GBSVM: Granular-ball Support Vector Machine

Abstract

GBSVM (Granular-ball Support Vector Machine) is an important attempt to use the coarse granularity of a granular-ball as the input to construct a classifier instead of a data point. It is the first classifier whose input contains no points, i.e., $x_i$, in the history of machine learning. However, on the one hand, its dual model is not derived, and the algorithm has not been implemented and can not be applied. On the other hand, there are some errors in its existing model. To address these problems, this paper has fixed the errors of the original model of GBSVM, and derived its dual model. Furthermore, an algorithm is designed using particle swarm optimization algorithm to solve the dual model. The experimental results on the UCI benchmark datasets demonstrate that GBSVM has good robustness and efficiency