Weighted Low-rank Approximation via Stochastic Gradient Descent on Manifolds

Conglong Xu; Peiqi Yang; Hao Wu

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arXiv · 2502.14174

Weighted Low-rank Approximation via Stochastic Gradient Descent on Manifolds

Conglong Xu·Peiqi Yang·Hao Wu

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Abstract

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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BibTeX RIS

Conglong Xu, Peiqi Yang, Hao Wu. 2025-02-20. Weighted Low-rank Approximation via Stochastic Gradient Descent on Manifolds. https://arxiv.org/abs/2502.14174

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