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arXiv · 2311.07907

Curve Stabbing Depth: Data Depth for Plane Curves

Stephane Durocher·Alexandre Leblanc·Spencer Szabados
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Abstract

Measures of data depth have been studied extensively for point data. Motivated by recent work on analysis, clustering, and identifying representative elements in sets of trajectories, we introduce {\em curve stabbing depth} to quantify how deeply a given curve $Q$ is located relative to a given set $\cal C$ of curves in $\mathbb{R}^2$. Curve stabbing depth evaluates the average number of elements of $\cal C$ stabbed by rays rooted along the length of $Q$. We describe an $O(n^3 + n^2 m\log^2m+nm^2\log^2 m)$-time algorithm for computing curve stabbing depth when $Q$ is an $m$-vertex polyline and $\cal C$ is a set of $n$ polylines, each with $O(m)$ vertices.

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Stephane Durocher, Alexandre Leblanc, Spencer Szabados. 2023-11-14. Curve Stabbing Depth: Data Depth for Plane Curves. https://arxiv.org/abs/2311.07907

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