  It is challenging to implement Kernel methods, if the data sources are
distributed and cannot be joined at a trusted third party for privacy reasons.
It is even more challenging, if the use case rules out privacy-preserving
approaches that introduce noise. An example for such a use case is machine
learning on clinical data. To realize exact privacy preserving computation of
kernel methods, we propose FLAKE, a Federated Learning Approach for KErnel
methods on horizontally distributed data. With FLAKE, the data sources mask
their data so that a centralized instance can compute a Gram matrix without
compromising privacy. The Gram matrix allows to calculate many kernel matrices,
which can be used to train kernel-based machine learning algorithms such as
Support Vector Machines. We prove that FLAKE prevents an adversary from
learning the input data or the number of input features under a semi-honest
threat model. Experiments on clinical and synthetic data confirm that FLAKE is
outperforming the accuracy and efficiency of comparable methods. The time
needed to mask the data and to compute the Gram matrix is several orders of
magnitude less than the time a Support Vector Machine needs to be trained.
Thus, FLAKE can be applied to many use cases.
