Reviews: Mixture-Rank Matrix Approximation for Collaborative Filtering

This is an excellent paper, proposing a sound idea of approximating a partially defined rating matrix with a combination of multiple low rank matrices of different ranks in order to learn well the head user/item pairs (users and items with lots of ratings) as well as the tail user/item pairs (users and items we few ratings). The idea is introduced clearly. The paper makes a good review of the state-of-the-art, and the experiment section is solid with very convincing results. In reading the introduction, the reader could find controversial the statement in lines 25-27 about the correlation between the number of user-item ratings and the desired rank. One could imagine that a subgroup of users and items have a large number of ratings but in a consistent way, which can be explained with a low rank matrix.