GBSVM: An Efficient and Robust Support Vector Machine Framework via Granular-Ball Computing.

Granular-ball support vector machine (GBSVM) 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, we fix the errors of the original model of the existing GBSVM and derive its dual model. Furthermore, a particle swarm optimization (PSO) algorithm is designed to solve the dual problem. The sequential minimal optimization (SMO) algorithm is also carefully designed to solve the dual problem. The latter is faster and more stable. The experimental results on the UCI benchmark datasets demonstrate that GBSVM is more robust and efficient. All codes have been released in the open source library available at: http://www.cquptshuyinxia.com/GBSVM.html or https://github.com/syxiaa/GBSVM.