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Manifold learning is one of the efficient nonlinear dimensionality reduction techniques, which can be used to fault feature extraction. But they are not taking the class information of the data into account. In this paper, a new supervised Laplacian Eigenmaps algorithm (S-LapEig) for classification is proposed first. Via utilizing class information to guide the procedure of nonlinear mapping, the S-LapEig enhances local within-class relations and help to classification. Based on the S-LapEig, a novel fault classification approach is proposed. The approach uses the S-LapEig to extract feature for class labels data, and utilizes RBF network to map the unlabeled data to the feature space, which easily implement pattern classification and fault diagnosis. The experiments on benchmark data and real fault dataset demonstrate that, the proposed approach excels compared to PCA and Laplacian Eigenmaps, and it is an accurate technique for classification.