[formula omitted]-MGSVM: Controllable multi-granularity support vector algorithm for classification and regression

The ν support vector machine (ν-SVM) is an enhanced algorithm derived from support vector machines using parameter ν to replace the original penalty coefficient C. Because of the narrower range of ν compared with the infinite range of C, ν-SVM generally outperforms the standard SVM. Granular ball computing is an information fusion method that enhances system robustness and reduces uncertainty. To further improve the efficiency and robustness of support vector algorithms, this paper introduces the concept of multigranularity granular balls and proposes the controllable multigranularity SVM (Con-MGSVM) and the controllable multigranularity support vector regression machine (Con-MGSVR). These models use granular computing theory, replacing original fine-grained points with coarse-grained “granular balls” as inputs to a classifier or regressor. By introducing control parameter ν, the number of support granular balls can be further reduced, thereby enhancing computational efficiency and improving robustness and interpretability. Furthermore, this paper derives and solves the dual models of Con-MGSVM and Con-MGSVR and conducts a comparative study on the relationship between the granular ball SVM (GBSVM) and the Con-MGSVM model, elucidating the importance of control parameters. Experimental results demonstrate that Con-MGSVM and Con-MGSVR not only improve accuracy and fitting performance but also effectively reduce the number of support granular balls.