  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.
