Robust Bichromatic Classification in 3D Using Planes and Slices

2026-07-22

AI Summary

This study addresses the problem of robust binary classification of red and blue point sets in three-dimensional space, with a focus on resilience against various types of outliers. Leveraging the duality between points and planes in 3D, the work extends existing two-dimensional robust bichromatic classification techniques to the three-dimensional setting and formulates a classifier centered on linear constraints. The authors develop several efficient geometric algorithms tailored to distinct outlier models, including spatial outliers and label noise. Experimental results demonstrate that the proposed approach consistently and accurately separates red and blue point sets across diverse contamination scenarios, significantly enhancing the practicality and adaptability of robust classification in three dimensions.

Abstract

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 $\mathbb{R}^2$ 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 $\mathbb{R}^3$.

Problem

• bichromatic classification
• 3D separation
• linear constraints
• robustness
• outliers

Innovation

• bichromatic classification
• robustness
• 3D duality
• outlier handling
• linear classifiers