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《Journal of Computer Research and Development》 2006-07
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Manifold Learning Algorithms Based on Spectral Graph Theory

Luo Siwei and Zhao Lianwei (School of Computer and Information Technology, Beijing Jiaotong University, Beijing 100044)  
In the problem of manifold learning, one seeks to find a smooth low-dimensional manifold embedded in the high-dimensional vector space, based on a set of sample points. Spectral graph theory studies the eigenvectors and eigenvalues of matrices associated with graphs and has been widely used in the manifold learning algorithm recently. In this paper, the relationship between the manifold and the manifold learning is introduced first, and then some typical manifold learning algorithms based on spectral graph theory are studied. Finally, some directions for further research are suggested.
【Key Words】: manifold learning spectral graph theory local tangent space random walk eigenmaps
【Fund】: 国家自然科学基金项目(60373029);; 国家教育部博士学科点基金项目(20050004001);; 北京市重点学科共建基金项目(XK100040415)
【CateGory Index】: TP181
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