Global Versus Local Methods in Nonlinear Dimensionality Reduction

Recently proposed algorithms for nonlinear dimensionality reduction fall broadly into two categories which have different advantages and disadvantages: global (Isomap [1]), and local (Locally Linear Embedding [2], Laplacian Eigenmaps [3]). We present two variants of Isomap which combine the advantages of the global approach with what have previously been exclusive advantages of local methods: computational sparsity and the ability to invert conformal maps.