| 基于谱图理论的流形学习算法 |
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| 引用本文： | 罗四维,赵连伟.基于谱图理论的流形学习算法[J].计算机研究与发展,2006,43(7):1173-1179. |
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| 作者姓名： | 罗四维 赵连伟 |
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| 作者单位： | 北京交通大学,计算机与信息技术学院,北京,100044 |
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| 基金项目： | 中国科学院资助项目;高等学校博士学科点专项科研项目;北京市重点学科建设项目 |
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| 摘 要： | 流形学习的主要目标是发现嵌入在高维数据空间的低维光滑流形．近年来基于谱图理论的学习算法受到研究者的广泛关注．介绍了流形与流形学习的关系，着重研究了几种有代表性的基于谱图理论的流形学习算法，并对算法进行了比较分析，最后进行总结和对进一步的研究做了展望．
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| 关 键 词： | 流形学习 谱图理论 局部切空间 随机游走 特征映射 |
| 收稿时间： | 05 19 2005 12:00AM |
| 修稿时间： | 2005-05-192006-02-22 |
Manifold Learning Algorithms Based on Spectral Graph Theory |
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| Luo Siwei,Zhao Lianwei.Manifold Learning Algorithms Based on Spectral Graph Theory[J].Journal of Computer Research and Development,2006,43(7):1173-1179. |
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| Authors: | Luo Siwei Zhao Lianwei |
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| Affiliation: | School of Computer and Information Technology, Beijing Jiaotong University, Beijing 100044 |
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| Abstract: | 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. |
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| Keywords: | manifold learning spectral graph theory local tangent space random walk eigenmaps |
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