Robust Bichromatic Classification using Two Lines

Given two sets 𝑅 and 𝐵 of at most 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) and O(n^4), depending on the type of region 𝑊_𝐵 and whether we wish to minimize only red outliers, only blue outliers, or both.