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arXiv · 2401.02897

Robust Bichromatic Classification using Two Lines

Erwin Glazenburg·Thijs van der Horst·Tom Peters·Bettina Speckmann·Frank Staals
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Abstract

Given two sets $R$ and $B$ of $n$ points in the plane, we present efficient algorithms to find a two-line linear classifier that best separates the "red" points in $R$ from the "blue" points in $B$ and is robust to outliers. More precisely, we find a region $\mathcal{W}_B$ bounded by two lines, so either a halfplane, strip, wedge, or double wedge, containing (most of) the blue points $B$, and few red points. Our running times vary between optimal $O(n\log n)$ and around $O(n^3)$, depending on the type of region $\mathcal{W}_B$ and whether we wish to minimize only red outliers, only blue outliers, or both.

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Erwin Glazenburg, Thijs van der Horst, Tom Peters, Bettina Speckmann, Frank Staals. 2024-01-05. Robust Bichromatic Classification using Two Lines. https://arxiv.org/abs/2401.02897

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