Nonlinear dimensionality reduction by locally linear embedding

Many areas of science depend on exploratory data analysis and visualization . The need to analyze Large amounts of multivariate data raises the fundame ntal problem of dimensionality reduction: how to discover compact represent ations of high-dimensional data. Here, we introduce Locally Linear embeddin g (LLE), an unsupervised Learning algorithm that computes Low-dimensional, neighborhood-preserving embeddings of high-dimensional inputs. Unlike clust ering methods for Local dimensionality reduction, LLE maps its inputs into a single global coordinate system of lower dimensionality, and its optimiza tions do not involve Local minima. By exploiting the local symmetries of Li near reconstructions, LLE is able to Learn the global structure of nonlinea r manifolds, such as those generated by images of faces or documents of tex t.