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Due to the fact that the training time and space complexities of SVMs are mainly dependent on the size of training set, SVMs are not suitable for classifying large data sets with several millions of examples. To solve this problem, we in this paper propose a new algorithm called minimum enclosing ball (MEB) based SVM (MEB-SVM). In MEB-SVM, the boundary of each class data set is first measured by several MEBs, and then an SVM is trained by the data locating on the two class boundaries. Experiments on the KDDCUP-99 intrusion detection data set with about five million examples, the Ringnorm artificial data set with one hundred million examples, and the NDC data set with two million examples show that the new algorithm has competitive performance in terms of running time, testing accuracy and number of support vectors.