On the Convergence of Maximum Variance Unfolding

Ery Arias-Castro, Bruno Pelletier.

Year: 2013, Volume: 14, Issue: 18, Pages: 1747−1770


Maximum Variance Unfolding is one of the main methods for (nonlinear) dimensionality reduction. We study its large sample limit, providing specific rates of convergence under standard assumptions. We find that it is consistent when the underlying submanifold is isometric to a convex subset, and we provide some simple examples where it fails to be consistent.