Matrix Completion with Side Information using Manifold Optimization

The authors solve the matrix completion (MC) problem based on manifold optimisation by incorporating the side information under which the columns of the intended matrix are drawn from a union of low-dimensional subspaces. It is proved that this side information leads us to construct new manifolds, as an embedded sub-manifold of the manifold of constant rank matrices, using which the MC problem is solved more accurately. The required geometrical properties of the aforementioned manifold are then presented for MC. Simulation results over both synthetic and real-world data show that the proposed method outperforms some recent techniques either based on side information or not.