  Matrix Factorization has been very successful in practical recommendation
applications and e-commerce. Due to data shortage and stringent regulations, it
can be hard to collect sufficient data to build performant recommender systems
for a single company. Federated learning provides the possibility to bridge the
data silos and build machine learning models without compromising privacy and
security. Participants sharing common users or items collaboratively build a
model over data from all the participants. There have been some works exploring
the application of federated learning to recommender systems and the privacy
issues in collaborative filtering systems. However, the privacy threats in
federated matrix factorization are not studied. In this paper, we categorize
federated matrix factorization into three types based on the partition of
feature space and analyze privacy threats against each type of federated matrix
factorization model. We also discuss privacy-preserving approaches. As far as
we are aware, this is the first study of privacy threats of the matrix
factorization method in the federated learning framework.
