通过移动数据点位置构建新分类算法，实现高效二分类。
On the Development of Binary Classification Algorithm Based on Principles of Geometry and Statistical Inference
- 基于几何向量与超平面原理，动态调整数据点位置来优化分类边界。
- 在多个标准数据集上表现优于传统方法，与SVM性能接近。
- 适合对几何直观和可解释性有要求的二分类任务研究者。
本文旨在探索一种基于几何原理（如向量、平面和向量代数）构建二分类算法的新方法。核心思想是：若数据点在n维空间中线性可分，则可通过超平面完全分离它们。由于点是几何构造的基本单元，通过调整用于构建超平面的数据点位置，即可控制超平面的位置。该算法被命名为“移动点算法”，因其在映射后的高维空间中动态移动数据点。实验在多个标准机器学习数据集上进行，重点与支持向量机（SVM）对比，因二者均基于超平面这一几何结构，且SVM具备良好的泛化能力，适合作为基准。结果表明，所提算法在多数数据集上表现优异，具备较强竞争力。
原文摘要 · Abstract (English)
The aim of this paper is to investigate an attempt to build a binary classification algorithm using principles of geometry such as vectors, planes, and vector algebra. The basic idea behind the proposed algorithm is that a hyperplane can be used to completely separate a given set of data points mapped to n dimensional space, if the given data points are linearly separable in the n dimensions. Since points are the foundational elements of any geometrical construct, by manipulating the position of points used for the construction of a given hyperplane, the position of the hyperplane itself can be manipulated. The paper includes testing data against other classifiers on a variety of standard machine learning datasets. With a focus on support vector machines, since they and our proposed classifier use the same geometrical construct of hyperplane, and the versatility of SVMs make them a good bench mark for comparison. Since the algorithm focuses on moving the points through the hyperspace to which the dataset has been mapped, it has been dubbed as moving points algorithm.
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