A new algorithm called classification-rejection sphere support vector machines (C-R sphere SVMs) is proposed based on the human thoughts of recognition and support vector machine (SVM) technology for multi-class classification problems. The new algorithm constructs a classifying sphere for each class instead of a minimum sphere. Like human being, C-R sphere SVMs can not only classify the multi-class data but reject the data which do not belong to any class known. In comparison with hyperplane SVMs, the algorithm can construct a new classifying sphere for a new class without affecting other classifying spheres so that it can reduce computational complexity obviously. The effect of the increment coefficient lambda and Gaussian kernel parameter ó on the performance of C-R sphere SVMs is analyzed. Numerical simulations are performed on a real dataset (from the UCI dataset repository). The results show that the C-R sphere SVM algorithm exhibits good performance when appropriate values of lambda and sigma are taken.
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