Survey of Matrix Completion Models

In recent years, matrix completion (MC), derived from CS, has increasingly become a hot research topic in the field of machine learning. Many researchers have done a large number of fruitful studies on MC. In order to better grasp the development process of MC, the existing matrix completion models (MCMs) are reviewed. First, the process of the evolution from CS to MC is described, illustrating that the development of CS theory has laid the foundation for the formation of MC theory. Second, the existing MCMs are divided into four categories from the perspective of the relaxation of nonconvex and nonsmooth rank function, aiming to provide reasonable solutions for specific matrix completion applications. Finally, the existing problems in current matrix completion technology are pointed out and analyzed, meanwhile possible solutions for these problems are proposed, and the future work is discussed.