Matrix Completion with Graph Side Information: Fundamental Limits and Efficient Algorithms

Dear Colleagues,

Recommender systems provide users with appropriate items based on their revealed preference, such as ratings and likes/dislikes. Due to their wide applicability, the systems have received significant attention in machine learning and data mining societies. The great success of social media during the last decade has created the possibility of further improving the recommender system with the help of additional information which is available in applications. One such piece of additional information can be social networks, like Facebook’s friendship graph. There has been a proliferation of recommendation algorithms which exploit such graph side information to enhance performance. However, we are lacking in a theoretical understanding of the maximal gain due to such side information.

During the past few years, information theory—including its key ideas, methods and tools—has played an important role in gaining a theoretical understanding of the role of such side information. In particular, it has served to quantify the maximal gain due to side information under particular yet insightful settings, as well as shed lights into the design of optimal efficient algorithms.

This Special Issue aims to make further progress towards establishing information theory of graph-assisted matrix completion for a variety of practically relevant settings. In particular, the papers shall cover a wide range of topics that can broadly be organized into four themes: (1) sample complexity analysis; (2) clustering and community detection; (3) nonconvex procedures with spectral initialization; and (4) computationally efficient and scalable algorithms.

Prof. Dr. Changho Suh
Guest Editor

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• matrix completion
• recommender systems
• social graphs
• item similarity graphs
• clustering
• community detection
• spectral methods
• nonconvex procedures
• sample complexity