  Recommender systems are widely used to predict personalized preferences of
goods or services using users' past activities, such as item ratings or
purchase histories. If collections of such personal activities were made
publicly available, they could be used to personalize a diverse range of
services, including targeted advertisement or recommendations. However, there
would be an accompanying risk of privacy violations. The pioneering work of
Narayanan et al.\ demonstrated that even if the identifiers are eliminated, the
public release of user ratings can allow for the identification of users by
those who have only a small amount of data on the users' past ratings.
  In this paper, we assume the following setting. A collector collects user
ratings, then anonymizes and distributes them. A recommender constructs a
recommender system based on the anonymized ratings provided by the collector.
Based on this setting, we exhaustively list the models of recommender systems
that use anonymized ratings. For each model, we then present an item-based
collaborative filtering algorithm for making recommendations based on
anonymized ratings. Our experimental results show that an item-based
collaborative filtering based on anonymized ratings can perform better than
collaborative filterings based on 5--10 non-anonymized ratings. This surprising
result indicates that, in some settings, privacy protection does not
necessarily reduce the usefulness of recommendations. From the experimental
analysis of this counterintuitive result, we observed that the sparsity of the
ratings can be reduced by anonymization and the variance of the prediction can
be reduced if $k$, the anonymization parameter, is appropriately tuned. In this
way, the predictive performance of recommendations based on anonymized ratings
can be improved in some settings.
