  Collaborative filtering is an effective recommendation approach in which the
preference of a user on an item is predicted based on the preferences of other
users with similar interests. A big challenge in using collaborative filtering
methods is the data sparsity problem which often arises because each user
typically only rates very few items and hence the rating matrix is extremely
sparse. In this paper, we address this problem by considering multiple
collaborative filtering tasks in different domains simultaneously and
exploiting the relationships between domains. We refer to it as a multi-domain
collaborative filtering (MCF) problem. To solve the MCF problem, we propose a
probabilistic framework which uses probabilistic matrix factorization to model
the rating problem in each domain and allows the knowledge to be adaptively
transferred across different domains by automatically learning the correlation
between domains. We also introduce the link function for different domains to
correct their biases. Experiments conducted on several real-world applications
demonstrate the effectiveness of our methods when compared with some
representative methods.
