AN EFFICIENT ONLINE ADAPTIVE SAMPLING STRATEGY FOR MATRIX COMPLETION

Matrix Completion (MC) i.e., estimating the missing values of an unknown matrix based on limited information, has been a prominent topic of study in the last decades. In this paper, we focus more precisely on a little-known aspect of MC, namely how the recommendation of new entries can help improve the accuracy of the reconstruction. We present an efficient online algorithm to solve the MC task, and propose an Adaptive Sampling under Smoothness Assumption (AdSSA) strategy, which is suitable for operation on smooth low-rank matrices. This technique is able to predict iteratively which entries are the most informative. Our numerical examples illustrate that AdSSA performs significantly better than the Uniform Random Sampling (URS) and the Query by Committee (QbC). In addition, AdSSA algorithm can be straightforwardly implemented in an online and efficient manner, which constitutes another advantage.