GBSVM: Granular-ball Support Vector Machine
Shuyin Xia, Xiaoyu Lian, Guoyin Wang, Xinbo Gao, Jiancu Chen, Xiaoli Peng
TL;DR
GBSVM replaces point inputs with granular-balls, enabling coarse-to-fine multi-granularity classification that is robust to label noise. The paper fixes prior errors, derives separable and inseparable linear duals, and develops kernel-space granular-ball generation for nonlinear cases, accompanied by PSO and SMO solvers. Empirical results on UCI datasets show improved robustness to label noise and faster training compared to traditional SVM, with further gains from kernelization and overlap removal in kernel space. The work provides a practical, reusable framework for granular-ball learning with potential extensions to diverse recognition tasks.
Abstract
GBSVM (Granular-ball Support Vector Machine) is a significant attempt to construct a classifier using the coarse-to-fine granularity of a granular-ball as input, rather than a single data point. It is the first classifier whose input contains no points. However, the existing model has some errors, and its dual model has not been derived. As a result, the current algorithm cannot be implemented or applied. To address these problems, this paper has fixed the errors of the original model of the existing GBSVM, and derived its dual model. Furthermore, a particle swarm optimization algorithm is designed to solve the dual model. The sequential minimal optimization algorithm is also carefully designed to solve the dual model. The solution is faster and more stable than the particle swarm optimization based version. The experimental results on the UCI benchmark datasets demonstrate that GBSVM has good robustness and efficiency. All codes have been released in the open source library at http://www.cquptshuyinxia.com/GBSVM.html or https://github.com/syxiaa/GBSVM.