Scaled gradients on grassmann manifolds for matrix Completion by Thanh Ngo and Yousef Saad. The abstract reads:
This paper describes gradient methods based on a scaled metric on the Grassmann manifold for low-rank matrix completion. The proposed methods signiﬁcantly improve canonical gradient methods, especially on ill-conditioned matrices, while maintaining established global convegence and exact recovery guarantees. A connection between a form of subspace iteration for matrix completion and the scaled gradient descent procedure is also established. The proposed conjugate gradient method based on the scaled gradient outperforms several existing algorithms for matrix completion and is competitive with recently proposed methods.
The attendant code is here. Also of interest the NIPS, 2012 Spotlight presentation and Poster. This algorithm and code will shortly be listed to the Advanced Matrix Factorization Jungle.
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