Speaker: Michael Trosset (Indiana University)

Title:    Locally Linear Embedding is a Laplacian Eigenmap


Abstract:

An approach to nonlinear dimension reduction called manifold learning
posits that high-dimensional data lie (approximately) on low-dimensional
manifolds.  In a seminal paper, Roweis and Saul (2000) proposed a widely
used manifold learning technique that attempts to characterize local
geometry by linear coefficients that reconstruct each point from its
neighbors.  We present a simple example that demonstrates that Locally
Linear Embedding (LLE) can profoundly distort data.  We relate LLE to
another manifold learning technique, Laplacian eigenmaps, demonstrating
that the former can be understood as a somewhat problematic special case
of the latter.

This research is supported by the Office of Naval Research.  It is joint
work with Brent Castle.