IMP: A message-passing algorithm for matrix completion

A new message-passing (MP) method is considered for the matrix completion problem associated with recommender systems. We attack the problem using a (generative) factor graph model that is related to a probabilistic low-rank matrix factorization. Based on the model, we propose a new algorithm, termed IMP, for the recovery of a data matrix from incomplete observations. The algorithm is based on a clustering followed by inference via MP (IMP). The algorithm is compared with a number of other matrix completion algorithms on real collaborative filtering (e.g., Netflix) data matrices. Our results show that, while many methods perform similarly with a large number of revealed entries, the IMP algorithm outperforms all others when the fraction of observed entries is small. This is helpful because it reduces the well-known cold-start problem associated with collaborative filtering (CF) systems in practice.