  Recommendation systems have received considerable attention in the recent
decades. Yet with the development of information technology and social media,
the risk in revealing private data to service providers has been a growing
concern to more and more users. Trade-offs between quality and privacy in
recommendation systems naturally arise. In this paper, we present a privacy
preserving recommendation framework based on groups. The main idea is to use
groups as a natural middleware to preserve users' privacy. A distributed
preference exchange algorithm is proposed to ensure the anonymity of data,
wherein the effective size of the anonymity set asymptotically approaches the
group size with time. We construct a hybrid collaborative filtering model based
on Markov random walks to provide recommendations and predictions to group
members. Experimental results on the MovieLens and Epinions datasets show that
our proposed methods outperform the baseline methods, L+ and ItemRank, two
state-of-the-art personalized recommendation algorithms, for both
recommendation precision and hit rate despite the absence of personal
preference information.
