Decomposing user-item matrix into locally low rank sub-matrices using social information

What is it about?

Matrix factorization assumes that the user-item matrix is low rank. However, in reality, it is not. We follow the local low rank assumption. That is, while the user-item matrix is not low rank, it can be decomposed into sub-matrices that are locally low rank. The assumption is reasonable in social network, where the user-item matrix aggregates the behaviors of all social groups, which are (locally) low rank individually but the aggregate matrix is not low rank. We propose methods to decompose the user-item matrix into sub-matrices, based on which we develop recommendation algorithms that have been shown to be better than the original local low rank approach that decomposes the matrix randomly.

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Why is it important?

Matrix factorization assumes that the input matrix is low rank. If the assumption is not true, factorization will generate poor results. Imagine that a large e-commer website with millions of users and items. It is hard to conceive such matrix, aggregating the behaviors of so many users, is low rank. Previous work has proposed local low rank decomposition. We follow the same approach but we exploit social information in the decompositon process to produce the sub-matrices that are more effective compared to randomly decomposing the matrix.