在流形上用随机梯度下降优化加权低秩逼近，提升推荐系统性能。
Weighted Low-rank Approximation via Stochastic Gradient Descent on Manifolds
- 在流形上设计随机梯度下降算法，保证收敛性。
- 在Netflix数据集上优于传统欧氏空间方法。
- 适合需要高效低秩建模的推荐系统研究者。
我们通过流形上的随机梯度下降求解正则化加权低秩逼近问题。为确保算法收敛，建立了基于投影的随机梯度下降在受限流形上的收敛定理。在Netflix Prize训练数据集的样本上，该算法性能优于现有欧氏空间随机梯度下降方法。同时，我们将该流形上的加速线搜索与欧氏空间方法进行了对比，验证了其有效性。
原文摘要 · Abstract (English)
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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