ISSN 1000-1239 CN 11-1777/TP

• 论文 •

### 基于谱图理论的流形学习算法

1. (北京交通大学计算机与信息技术学院 北京 100044) (swluo@center.njtu.edu.cn)
• 出版日期: 2006-07-15

### Manifold Learning Algorithms Based on Spectral Graph Theory

Luo Siwei and Zhao Lianwei

1. (School of Computer and Information Technology, Beijing Jiaotong University, Beijing 100044)
• Online: 2006-07-15

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.