GBSVM: Granular-ball Support Vector Machine

TL;DR

GBSVM introduces a novel classifier that uses granular-balls instead of individual data points, with corrected models and optimized algorithms, demonstrating robustness and efficiency on benchmark datasets.

Contribution

This paper corrects the errors in the original GBSVM model, derives its dual form, and develops faster algorithms for practical implementation.

Findings

Demonstrates GBSVM's robustness on benchmark datasets

Shows improved speed and stability with the designed algorithms

Provides open-source implementation for reproducibility

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.