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A method based on Riemannian metric to the classification problem with imbalanced training data was proposed. The idea is based on the analysis of the optimizing hyper-plane and support vectors induced by an RBF kernel. We use the conformal transformation and Riemannian metric to modify this RBF kernel, and reconstruct a new SVM with the modified kernel. The later SVM is shown to be superior to the traditional SVM classifier. Experimental results show that this method can improve the accuracy of the class with less training data under a high total accuracy.