Speaker: Dr. Wotao Yin Inviter: Prof. Ya-xiang Yuan Title: Completing Low-Rank Matrices with Nonnegative Factors Time: 15:30-17:30, July 12th (Tuesday) Venue: Lecture Room 401, Lan-Bai Building Abstract: We identify the need for recovering nonnegative matrices X and Y, as well as their low-rank product M=XY, from very few entries of M. This problem is closely related to the two existing problems: nonnegative matrix factorization and low-rank matrix completion, in the sense that it kills two birds with one stone. By taking advantages of both nonnegativity and low rank, the recovery is superior than those of the two problems alone. Our algorithm is applied to minimizing a non-convex constrained least-squares formulation and is based on the classic alternating direction augmented Lagrangian method. Preliminary convergence properties and numerical simulation results are presented. Compared to a recent algorithm for nonnegative random matrix factorization, the proposed algorithm yields comparable factorization through accessing only half of the matrix entries. On tasks of recovering incomplete grayscale and hyperspectral images, the results of the proposed algorithm have overall better qualities than those of two recent algorithms for matrix completion. Joint work with Yangyang Xu, Zaiwen Wen (Shanghai Jiaotong U), and Yin Zhang