Granular-Balls based Fuzzy Twin Support Vector Machine for Classification

TL;DR

This work introduces two novel classifiers that fuse Granular-Ball Computing with SVM-based frameworks to tackle noise and outliers in high-dimensional data. The GBTWSVM uses granular-balls as inputs to produce two non-parallel hyperplanes, achieving substantially faster training and robust performance. The GBFTSVM further enhances robustness by employing Pythagorean fuzzy memberships and region-aware scoring to weigh granular-balls differently by their proximity to decision boundaries. Across twenty UCI benchmarks and controlled noise experiments, GBFTSVM delivers top accuracy and stability, with Friedman/Nemenyi statistics confirming its superiority. Together, these methods offer scalable, robust alternatives for classification tasks in noisy or imperfect data environments.

Abstract

The twin support vector machine (TWSVM) classifier has attracted increasing attention because of its low computational complexity. However, its performance tends to degrade when samples are affected by noise. The granular-ball fuzzy support vector machine (GBFSVM) classifier partly alleviates the adverse effects of noise, but it relies solely on the distance between the granular-ball's center and the class center to design the granular-ball membership function. In this paper, we first introduce the granular-ball twin support vector machine (GBTWSVM) classifier, which integrates granular-ball computing (GBC) with the twin support vector machine (TWSVM) classifier. By replacing traditional point inputs with granular-balls, we demonstrate how to derive a pair of non-parallel hyperplanes for the GBTWSVM classifier by solving a quadratic programming problem. Subsequently, we design the membership and non-membership functions of granular-balls using Pythagorean fuzzy sets to differentiate the contributions of granular-balls in various regions. Additionally, we develop the granular-ball fuzzy twin support vector machine (GBFTSVM) classifier by incorporating GBC with the fuzzy twin support vector machine (FTSVM) classifier. We demonstrate how to derive a pair of non-parallel hyperplanes for the GBFTSVM classifier by solving a quadratic programming problem. We also design algorithms for the GBTSVM classifier and the GBFTSVM classifier. Finally, the superior classification performance of the GBTWSVM classifier and the GBFTSVM classifier on 20 benchmark datasets underscores their scalability, efficiency, and robustness in tackling classification tasks.

Figures (4)

• Figure 1: The GBTWSVM classifier.
• Figure 2: The GBFTSVM classifier.
• Figure 3: $Acc$ of GBFTSVM with different $C_1$, $C_3$ and $C_2$, $C_4$.
• Figure 4: The comparison of various models in terms of CD diagrams.