Granular-Ball Computing-Based Fuzzy Twin Support Vector Machine for Pattern Classification

Abstract

The twin support vector machine (TWSVM) classifier and its fuzzy variant fuzzy twin support vector machine (FTSVM) have received considerable attention due to their low computational complexity. However, their performance often deteriorates when the input data is affected by noise. To overcome this limitation, this study leverages the robustness of granular-ball computing (GBC) against noise to develop more effective classification models by integrating GBC with TWSVM and FTSVM. First, we introduce the granular-ball TWSVM (GBTWSVM) classifier, which incorporates GBC with the TWSVM framework. By replacing traditional point-wise inputs with granular-ball representations, we derive a pair of nonparallel hyperplanes for the GBTWSVM classifier by solving a quadratic programming problem. Afterwards, we develop the granular-ball FTSVM (GBFTSVM) classifier, where the membership and nonmembership functions of granular-balls are defined using Pythagorean fuzzy sets, enabling a more nuanced differentiation of the contributions of granular-balls from distinct regions within the input space. By incorporating these functions into the FTSVM framework, we derive a pair of nonparallel hyperplanes for the GBFTSVM classifier through the solution of a quadratic programming problem. Finally, we present algorithms for the GBTWSVM and GBFTSVM classifiers and evaluate their performance on 21 benchmark datasets. Experimental results demonstrate the superior scalability, computational efficiency, and robustness of the proposed classifiers in pattern recognition, highlighting their potential as advanced tools for noise-tolerant classification.