  Matrix completion problem has been investigated under many different
conditions since Netflix announced the Netflix Prize problem. Many research
work has been done in the field once it has been discovered that many real life
dataset could be estimated with a low-rank matrix. Since then compressed
sensing, adaptive signal detection has gained the attention of many
researchers. In this survey paper we are going to visit some of the matrix
completion methods, mainly in the direction of passive and adaptive directions.
First, we discuss passive matrix completion methods with convex optimization,
and the second active matrix completion techniques with adaptive signal
detection methods. Traditionally many machine learning problems are solved in
passive environment. However, later it has been observed that adaptive sensing
algorithms many times performs more efficiently than former algorithms. Hence
algorithms in this setting has been extensively studied. Therefore, we are
going to present some of the latest adaptive matrix completion algorithms in
this paper meanwhile providing passive methods.
