Adaptive Subspace Clustering for Matrix Completion

This paper deals with subspace clustering for a matrix completion, which is a problem of estimating missing entries in a matrix under the assumption that row or column vectors belongs to multiple low-dimensional linear spaces. Various methods for the problem have been proposed. Some of them assume that row or column vectors in a matrix can be divided into several clusters where vectors span a low-dimensional linear space and provide mathematical optimization techniques which divide a matrix into several smaller low rank matrices. However, the performance of these approaches depends on the initial values and conditions, and the accuracy of a matrix completion becomes worse when each subspace is not strictly low-dimensional due to noise. In order to improve the accuracy of a matrix completion, this paper proposes a method to reduce the dependence of initial values and to enhance robustness against noise. Numerical examples show that the proposed method achieves higher accuracy in subspace clustering and matrix completion compared to conventional methods.