# Hyperspectral Trajectory Image for Multi-Month Trajectory Anomaly Detection

arXiv: https://arxiv.org/abs/2603.25255 · HTML: https://mlsanity.com/paper/2603.25255/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 46 references that are in the map.
- First posted on arXiv 26 Mar 2026.

## Builds on (most cited first, 26 of 26)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [SegFormer: Simple and Efficient Design for Semantic Segmentation with Transformers](https://mlsanity.com/paper/2105.15203/) (2021)
- [Is Space-Time Attention All You Need for Video Understanding?](https://mlsanity.com/paper/2102.05095/) (2021)
- [ViViT: A Video Vision Transformer](https://mlsanity.com/paper/2103.15691/) (2021)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [Muon is Scalable for LLM Training](https://mlsanity.com/paper/2502.16982/) (2025)
- [Axial-DeepLab: Stand-Alone Axial-Attention for Panoptic Segmentation](https://mlsanity.com/paper/2003.07853/) (2020)
- [Chronos-2: From Univariate to Universal Forecasting](https://mlsanity.com/paper/2510.15821/) (2025)
- [TimeMixer++: A General Time Series Pattern Machine for Universal Predictive Analysis](https://mlsanity.com/paper/2410.16032/) (2024)
- [Imaging Time-Series to Improve Classification and Imputation](https://mlsanity.com/paper/1506.00327/) (2015)
- [Time Series as Images: Vision Transformer for Irregularly Sampled Time Series](https://mlsanity.com/paper/2303.12799/) (2023)
- [Classification of Time-Series Images Using Deep Convolutional Neural Networks](https://mlsanity.com/paper/1710.00886/) (2017)
- [UniTraj: Learning a Universal Trajectory Foundation Model from Billion-Scale Worldwide Traces](https://mlsanity.com/paper/2411.03859/) (2024)
- [NUMOSIM: A Synthetic Mobility Dataset with Anomaly Detection Benchmarks](https://mlsanity.com/paper/2409.03024/) (2024)
- [Urban Anomalies: A Simulated Human Mobility Dataset with Injected Anomalies](https://mlsanity.com/paper/2410.01844/) (2024)
- [Trajectory Anomaly Detection with Language Models](https://mlsanity.com/paper/2409.15366/) (2024)
- [CoBAD: Modeling Collective Behaviors for Human Mobility Anomaly Detection](https://mlsanity.com/paper/2508.14088/) (2025)
- [Kinematic Detection of Anomalies in Human Trajectory Data](https://mlsanity.com/paper/2409.19136/) (2024)
- [BeSTAD: Behavior-Aware Spatio-Temporal Anomaly Detection for Human Mobility Data](https://mlsanity.com/paper/2510.12076/) (2025)
- [TrajMamba: An Efficient and Semantic-rich Vehicle Trajectory Pre-training Model](https://mlsanity.com/paper/2510.17545/) (2025)

## Abstract (arXiv)

Trajectory anomaly detection underpins applications from fraud detection to urban mobility analysis. Dense GPS preserves fine-grained evidence such as abnormal speeds and short-duration events, but its quadratic cost makes multi-month analysis intractable; sparse stay-point methods scale by discarding that evidence and require a separate modeling regime. We argue that this bottleneck is unnecessary: dense and sparse trajectories share a natural two-dimensional cyclic structure along within-day and across-day axes. TITAnD (Trajectory Image Transformer for Anomaly Detection) is the first framework to cast both in a single representation, a Hyperspectral Trajectory Image (HTI), a day × time-of-day grid whose channels encode spatial, semantic, temporal, and kinematic information. Under this formulation, agent-level detection reduces to image classification and temporal localization to semantic segmentation. The Cyclic Factorized Transformer (CFT) models the two temporal axes directly, reducing attention cost by up to two orders of magnitude. With the HTI, multi-month dense anomaly detection becomes feasible for the first time, and CFT keeps it accurate and fast. Empirically, TITAnD matches or beats every evaluated baseline in AUC-PR on all four benchmarks. It surpasses vision models such as U-Net while using as few as 6.5M parameters, and it runs 11--75× faster than a capacity-matched flat Transformer on the same trajectory images.