# Simple Distances for Trajectories via Landmarks

arXiv: https://arxiv.org/abs/1804.11284 · HTML: https://mlsanity.com/paper/1804.11284/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Apr 2018.

## Built on by (most cited first, 2 of 2)

- [Classifying Spatial Trajectories](https://mlsanity.com/paper/2209.01322/) (2022)
- [Movement Analytics: Current Status, Application to Manufacturing, and Future Prospects from an AI Perspective](https://mlsanity.com/paper/2210.01344/) (2022)

## Abstract (arXiv)

We develop a new class of distances for objects including lines, hyperplanes, and trajectories, based on the distance to a set of landmarks. These distances easily and interpretably map objects to a Euclidean space, are simple to compute, and perform well in data analysis tasks. For trajectories, they match and in some cases significantly out-perform all state-of-the-art other metrics, can effortlessly be used in k-means clustering, and directly plugged into approximate nearest neighbor approaches which immediately out-perform the best recent advances in trajectory similarity search by several orders of magnitude. These distances do not require a geometry distorting dual (common in the line or halfspace case) or complicated alignment (common in trajectory case). We show reasonable and often simple conditions under which these distances are metrics.