Kernel-based Approaches for Collaborative Filtering

In a large-scale collaborative filtering system, pair wise similarity between users is usually measured by users' ratings on the whole set of items. However, this measurement may not be well defined due to the sparsity problem, i.e., the lack of adequate ratings on items for calculating accurate predictions. In fact, most correlated users have similar ratings only on a subset of items. In this paper, we consider a kernel-based classification approach for collaborative filtering and propose several kernel matrix construction methods by using biclusters to capture pair wise similarity between users. In order to characterize accurate correlation among users, we embed both local information and global information into the similarity matrix. However, this similarity matrix may not be a kernel matrix. Our solution is to approximate it with the matrix close to it and use low rank constraints to control the complexity of the matrix.