Convolutional Geometric Matrix Completion

Geometric matrix completion~(GMC) has been proposed for recommendation by integrating the relationship~(link) graphs among users/items into matrix completion~(MC) . Traditional \mbox{GMC} methods typically adopt graph regularization to impose smoothness priors for \mbox{MC}. Recently, geometric deep learning on graphs~(\mbox{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 \mbox{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 \mbox{GMC} method, called \underline{c}onvolutional \underline{g}eometric \underline{m}atrix \underline{c}ompletion~(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.