On the Development of Binary Classification Algorithm Based on Principles of Geometry and Statistical Inference

2025-03-03

AI Summary

This paper addresses binary classification of linearly separable data in high-dimensional spaces. Unlike conventional approaches—such as support vector machines (SVMs)—that optimize hyperplane parameters, the proposed method introduces a geometrically driven algorithm centered on a novel “moving-point” mechanism: the separating hyperplane remains fixed, while sample points’ projections in feature space are iteratively adjusted via vector algebra and statistical discriminant criteria to achieve optimal linear separation. The approach integrates vector-space modeling, geometric hyperplane construction, and dynamic point-position optimization, thereby enhancing both geometric interpretability and structural flexibility. Experiments across multiple benchmark datasets demonstrate classification accuracy comparable to SVM, yet with markedly improved transparency and intuitive geometric insight. This work establishes a new geometric paradigm for explainable machine learning.

Technology Category

• Machine Learning: Learning with Manifolds
• Search and Optimization: Mixed Discrete/Continuous Search
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

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.

Problem

• Develops a binary classification algorithm using geometric principles.
• Uses hyperplanes to separate data points in n-dimensional space.
• Compares performance with support vector machines on standard datasets.

Innovation

• Uses geometry principles for binary classification
• Employs hyperplanes in n-dimensional space
• Introduces moving points algorithm technique