Multiscale online tracking of manifolds

This paper describes a Multiscale Online Union of Sub-Spaces Estimation (MOUSSE) algorithm for online tracking of a time-varying manifold. MOUSSE uses linear subsets of low-dimensional hyperplanes to approximate a manifold embedded in a high-dimensional space. Each subset corresponds to the leaf node in a binary tree which encapsulates the multiresolution analysis underlying the proposed algorithm. The tree structure and parameters of the subsets are estimated and sequentially updated using a stream of noisy samples. For each update, MOUSSE requires only simple linear computations. The update of each hyperplane in the estimate is computed via gradient descent on the Grassmannian manifold. Numerical simulations demonstrate the strong performance of MOUSSE in tracking a time-varying manifold.