Weighted Low-rank Approximation via Stochastic Gradient Descent on Manifolds
This work addresses matrix completion for recommender systems, offering an incremental improvement over existing stochastic gradient descent techniques.
The authors tackled the regularized weighted low-rank approximation problem by developing a stochastic gradient descent method on manifolds, which outperformed Euclidean space methods on Netflix Prize data with concrete performance gains.
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.