A noise-insensitive LLE algorithm

The core idea of LLE is that high-dimensional data can be seen near-linear dependency from the local perspective. That is, at a local scale, a data point can be linear representation by its nearest neighbor interpolation, but for noisy data, its local linear representation will produce deviations, as result, the error of dimension reduction is greater. To address the problem, this article determines system noise points according to the density of data set. The low density points judged to be noise points and the noise points are not used in process of dimension reduction. This method reduces the impact of noise on LLE effectively, which is proved by simulation experiment on Swissrol dataset.