Locally linear embedding greatly depends on whether the neighborhood graph can realistically reflect the underlying geometry structure of the data manifolds. The topological structure of constructed neighborhood with the existing approaches is unstable. It is sensitive to the noisy and sparse data sets. Based on the relative cognitive law, the relative transformation is presented, by which the relative space and the relative manifold are further constructed. The relative transformation can improve the distinguishing ability between data points and reduce the impact of noise and sparsity of data. To determine the neighborhood in the relative space and the relative manifold can more truly reflect the manifold structure, based on which the enhanced local linear embedding algorithms are developed with significantly improved performance. Besides, the speed is also enhanced with this approach. The experiments on challenging benchmark data sets validate the proposed approach.