Abstract: Aiming at the high computational cost issue for large data sets in kernel space, the non-linear support vector machine (NSVM) is proposed to reduce training data of classifier. First, a subset of training classifier is extracted from full training data by using NSVM, kernel principal component analysis (KPCA), and greedy kernel principal component analysis (GKPCA), respectively. Then, the classifier is trained by those subsets, respectively. Finally, the classification results are evaluated by the error rate of the training and test data. The classification performance of the classifier trained by the subsets from the KPCA method is inferior to those of from the NSVM and the GKPCA methods, but the generalization of the classifier trained by the subset from the GKPCA method is inferior to those of from the NSVM method for two data sets through two the classifiers. Simulation results indicate that the classifier trained by the subset from the NSVM method not only ensures the generalization ability of classifier, but also reduces the computational complexity of the classification algorithm.