We propose a totally functional view of geometric matrix completion problem.
Differently from existing work, we propose a novel regularization inspired from
the functional map literature that is more interpretable and theoretically
sound. On synthetic tasks with strong underlying geometric structure, our
framework outperforms state of the art by a huge margin (two order of
magnitude) demonstrating the potential of our approach. On real datasets, we
achieve state-of-the-art results at a fraction of the computational effort of
previous methods. Our code is publicly available at
this https URL

我们提出了一种全面功能的几何矩阵完成问题视图，相比现有作品，我们提出了一种新颖的正则化方法，受到功能映射文献的启发，更具可解释性和理论上的可靠性，并在强烈的基础几何结构的合成任务上表现出比现有技术高出数个数量级的潜力，在真实数据集上，我们仅以先前方法的一小部分计算成本取得了最先进的结果。

几何矩阵补全：功能观点

Geometric Matrix Completion: A Functional View

Geometric matrix completion (GMC) has been proposed for recommendation by
integrating the relationship (link) graphs among users/items into matrix
completion (MC). Traditional GMC methods typically adopt graph regularization
to impose smoothness priors for MC. Recently, geometric deep learning on graphs
(GDLG) is proposed to solve the GMC problem, showing better performance than
existing GMC methods including traditional graph regularization based methods.
To the best of our knowledge, there exists only one GDLG method for GMC, which
is called RMGCNN. RMGCNN combines graph convolutional network (GCN) and
recurrent neural network (RNN) together for GMC. In the original work of
RMGCNN, RMGCNN demonstrates better performance than pure GCN-based method. In
this paper, we propose a new GMC method, called convolutional geometric matrix
completion (CGMC), for recommendation with graphs among users/items. CGMC is a
pure GCN-based method with a newly designed graph convolutional network.
Experimental results on real datasets show that CGMC can outperform other
state-of-the-art methods including RMGCNN in terms of both accuracy and speed.

本论文提出了一种新的纯以 GCN 为基础的 GMC 方法，叫做卷积几何矩阵完成（CGMC），通过新设计的图卷积网络在用户 / 物品之间进行图推荐，实验结果显示 CGMC 在准确性和速度方面优于其他最先进的方法，包括 RMGCNN。