一种基于扩散映射的非线性降维算法

doi:10.3969/j.issn.1001-2400.2010.01.023

J4 ›› 2010, Vol. 37 ›› Issue (1): 130-135.doi: 10.3969/j.issn.1001-2400.2010.01.023

一种基于扩散映射的非线性降维算法

尚晓清;宋宜美

(西安电子科技大学理学院，陕西西安 710071)

收稿日期:2009-01-02 出版日期:2010-02-20 发布日期:2010-03-29
通讯作者: 尚晓清
作者简介:尚晓清(1975-)，女，副教授，博士，E-mail: xqshang@xidian.edu.cn．
基金资助:
国家自然科学基金资助项目(60872138)

Nonlinear dimensionality reduction of manifolds by diffusion maps

SHANG Xiao-qing;SONG Yi-mei

(School of Science, Xidian Univ., Xi'an 710071， China)

Received:2009-01-02 Online:2010-02-20 Published:2010-03-29
Contact: SHANG Xiao-qing

摘要/Abstract

摘要：

非线性降维方法旨在保持数据局部结构的同时，使不在一个邻域内的点之间的距离变得松弛．作为一种新的流形学习框架，扩散映射通过在扩散过程中保持扩散距离进行降维．基于扩散映射的理论背景，建立了多层谱分解的数值算法，并具体给出了用扩散映射进行非线性降维的算法．实验结果表明，与传统的非线性降维方法相比较，该算法能够发现非线性高维数据的本征维数，并且对噪声具有很好的鲁棒性．

关键词: 扩散映射, 流形学习, 非线性降维

Abstract:

Nonlinear dimensionality reduction programs keep the local properties but relax the distances between points which are not in a neighborhood. As a new learning framework, the diffusion method realizes dimensionality reduction in a diffusion processing. Based on the theory of diffusion maps, this paper discusses the numerical method for spectral decomposition and presents the diffusion maps algorithm(DMA). Experimental results show that the DMA technique can detect the intrinsic dimensionality in high-dimensional data and is more stable in noise case.

Key words: diffusion maps, manifold learning, nonlinear dimensionality reduction

尚晓清;宋宜美. 一种基于扩散映射的非线性降维算法[J]. J4, 2010, 37(1): 130-135.

SHANG Xiao-qing;SONG Yi-mei. Nonlinear dimensionality reduction of manifolds by diffusion maps[J]. J4, 2010, 37(1): 130-135.

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一种基于扩散映射的非线性降维算法

Nonlinear dimensionality reduction of manifolds by diffusion maps

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