  As a prevailing collaborative filtering method for recommendation systems,
one-bit matrix completion requires data collected by users to provide
personalized service. Due to insidious attacks and unexpected inference, the
release of users' data often raises serious privacy concerns. To address this
issue, differential privacy(DP) has been widely used in standard matrix
completion models. To date, however, little has been known about how to apply
DP to achieve privacy protection in one-bit matrix completion. In this paper,
we propose a unified framework for ensuring a strong privacy guarantee of
one-bit matrix completion with DP. In our framework, we develop four different
private perturbation mechanisms corresponding to different stages of one-bit
matrix completion. For each mechanism, we design a privacy-preserving algorithm
and provide a theoretical recovery error bound under the proper conditions.
Numerical experiments on synthetic and real-world datasets demonstrate the
effectiveness of our proposal. Compared to the one-bit matrix completion
without privacy protection, our proposed mechanisms can maintain high-level
privacy protection with marginal loss of completion accuracy.
