Community Detection and Matrix Completion with Social and Item Similarity Graphs
This work addresses matrix completion and community detection for recommendation systems, but it is incremental as it builds on existing stochastic block model frameworks.
The paper tackles the problem of recovering a binary rating matrix and clustering users and items using partially observed data and side-information from social and item similarity graphs, showing that these graphs reduce sample complexity and can have a synergistic effect.
We consider the problem of recovering a binary rating matrix as well as clusters of users and items based on a partially observed matrix together with side-information in the form of social and item similarity graphs. These two graphs are both generated according to the celebrated stochastic block model (SBM). We develop lower and upper bounds on sample complexity that match for various scenarios. Our information-theoretic results quantify the benefits of the availability of the social and item similarity graphs. Further analysis reveals that under certain scenarios, the social and item similarity graphs produce an interesting synergistic effect. This means that observing two graphs is strictly better than observing just one in terms of reducing the sample complexity.