In this paper, we design and analyze MC2G (Matrix Completion with 2 Graphs), an algorithm that performs matrix completion in the presence of social and item similarity graphs. MC2G runs in quasilinear time and is parameter free. It is based on spectral clustering and local refinement steps. The expected number of sampled entries required for MC2G to succeed (i.e., recover the clusters in the graphs and complete the matrix) matches an information-theoretic lower bound up to a constant factor for a wide range of parameters. We show via extensive experiments on both synthetic and real datasets that MC2G outperforms other state-of-the-art matrix completion algorithms that leverage graph side information.

翻译：在本文中,我们设计和分析 MC2G (Matrix Finishing with 2 Graps),这是一种算法,在社会和项目相似性图中进行矩阵完成。 MC2G 以准线性时间运行, 参数是免费的。 它基于光谱组和本地精细步骤。 MC2G 成功所需的样本条目( 即恢复图中的数据组并完成矩阵) 的预期数量, 匹配一种信息- 理论下至一个常数系数以至一系列参数。 我们通过对合成和真实数据集的广泛实验, 显示 MC2G 优于其他最先进的矩阵完成算法, 以图边信息为杠杆 。