Abstract

A Kernel View of the Dimensionality Reduction of Manifolds
Jihun Ham - University of Pennsylvania Daniel Lee - University of Pennsylvania Sebastian Mika - Fraunhofer FIRST.IDA Bernhard Schoelkopf - Max-Planck-Institut fuer biologische Kybernetik
We interpret several well-known algorithms for dimensionality reduction of manifolds as kernel methods. Isomap, graph Laplacian eigenmap, and locally linear embedding (LLE) all utilize local neighborhood information to construct a global embedding of the manifold. We show how all three algorithms can be described as kernel PCA on specially constructed Gram matrices, and illustrate the similarities and differences between the algorithms with representative examples.

A Kernel View of the Dimensionality Reduction of Manifolds

Jihun Ham - University of Pennsylvania
Daniel Lee - University of Pennsylvania
Sebastian Mika - Fraunhofer FIRST.IDA
Bernhard Schoelkopf - Max-Planck-Institut fuer biologische Kybernetik

We interpret several well-known algorithms for dimensionality reduction of manifolds as kernel methods. Isomap, graph Laplacian eigenmap, and locally linear embedding (LLE) all utilize local neighborhood information to construct a global embedding of the manifold. We show how all three algorithms can be described as kernel PCA on specially constructed Gram matrices, and illustrate the similarities and differences between the algorithms with representative examples.