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Weighted Low-rank Approximation via Stochastic Gradient Descent on Manifolds
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Weighted Low-rank Approximation via Stochastic Gradient Descent on Manifolds
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We solve a regularized weighted low-rank approximation problem by a stochastic gradient descent on a manifold. To guarantee the convergence of our stochastic gradient descent, we establish a convergence theorem on manifolds for retraction-based stochastic gradient descents admitting confinements. On sample data from the Netflix Prize training dataset, our algorithm outperforms the existing stochastic gradient descent on Euclidean spaces. We also compare the accelerated line search on this manifold to the existing accelerated line search on Euclidean spaces.
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Cited by 1 Pith paper
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Convergence of Riemannian Stochastic Gradient Descents: Varying Batch Sizes And Nonstandard Batch Forming
Convergence theorems are established for Riemannian SGD with iteration-varying probability spaces, applying to varying batch sizes and unbiased batch forming schemes.
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