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《Chinese Journal of Computers》 2005-12
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Investigating Manifold Learning Algorithms Based on Magnification Factors and Principal Spread Directions

HE Li 1),3) ZHANG Jun-Ping 1),2) ZHOU Zhi-Hua 4) 1) (Shanghai Key Laboratory of Intelligent Information Processing, Department of Computer Science and Engineering, Fudan University, Shanghai 200433) 2) (Key Laboratory of Complex Systems and Intelligence Science, Chinese Academy of Sciences, Shanghai 200433) 3) (Department of Computer Science and Engineering, School of Mathematical Sciences, Fudan University, Shanghai 200433) 4) (National Laboratory for Novel Software Technology, Nanjing University, Nanjing 210093)  
As a new unsupervised learning technique, manifold learning has captured the attention of many researchers in the field of machine learning and cognitive sciences. The major algorithms include Isometric mapping (ISOMAP) and Locally Linear Embedding (LLE). The approaches can be used for discovering the intrinsic dimensions of nonlinear high-dimensional data effectively and aim researchers to analyze the data better. How to quantitatively analyze the relationship between the intrinsic dimensions and the observation space, however, has fewer reports. And thus further works in manifold learning may have suffered some difficulties. The paper focuses on two kinds of manifold learning algorithms (ISOMAP, LLE), and discusses magnification factors and principal spread directions from the observation space to the intrinsic low-dimensional space. Also the corresponding algorithm is proposed. Experiments show the effectiveness and advantages of the research.
【Fund】: IIPL-04-014;; 国家杰出青年科学基金(60325207);; 国家自然科学基金重大项目(60496320)资助.
【CateGory Index】: TP181
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