On the convergence of maximum variance unfolding
This work addresses theoretical gaps in a widely used dimensionality reduction technique, though it is incremental as it builds on existing methods without introducing new paradigms.
The paper tackles the problem of understanding the large sample limit and convergence rates of Maximum Variance Unfolding, a nonlinear dimensionality reduction method, finding that it is consistent under specific conditions like isometry to convex subsets but fails in some simple cases.
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.