A characterization of sampling patterns for low-rank multi-view data completion problem

Abstract

In this paper, we consider the problem of completing a sampled matrix U = [U1|U2] given the ranks of U, U1, and U2 which is known as the multi-view data completion problem. We characterize the deterministic conditions on the locations of the sampled entries that is equivalent (necessary and sufficient) to finite completability of the sampled matrix. To this end, in contrast with the existing analysis on Grassmannian manifold for a single-view matrix, i.e., conventional matrix completion, we propose a geometric analysis on the manifold structure for multi-view data to incorporate more than one rank constraint. Then, using the proposed geometric analysis, we propose sufficient conditions on the sampling pattern, under which there exists only one completion (unique completability) given the three rank constraints.