Bounded manifold completion

Enhanced Matrix Completion with Manifold Learning

We study the problem of matrix completion when information about row or column proximities is available, in the form of weighted graphs. The problem can be formulated as the optimization of a convex function that can be solved efficiently using the alternating direction multipliers method. Experiments show that our model offers better reconstruction than the standard method that only uses a low...

The Information Manifold for Relatively Bounded Potentials

We construct a Banach manifold of states, which are Gibbs states for potentials that are form-bounded relative to the free Hamiltonian. We construct the (+1)-affine structure and the (+1)−connection. keywords Information manifold, Fisher metric, quantum geometry, Bogoliubov metric, Kubo theory, statistical manifold.

Mean-shift algorithms for manifold denoising, matrix completion and clustering

The Completion of the Manifold of Riemannian Metrics

We give a description of the completion of the manifold of all smooth Riemannian metrics on a fixed smooth, closed, finite-dimensional, orientable manifold with respect to a natural metric called the L metric. The primary motivation for studying this problem comes from Teichmüller theory, where similar considerations lead to a completion of the well-knownWeil-Petersson metric. We give an applic...

Tensor Completion with Side Information: A Riemannian Manifold Approach

By restricting the iterate on a nonlinear manifold, the recently proposed Riemannian optimization methods prove to be both efficient and effective in low rank tensor completion problems. However, existing methods fail to exploit the easily accessible side information, due to their format mismatch. Consequently, there is still room for improvement. To fill the gap, in this paper, a novel Riemann...