Many supervized learning systems have been studied, such as multilayer perceprtons, support vector machines (SVM), e.g. RBF networks and polynomial networks, which utilize inner product kernels. Especially, SVM is attracting attention as provideing a good generalization and classification performance. Those properties of SVM are based on the fact that the learning is optimized with both the training error rate and the generalization performance. However, for practical problems, it is difficult to compute its support vectors directly since the high computation cost. In this paper, we propose fast algorithms of polynomial SVM and extensions of SVM.
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