SCALABLE SEMIDEFINITE MANIFOLD LEARNING Nikolaos Vasiloglou, Alexander G. Gray, David V. Anderson Georgia Institute of Technology
Atlanta Ga · 2008
Maximum Variance Unfolding (MVU) is among the state of the art Manifold Learning (ML) algorithms and experimentally proven to be the best method to unfold a manifold to its intrinsic dimension. Unfortunately it doesn’t scale for more than a few hundred points. A non convex formulation of MVU made it possible to scale up to a few thousand points with the risk of getting trapped in local minima. In this paper we demonstrate techniques based on the dual-tree algorithm and L-BFGS that allow MVU to scale up to 100,000 points. We also present a new variant called Maximum Furthest Neighbor Unfolding (MFNU) which performs even better than MVU in terms of avoiding local minima.