MC2G: An Efficient Algorithm for Matrix Completion with Social and Item Similarity Graphs

TL;DR

MC2G is a fast, parameter-free matrix completion algorithm that effectively utilizes social and item similarity graphs, achieving near-optimal sampling efficiency and outperforming existing methods in experiments.

Contribution

Introduces MC2G, a novel spectral clustering-based matrix completion algorithm that is efficient, parameter-free, and theoretically near-optimal in sample complexity.

Findings

MC2G runs in quasilinear time.

MC2G matches information-theoretic lower bounds in sample complexity.

MC2G outperforms state-of-the-art algorithms in experiments.

Abstract

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.