Scalable semidefinite manifold learning

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 doesnpsilat 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.