Simple Distances for Trajectories via Landmarks

TL;DR

This paper introduces a new, simple, and interpretable class of distance measures for objects like trajectories that outperform existing metrics in data analysis and similarity search tasks, without complex computations.

Contribution

The authors propose a novel class of landmark-based distances for trajectories and geometric objects that are easy to compute, interpret, and integrate into data analysis methods.

Findings

Outperform state-of-the-art trajectory metrics in data analysis tasks.

Enable efficient k-means clustering and nearest neighbor search for trajectories.

Distances are often metrics under reasonable conditions.

Abstract

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.