Iterative Method for Unsupervised Robust Anomaly Detection Under Data Contamination](https://mlsanity.com/paper/2309.09436/) (2023)
- [Unsupervised Anomaly Detection through Mass Repulsing Optimal Transport](https://mlsanity.com/paper/2502.12793/) (2025)
- [An Automated Analysis Framework for Trajectory Datasets](https://mlsanity.com/paper/2202.07438/) (2022)
- [GADformer: A Transparent Transformer Model for Group Anomaly Detection on Trajectories](https://mlsanity.com/paper/2303.09841/) (2023)
- [Generative Anomaly Detection for Time Series Datasets](https://mlsanity.com/paper/2206.14597/) (2022)

## Abstract (arXiv)

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.