Manifold contraction for semi-supervised classification

The generalization ability of classification is often closely related to both the intra-class compactness and the inter-class separability.Owing to the fact that many current dimensionality reduction methods, regarded as a pre-processor, often lead to the poor classification performance on real-life data, in this paper, a new data preprocessing technique called manifold contraction(MC) is proposed for the classification-oriented learning task.The main motivation behind MC lies in seeking a proper mapping of contracting the given multiple-manifold data such that the ratio of the intra-class to the inter-class scatters is minimized.Moreover, in order to properly control the contraction level in MC, an adaptive MC(AMC) criterion is developed in the semi-supervised setting.Due to its generality, MC can be not only applied in original space and reproducing kernel Hilbert space(RKHS), but also easily incorporated with dimensionality reduction method for further improvement of classification performance.The final experimental results show that MC, as a data preprocessor, is effective and promising in the subsequent classification learning, especially in small-size labeled sample case.