  Recommendation systems rely heavily on users behavioural and preferential
data (e.g. ratings, likes) to produce accurate recommendations. However, users
experience privacy concerns due to unethical data aggregation and analytical
practices carried out by the Service Providers (SP). Local differential privacy
(LDP) based perturbation mechanisms add noise to users data at user side before
sending it to the SP. The SP then uses the perturbed data to perform
recommendations. Although LDP protects the privacy of users from SP, it causes
a substantial decline in predictive accuracy. To address this issue, we propose
an LDP-based Matrix Factorization (MF) with a Gaussian Mixture Model (MoG). The
LDP perturbation mechanism, Bounded Laplace (BLP), regulates the effect of
noise by confining the perturbed ratings to a predetermined domain. We derive a
sufficient condition of the scale parameter for BLP to satisfy $\epsilon$ LDP.
At the SP, The MoG model estimates the noise added to perturbed ratings and the
MF algorithm predicts missing ratings. Our proposed LDP based recommendation
system improves the recommendation accuracy without violating LDP principles.
The empirical evaluations carried out on three real world datasets, i.e.,
Movielens, Libimseti and Jester, demonstrate that our method offers a
substantial increase in predictive accuracy under strong privacy guarantee.
