Global Versus Local Methods in Nonlinear Dimensionality Reduction

Part of Advances in Neural Information Processing Systems 15 (NIPS 2002)

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Vin Silva, Joshua Tenenbaum


Recently proposed algorithms for nonlinear dimensionality reduction fall broadly into two categories which have different advantages and disad- vantages: 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 previ- ously been exclusive advantages of local methods: computational spar- sity and the ability to invert conformal maps.