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Robust Bichromatic Classification Using Two Lines

Authors Erwin Glazenburg , Thijs van der Horst , Tom Peters , Bettina Speckmann , Frank Staals

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ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Geometric Algorithms
  • Separating Line
  • Classification
  • Bichromatic
  • Duality

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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 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(nlog n) up to around O(n³), depending on the type of region 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, and Frank Staals. Robust Bichromatic Classification Using Two Lines. In 35th International Symposium on Algorithms and Computation (ISAAC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 322, pp. 33:1-33:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ISAAC.2024.33

Author Details

Erwin Glazenburg
  • Utrecht University, The Netherlands
Thijs van der Horst
  • Utrecht University, The Netherlands
  • TU Eindhoven, The Netherlands
Tom Peters
  • TU Eindhoven, The Netherlands
Bettina Speckmann
  • TU Eindhoven, The Netherlands
Frank Staals
  • Utrecht University, The Netherlands

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