  Federated learning forms a global model using data collected from a
federation agent. This type of learning has two main challenges: the agents
generally don't collect data over the same distribution, and the agents have
limited capabilities of storing and transmitting data. Therefore, it is
impractical for each agent to send the entire data over the network. Instead,
each agent must form a local model and decide what information is fundamental
to the learning problem, which will be sent to a central unit. The central unit
can then form the global model using only the information received from the
agents. We propose a method that tackles these challenges. First each agent
forms a local model using a low complexity reproducing kernel Hilbert space
representation. From the model the agents identify the fundamental samples
which are sent to the central unit. The fundamental samples are obtained by
solving the dual problem. The central unit then forms the global model. We show
that the solution of the federated learner converges to that of the centralized
learner asymptotically as the sample size increases. The performance of the
proposed algorithm is evaluated using experiments with both simulated data and
real data sets from an activity recognition task, for which the data is
collected from a wearable device. The experimentation results show that the
accuracy of our method converges to that of a centralized learner with
increasing sample size.
