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Scaled Gradients on Grassmann Manifolds for Matrix Completion

Scaled Gradients on Grassmann Manifolds for Matrix Completion

This video was recorded at Video Journal of Machine Learning Abstracts - Volume 3. 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.

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