  Conventional matrix factorization relies on centralized collection of users'
data for recommendation, which might introduce an increased risk of privacy
leakage especially when the recommender is untrusted. Existing differentially
private matrix factorization methods either assume the recommender is trusted,
or can only provide a uniform level of privacy protection for all users and
items with untrusted recommender. In this paper, we propose a novel
Heterogeneous Differentially Private Matrix Factorization algorithm (denoted as
HDPMF) for untrusted recommender. To the best of our knowledge, we are the
first to achieve heterogeneous differential privacy for decentralized matrix
factorization in untrusted recommender scenario. Specifically, our framework
uses modified stretching mechanism with an innovative rescaling scheme to
achieve better trade off between privacy and accuracy. Meanwhile, by allocating
privacy budget properly, we can capture homogeneous privacy preference within a
user/item but heterogeneous privacy preference across different users/items.
Theoretical analysis confirms that HDPMF renders rigorous privacy guarantee,
and exhaustive experiments demonstrate its superiority especially in strong
privacy guarantee, high dimension model and sparse dataset scenario.
