Unsupervised learning procedures have been the dominant method to capture manifolds. These techniques are based on the nearest neighbor graph, where there is one node per training example and there are edges connecting these nodes. Each node is associated with a tangent plane that spans the directions of variations associated with the difference vectors between a node and its neighbors. Optimization or solving a linear system can be used to form a global coordinate system, where a manifold is tiled by "pancakes" or regions of variance around a training point and there is interpolation between these "pancakes". This of course poses a weakness in the case of a complex shaped manifold as is the case with many machine learning problems, where a lot of training points would be needed to capture the shape and prevent the interpolation from being inaccurate.