Information-theoretic Bounds on Matrix Completion under Union of Subspaces Model

In this short note we extend some of the recent results on matrix completion under the assumption that the columns of the matrix can be grouped (clustered) into subspaces (not necessarily disjoint or independent). This model deviates from the typical assumption prevalent in the literature dealing with compression and recovery for big-data applications. The results have a direct bearing on the problem of subspace clustering under missing or incomplete information.