Robust Bichromatic Classification in 3D Using Planes and Slices

Given two sets of points in 3-dimensional space R and B, we want to separate these two sets of points using a classifier based on linear constraints, while ensuring robustness against outliers. The problem was studied in ℝ<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> by Glazenburg et al. We follow their approach and present various algorithms for many types of classifiers under various definitions of outliers. Our algorithms rely mainly on the duality of points and planes in ℝ<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup>.