Local linear embedding in dimensionality reduction based on small world principle

Analysis of large amount of data is needed in many areas of science, and this depends on dimensionality reduction of the multivariate data. Local linear embedding (LLE) is efficient for many nonlinear dimension reduction problems because of its low computation complexity and high efficiency, however LLE often leads to invalidation in the event that the data is sparse or noise contaminated. In order to improve the ability of LLE to deal with the sparse and noise data, small world neighborhood optimized LLE algorithm (SLLE) is proposed based on the complex networks theory in the paper. The local parameters of SLLE are optimized by using the shortest path and the local neighbor set clustering coefficient. As a result, the problem of embedding distortion using locally linear patch of the manifold only defining neighborhood in Euclidean space is efficiently solved. The results of standard experiments show that SLLE algorithm makes LLE more robust against no-ideal data.