Learning Low-Rank Representation for Matrix Completion

In this paper, we address the low-rank matrix completion problem where column vectors are lying in a union of multiple subspaces. We propose a matrix completion method that predicts the value of the missing entries by learning a low-rank representation from the observed entries. Our method effectively recovers the missing entries by capturing the multi-subspace structure of the data points. We reformulate our method as the unconstrained regularized form, which can scale up to large matrix and learn the low -rank representation more efficiently. In addition, subspace clustering is conducted with the low-rank representation which reveals the memberships of the data points. In both synthetic and real experiments, the proposed methods accurately recover the missing entries of the matrix and cluster the data points by capturing the multisubspace structure effectively.