Abstract

Locally linear embedding (LLE) is a nonlinear dimension reduction technique that only relies on the assumption of local linearity. While it is known to produce good results and is computationally efficient, it does not perform well when the observations are distorted by noises, as the fundamental assumption of local linearity becomes violated. In this work, we present a modification of locally linear embedding which is designed to handle such situations. This new modification is termed LLEAN, short for locally linear embedding with additive noise, which has been seen to perform better in the presence of noise distortion. In LLEAN, we seek to recover the noiseless data from the noisy data by exploiting the relationship between local linearity and reconstruction potential, and we then use the recovered noiseless data while performing the dimension reduction. The LLEAN algorithm includes a tuning parameter, and our work includes an automatic selection method for the tuning parameter to remove the burden from the user.