  As a paradigm to recover unknown entries of a matrix from partial
observations, low-rank matrix completion (LRMC) has generated a great deal of
interest. Over the years, there have been lots of works on this topic but it
might not be easy to grasp the essential knowledge from these studies. This is
mainly because many of these works are highly theoretical or a proposal of new
LRMC technique. In this paper, we give a contemporary survey on LRMC. In order
to provide better view, insight, and understanding of potentials and
limitations of LRMC, we present early scattered results in a structured and
accessible way. Specifically, we classify the state-of-the-art LRMC techniques
into two main categories and then explain each category in detail. We next
discuss issues to be considered when one considers using LRMC techniques. These
include intrinsic properties required for the matrix recovery and how to
exploit a special structure in LRMC design. We also discuss the convolutional
neural network (CNN) based LRMC algorithms exploiting the graph structure of a
low-rank matrix. Further, we present the recovery performance and the
computational complexity of the state-of-the-art LRMC techniques. Our hope is
that this survey article will serve as a useful guide for practitioners and
non-experts to catch the gist of LRMC.
