On the Development of Binary Classification Algorithm Based on Principles of Geometry and Statistical Inference
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912257015808000 |
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| author | Srivastava, Vatsal |
| author_facet | Srivastava, Vatsal |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_01703 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Development of Binary Classification Algorithm Based on Principles of Geometry and Statistical Inference Srivastava, Vatsal Machine Learning Algebraic Geometry I.5.2; I.2.6 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. |
| title | On the Development of Binary Classification Algorithm Based on Principles of Geometry and Statistical Inference |
| topic | Machine Learning Algebraic Geometry I.5.2; I.2.6 |
| url | https://arxiv.org/abs/2503.01703 |