HLLE Algorithm Based on the Weighted Distance

HLLE is an effective nonlinear dimension reduction algorithm and is widely explored into machine learning, pattern recognition, data mining and etc. However, HLLE is very sensitive to the neighborhood selection and non-uniformed data sampling. In this paper, an improved HLLE based on weighted distance named WHLLE is proposed which can avoid the unreasonable neighborhood selection by using weighted Euclidean distance. Furthermore, WHLLE not only can have a better effect of dimension reduction but also can preserve the intrinsic geometry structure of the original manifolds. We validate the performances of WHLLE on the two classical artificial manifolds. The experiments on artificial manifolds confirm that WHLLE can keep the relationship of neighborhood of the data point, global distributions and intrinsic structures of the data better than other related Algorithms.