Multiple k-Means Clustering Based Locally Low-Rank Approach to Nonlinear Matrix Completion

This paper deals with nonlinear matrix completion problem, which is a problem of restoring missing entries in a given matrix, where its column vectors belong to a low dimensional manifold. Assuming that a low dimensional manifold can be approximated locally as a low dimensional linear subspace, this paper proposes a new locally low-rank approach. In this approach iteratively solves low-rank matrix completion problems for submatrices generated by using the k-means clustering for several values of k and restores missing entries. Numerical examples show that the proposed algorithm achieves better performance than other algorithms.