Improved weighted local linear embedding algorithm based on Laplacian eigenmaps

Abstract

To solve the shortcomings of local linear embedding (LLE), such as sensitive to noise and poor generalization ability for new samples, an improved weighted local linear embedding algorithm based on Laplacian eigenmaps (IWLLE-LE) is proposed in this paper. In the proposed algorithm, Laplacian eigenmaps are used to reconstruct the objective function of dimensionality reduction. The weights of it are introduced by combining the geodesic distance with Euclidean distance, which can effectively represent the manifold structure of nonlinear data. Compared the existing LLE algorithm, the proposed one better maintains the original manifold structure of the data. The merit of the proposal is enhanced by the theoretical analysis and numerical experiments, where the classification recognition rate is 2%–8% higher than LLE.