Nonlinear dimensionality reduction of manifolds by diffusion maps

被引：0

作者：

Shang X.-Q. ^{[1
]}

Song Y.-M. ^{[1
]}

机构：

[1] School of Science, Xidian Univ.

来源：

Xi'an Dianzi Keji Daxue Xuebao/Journal of Xidian University | 2010年 / 37卷 / 01期

关键词：

Diffusion maps; Manifold learning; Nonlinear dimensionality reduction;

D O I：

10.3969/j.issn.1001-2400.2010.01.023

中图分类号：

学科分类号：

摘要：

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.

引用

页码：130 / 135

页数：5

共 13 条

[1] Partridge M., Calyo R., Fast dimensionality reduction and simple PCA, Intelligent Data Analysis, 2, 3, pp. 292-298, (1997)
[2] Hyvrinen A., Survey on independent component analysis, Neural Computing Surveys, 2, 4, pp. 94-128, (1999)
[3] Tenenbaum J.B., de Silva V., Langford J.C., A global geometric framework for nonlinear dimensionality reduction, Science, 290, pp. 2319-2323, (2000)
[4] Roweis S.T., Saul L.K., Nonlinear dimensionality reduction by locally linear embedding, Science, 290, pp. 2323-2326, (2000)
[5] Belkin M., Niyogi P., Laplacian Eigenmaps for dimensionality reduction and data representation, Neural Computation, 15, 6, pp. 1373-1396, (2003)
[6] Zhang Z., Zha H., Priciple manifolds and nonlinear dimensionality reduction via local tangent space alignment, SIAM Journal of Scientific Computing, 26, 1, pp. 313-338, (2005)
[7] Xiao G., Liu S., Yin X., Optimization algorithm on differentiable manifolds, Journal of Xidian University, 34, 3, pp. 472-475, (2007)
[8] Ma R., Wang J., Song Y., Multi-manifold learning using locally linear embedding(LLE) nonlinear dimensionality reduction, Journal of Tsinghua University, 48, 4, pp. 582-585, (2008)
[9] Wen G., Jiang L., Wen J., Dynamically determining neighborhood parameter for locally linear embedding, Journal of Software, 19, 7, pp. 1666-1672, (2008)
[10] Nadler B., Lafon S., Coifman R.R., Et al., Diffusion maps, spectral clustering and the reaction coordinate of dynamical systems, Applied and Computation Harmonic Analysis: Special Issue on Diffusion Maps and Wavelets, 21, 1, pp. 113-127, (2006)

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