A general maximal margin hyper-sphere SVM for multi-class classification

Traditional SVM algorithms for multi-class (k > 2 classes) classification tasks include "one-against-one", "one -against-rest", and "one-against-one-against-rest", which build k(k-1)/2 or k classifiers for space partitioning and classification decision. However, they may cause a variety of problems, such as an imbalanced problem, a high temporal complexity, and trouble establishing the decision boundary. In this study, we use the notion of minimizing structural risks (SRM) to recognize k classes by designing only one optimization problem, which we call (MHS)-H-3-SVM. The (MHS)-H-3-SVM offers numerous benefits. In summary, the following points should be emphasized: (1) Rather than dividing the space with hyper-planes, (MHS)-H-3-SVM describes the structural characteristics of various classes of data and trains the hyper-sphere classifier of each class based on the data distribution. (2) (MHS)-H-3-SVM inherits all of the advantages of classical binary SVM, such as the maximization spirit, the use of kernel techniques to solve nonlinear separable problems, and excellent generalization ability. (3) In the dual problem, we develop an SMO algorithm to effectively reduce the complexity of time and space. We eventually validate the preceding statement with comprehensive experiments. The experiment findings show that our method outperforms other mainstream methods in terms of computing time and classification performance on synthetic datasets, UCI datasets, and NDC datasets.