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A supervised nonlinear classification approach is proposed in this paper. It can classify data in original feature space without concerning kernel transformation to map data into linear high dimension space, Belonging degree measure used in this approach is more rational than some conventional distance measures such as Euclidean distance, Under ERM principle, union of hyper ellipsoids and hyper planes are learned to approximate decision regions, but with much less parameters of hyper ellipsoid to learn than other ellipsoid-based classification methods. We compared the proposed approach with k-NN, SVM and linear subspace method on data sets from UCI Machine Learning Repository. Experiment results showed that the proposed approach achieved higher prediction accuracy than the other 3 methods.