# Scalable Spatial Scan Statistics for Trajectories

## TL;DR

This paper introduces scalable models and algorithms for detecting anomalous regions in large sets of trajectories using spatial scan statistics, with extensive experiments and theoretical guarantees.

## Contribution

It proposes new models for defining anomalous regions among trajectories based on different contribution measures, extending a recent sampling approach for high accuracy at large scales.

## Key findings

- Effective detection of anomalous regions in millions of trajectories
- Models accommodate various contribution measures like full trajectory, time, or flux
- Theoretical guarantees support the methods' reliability

## Abstract

We define several new models for how to define anomalous regions among enormous sets of trajectories. These are based on spatial scan statistics, and identify a geometric region which captures a subset of trajectories which are significantly different in a measured characteristic from the background population. The model definition depends on how much a geometric region is contributed to by some overlapping trajectory. This contribution can be the full trajectory, proportional to the time spent in the spatial region, or dependent on the flux across the boundary of that spatial region. Our methods are based on and significantly extend a recent two-level sampling approach which provides high accuracy at enormous scales of data. We support these new models and algorithms with extensive experiments on millions of trajectories and also theoretical guarantees.