Mc2g: An Efficient Algorithm for Matrix Completion With Social and Item Similarity Graphs

In this paper, we design and analyze
Mc2g
(
M
atrix
C
ompletion with
2

G
raphs), an efficient 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. For the matrix completion problem which possesses additional block structures in its rows and columns, we derive the expected number of sampled entries required for
Mc2g
to succeed, and further show that it matches an information-theoretic lower bound up to a constant factor for a wide range of parameters. We perform extensive experiments on both synthetic datasets and a semi-real dataset inspired by real graphs. The experimental results show that
Mc2g
outperforms other state-of-the-art matrix completion algorithms.