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Granular Ball K-Class Twin Support Vector Classifier

M. A. Ganaie, Vrushank Ahire, Anouck Girard

TL;DR

GB-TWKSVC presents a robust, scalable framework for multi-class classification by fusing granular-ball data representation with Twin SVM, formulating pairwise class comparisons via a 1-versus-1-versus-rest scheme and an epsilon-tube. It generates granular balls through hierarchical clustering, constructs an augmented training set, and solves smaller QPPs for each class pair, achieving high accuracy and favorable training times. Empirical results across 10 diverse datasets show GB-TWKSVC outperforming state-of-the-art baselines, with strong statistical support for its superiority and scalability. The work advances practical multi-class SVM methods by leveraging granular computing to enhance noise robustness and local information exploitation while maintaining computational efficiency.

Abstract

This paper introduces the Granular Ball K-Class Twin Support Vector Classifier (GB-TWKSVC), a novel multi-class classification framework that combines Twin Support Vector Machines (TWSVM) with granular ball computing. The proposed method addresses key challenges in multi-class classification by utilizing granular ball representation for improved noise robustness and TWSVM's non-parallel hyperplane architecture solves two smaller quadratic programming problems, enhancing efficiency. Our approach introduces a novel formulation that effectively handles multi-class scenarios, advancing traditional binary classification methods. Experimental evaluation on diverse benchmark datasets shows that GB-TWKSVC significantly outperforms current state-of-the-art classifiers in both accuracy and computational performance. The method's effectiveness is validated through comprehensive statistical tests and complexity analysis. Our work advances classification algorithms by providing a mathematically sound framework that addresses the scalability and robustness needs of modern machine learning applications. The results demonstrate GB-TWKSVC's broad applicability across domains including pattern recognition, fault diagnosis, and large-scale data analytics, establishing it as a valuable addition to the classification algorithm landscape.

Granular Ball K-Class Twin Support Vector Classifier

TL;DR

GB-TWKSVC presents a robust, scalable framework for multi-class classification by fusing granular-ball data representation with Twin SVM, formulating pairwise class comparisons via a 1-versus-1-versus-rest scheme and an epsilon-tube. It generates granular balls through hierarchical clustering, constructs an augmented training set, and solves smaller QPPs for each class pair, achieving high accuracy and favorable training times. Empirical results across 10 diverse datasets show GB-TWKSVC outperforming state-of-the-art baselines, with strong statistical support for its superiority and scalability. The work advances practical multi-class SVM methods by leveraging granular computing to enhance noise robustness and local information exploitation while maintaining computational efficiency.

Abstract

This paper introduces the Granular Ball K-Class Twin Support Vector Classifier (GB-TWKSVC), a novel multi-class classification framework that combines Twin Support Vector Machines (TWSVM) with granular ball computing. The proposed method addresses key challenges in multi-class classification by utilizing granular ball representation for improved noise robustness and TWSVM's non-parallel hyperplane architecture solves two smaller quadratic programming problems, enhancing efficiency. Our approach introduces a novel formulation that effectively handles multi-class scenarios, advancing traditional binary classification methods. Experimental evaluation on diverse benchmark datasets shows that GB-TWKSVC significantly outperforms current state-of-the-art classifiers in both accuracy and computational performance. The method's effectiveness is validated through comprehensive statistical tests and complexity analysis. Our work advances classification algorithms by providing a mathematically sound framework that addresses the scalability and robustness needs of modern machine learning applications. The results demonstrate GB-TWKSVC's broad applicability across domains including pattern recognition, fault diagnosis, and large-scale data analytics, establishing it as a valuable addition to the classification algorithm landscape.

Paper Structure

This paper contains 23 sections, 68 equations, 5 figures, 5 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Twin Support Vector Machines (TSVM)
  4. Granular Ball Support Vector Machines (GB-SVM)
  5. K-SVCR
  6. Twin-KSVC
  7. Proposed Model: GB-TWKSVC
  8. Model Overview
  9. Granular Ball Generation
  10. Classification Framework
  11. Augmented Training Set
  12. Linear Case
  13. Nonlinear Twin-KSVC
  14. Algorithm Design and Implementation
  15. Experimental Results and Analysis
  16. ...and 8 more sections

Figures (5)

  • Figure 1: Granular Ball Generation Flowchart
  • Figure 2: Visual representation of the GB-TWKSVC classification framework
  • Figure 3: Scalability Comparison Across Datasets. The plot shows the training time of different models across various datasets, with the y-axis on a logarithmic scale to better visualize differences.
  • Figure 4: 3D Surface Plots for the Seeds (left), Iris (middle), and Ecoli (right) Datasets. Each plot maps the accuracy of GB-TWKSVC against different combinations of purity and the number of data points.
  • Figure 5: Sensitivity Curve of Accuracy vs. $\epsilon$ (Epsilon).