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In this paper, we derive an efficient nonlinear feature extraction method from naive Kernel Minimum Squared Error (KMSE) method. The most contribution of the derived method is its feature extraction procedure that is much more computationally efficient than naive KMSE. Differing from naive KMSE that exploits some linear combination of the total training patterns to express the discriminant vector in feature space, the derived method attempts to select out a small number of patterns (referred to as ¿significant nodes¿ in this paper) from the training set and exploits some linear combination of ¿significant nodes¿ to approximate to the discriminant vector in feature space. According to the following two principles, an algorithm for producing ¿significant nodes¿ is designed. The ¿significant node¿ set should well represent the whole training patterns, and each ¿significant node¿ should contribute much for the feature …