In 2000, Roweis and Saul developed Locally Linear Embedding (LLE) for nonlinear dimensional reduction of high dimensional data. LLE is an unsupervised learning algorithm that computes low-dimensional, neighborhood preserving embeddings of high-dimensional inputs. LLE maps its inputs into a single global coordinate system of lower dimensionality, and its optimizations do not involve local minima. By exploiting the local symmetries of linear reconstructions, LLE is able to learn the global structure of nonlinear manifolds.