Geometric algorithms to large margin classifier based on affine hulls

The geometric framework for binary data classification problems provides an intuitive foundation for the comprehension and application of geometric optimization algorithms, leading to practical solutions of real-world classification problems. In this paper, some theoretical results on the candidate extreme points of the notion of reduced affine hull (RAH) are introduced. These results allow the existing nearest point algorithms to be directly applied to solve both separable and inseparable classification problems based on RAHs successfully and efficiently. As the practical applications of the new theoretical results, the popular Gilbert-Schlesinger-Kozinec and Mitchell-Dem'yanov-Malozemov algorithms are presented to solve binary classification problems in the context of the RAH framework. The theoretical analysis and some experiments show that the proposed methods successfully achieve significant performance.