Matrix Completion with Noisy Side Information
We study the matrix completion problem with side information. Side information has been considered in several matrix completion applications, and has been empirically shown to be useful in many cases. Recently, researchers studied the effect of side information for matrix completion from a theoretical viewpoint, showing that sample complexity can be significantly reduced given completely clean features. However, since in reality most given features are noisy or only weakly informative, the development of a model to handle a general feature set, and investigation of how much noisy features can help matrix recovery, remains an important issue. In this paper, we propose a novel model that balances between features and observations simultaneously in order to leverage feature information yet be robust to feature noise. Moreover, we study the effect of general features in theory and show that by using our model, the sample complexity can be lower than matrix completion as long as features are sufficiently informative. This result provides a theoretical insight into the usefulness of general side information. Finally, we consider synthetic data and two applications -relationship prediction and semisupervised clustering -and show that our model outperforms other methods for matrix completion that use features both in theory and practice.
This paper is suitable for all level of readers.Overall This paper is very well written. The idea is novel while some assumptions may not be quite valid, For example, the authors assume the M matrix to be low rank, and did not prove that.I understand R matrix is low rank, but why the smaller matrix M is also low rank?I would expect more elaboration on this assumption.  The contribution and proposal is straight froward and the presentation is easy to follow.I like the idea of updating the side information, and setting of the problem is nicely formulated.The comments to help further improvement is the author did not discuss the details about the implementation.Solving the optimization problem is not trivial, especially get to the global optimal.I do believe there are some constraints or further assumptions needed before this problem is solvable.The variation of solutions might be another problem.how to find the global optimal.the idea is quite original, especially the estimation of the transform matrix.While the authors may need to read some of the related work on noisy side information.Some may be quite inspiring as well in how to solve this type of problem.And it is highly recommend the authors compare and discuss similar methods in literature and experimental section. For example: Matrix Completion with Noise Noisy Matrix Completion Using Alternating Minimization Distance Metric Learning from Uncertain Side Information with Application to Automated Photo Tagging\the problem itself is common and practically useful. the idea seems interesting but involves some assumption, which is my major concern can be some problem affecting the results.The authors needs further investigate, either prove the assumptions are valid, or remove the assumptions and reformulate the problem in a more natural / organic way.