  The neighbourhood-based Collaborative Filtering is a widely used method in
recommender systems. However, the risks of revealing customers' privacy during
the process of filtering have attracted noticeable public concern recently.
Specifically, $k$NN attack discloses the target user's sensitive information by
creating $k$ fake nearest neighbours by non-sensitive information. Among the
current solutions against $k$NN attack, the probabilistic methods showed a
powerful privacy preserving effect. However, the existing probabilistic methods
neither guarantee enough prediction accuracy due to the global randomness, nor
provide assured security enforcement against $k$NN attack. To overcome the
problems of current probabilistic methods, we propose a novel approach,
Partitioned Probabilistic Neighbour Selection, to ensure a required security
guarantee while achieving the optimal prediction accuracy against $k$NN attack.
In this paper, we define the sum of $k$ neighbours' similarity as the accuracy
metric $\alpha$, the number of user partitions, across which we select the $k$
neighbours, as the security metric $\beta$. Differing from the present methods
that globally selected neighbours, our method selects neighbours from each
group with exponential differential privacy to decrease the magnitude of noise.
Theoretical and experimental analysis show that to achieve the same security
guarantee against $k$NN attack, our approach ensures the optimal prediction
accuracy.
