Yan-Ming Zhang, Institute of Automation, Chinese Academy of Sciences, P.R. China
Xinwen Hou, Institute of Automation, Chinese Academy of Sciences, P.R. China
Shiming Xiang, Institute of Automation, Chinese Academy of Sciences, P.R. China
Cheng-Lin Liu, Institute of Automation, Chinese Academy of Sciences, P.R. China

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Abstract

Most existing semi-supervised learning methods are based on the smoothness assumption that data points in the same high density region should have the same label. This assumption, though works well in many cases, has limitations. To overcome this problems, we introduce into semi-supervised learning the classic low-dimensionality embedding assumption, stating that most geometric information of high dimensional data is embedded in a low dimensional manifold. Based on this, we formulate the problem of semi-supervised learning as a task of finding a subspace and a decision function on the subspace such that the projected data are well separated and the original geometric information is preserved as much as possible. Under this framework, the optimal subspace and decision function are iteratively found via a projection pursuit procedure. The low computational complexity of the proposed method lends it to applications on large scale data sets. Experimental results demonstrates the effectiveness of our method.