An Improved Weighted Local Linear Embedding Algorithm

Abstract

Local linear embedding has the characteristics of nonlinearity and simple implementation, but it cannot accurately handle the selection of neighborhoods under the conditions of noise, large curvature and sparse sampling. To solve this problem, an improved weighted local linear embedding method (WLE-LLE) is proposed. In WLE-LLE, the dimensionality reduction objective function is reconstructed by utilizing Laplacian Eigenmaps, which can effectively represent the manifold structure of nonlinear data. Theoretical analyses show the proposed method is better than LLE algorithm in preserving the original manifold structure of the data. And numerical experiments show its classification recognition rate is greatly improved, which is 2%-8% higher than LLE.