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Geometric Algorithms to Large Margin Classifier Based on Affine Hulls

机译：基于仿射壳的大余量分类器几何算法

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摘要

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.
机译：二进制数据分类问题的几何框架为理解和应用几何优化算法提供了直观的基础，从而为实际分类问题提供了实用的解决方案。本文介绍了关于简化仿射外壳（RAH）概念的候选极点的一些理论结果。这些结果使现有的最近点算法可以直接有效地解决基于RAH的可分离和不可分离的分类问题。作为新理论结果的实际应用，提出了流行的Gilbert-Schlesinger-Kozinec和Mitchell-Dem'yanov-Malozemov算法，以解决RAH框架中的二进制分类问题。理论分析和一些实验表明，提出的方法成功地取得了显着的性能。

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