We present a mathematical analysis of a non-convex energy landscape for Robust Subspace Recovery. We prove that if a deterministic condition holds in a neighborhood of an underlying subspace, then the underlying subspace is the only stationary point and local minimizer in this neighborhood. We further show that if the deterministic condition is satisfied, a geodesic gradient descent method over the Grassmannian manifold can exactly recover the underlying subspace with proper initialization. The condition is shown to hold with high probability for a certain model of data.
Joint work with Teng Zhang and Gilad Lerman.