  Probabilistic matrix factorization (PMF) plays a crucial role in
recommendation systems. It requires a large amount of user data (such as user
shopping records and movie ratings) to predict personal preferences, and
thereby provides users high-quality recommendation services, which expose the
risk of leakage of user privacy. Differential privacy, as a provable privacy
protection framework, has been applied widely to recommendation systems. It is
common that different individuals have different levels of privacy requirements
on items. However, traditional differential privacy can only provide a uniform
level of privacy protection for all users.
  In this paper, we mainly propose a probabilistic matrix factorization
recommendation scheme with personalized differential privacy (PDP-PMF). It aims
to meet users' privacy requirements specified at the item-level instead of
giving the same level of privacy guarantees for all. We then develop a modified
sampling mechanism (with bounded differential privacy) for achieving PDP. We
also perform a theoretical analysis of the PDP-PMF scheme and demonstrate the
privacy of the PDP-PMF scheme. In addition, we implement the probabilistic
matrix factorization schemes both with traditional and with personalized
differential privacy (DP-PMF, PDP-PMF) and compare them through a series of
experiments. The results show that the PDP-PMF scheme performs well on
protecting the privacy of each user and its recommendation quality is much
better than the DP-PMF scheme.
