An Introduction to Locally Linear Embedding
Many problems in information processing involve some form of dimensionality reduction. Here we describe locally linear embedding (LLE), an unsupervised learning algorithm that computes low dimensional, neighborhood preserving embeddings of high dimensional data. LLE attempts to discover nonlinear structure in high dimensional data by exploiting the local symmetries of linear reconstructions. Notably, LLE maps its inputs into a single global coordinate system of lower dimensionality, and its optimizations— though capable of generating highly nonlinear embeddings—do not involve local minima. We illustrate the method on images of lips used in audiovisual speech synthesis.