@article {12502, title = {Large-scale matrix factorization with missing data under additional constraints}, journal = {Advances in Neural Information Processing Systems}, volume = {23}, year = {2010}, month = {2010///}, pages = {1642 - 1650}, abstract = {Matrix factorization in the presence of missing data is at the core of many com-puter vision problems such as structure from motion (SfM), non-rigid SfM and photometric stereo. We formulate the problem of matrix factorization with miss- ing data as a low-rank semidefinite program (LRSDP) with the advantage that: 1) an efficient quasi-Newton implementation of the LRSDP enables us to solve large-scale factorization problems, and 2) additional constraints such as ortho- normality, required in orthographic SfM, can be directly incorporated in the new formulation. Our empirical evaluations suggest that, under the conditions of ma- trix completion theory, the proposed algorithm finds the optimal solution, and also requires fewer observations compared to the current state-of-the-art algorithms. We further demonstrate the effectiveness of the proposed algorithm in solving the affine SfM problem, non-rigid SfM and photometric stereo problems. }, author = {Mitra, K. and Sheorey,S. and Chellapa, Rama} }