Nonlinear dimensionality reduction of manifolds by diffusion maps

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.