Nesting algorithm for multi-classification problems

Support vector machines (SVMs) are originally designed for binary classifications. As for multi-classifications, they are usually converted into binary ones. In the conventional multi-classifiable algorithms, One-against-One algorithm is a very power method. However, there exists a middle unclassifiable region. In order to overcome this drawback, a novel method called Nesting Algorithm is presented in this paper. Our ideas are as follows: firstly, construct the optimal hyperplanes based on One-against-One approach. Secondly, if there exist data points in the middle unclassifiable region, select them to construct the optimal hyperplanes with the same hyperparameters. Thirdly, repeat the second step until there are no data points in the unclassifiable region or the region is disappeared. In this paper, we also prove the validity of the proposed algorithm for unclassifiable region and give the computational complexity analysis of the method. In order to examine the training accuracy and the generalization performance of the proposed algorithm, One-against-One algorithm, fuzzy least square support vector machine (FLS-SVM) and the proposed algorithm are applied to five UCI datasets. The results show that the training accuracy of the proposed algorithm is higher than the others, and its generalization performance is also comparable with them.