## 2 Federated Learning Paradigm  
In 2016, [PERSON] et al. proposed a novel computational paradigm of distributed machine learning [9]. According to it, data are trained directly on the nodes where the data are stored. Then, the results of local training are transferred to the node that performs the aggregation of the parameters of local models and the calculation of the global analysis model. Thus, the global model considers the data belonging to different nodes, without transferring them over the network and collecting them in a single storage.  
The key difference between federated learning and distributed machine learning is the usage of data sources and performing calculations directly on them, thus bringing computations as close to data as possible. On the contrary, in distributed machine learning, the nodes are used as sources of the computing resources to scale parallel processing of large amounts of data. Thus, the application of federated learning allows for decreasing the risk of unauthorized access to the data as soon as they are not transferred over the network. In addition, it allows for decreasing the volumes of the transferred traffic as soon as the training results are usually much lower in volume than the data itself.  
The scheme of federated learning is represented in Figure 1. It includes three following components:  
* the clients, i.e., data owners or data sources;
* the server that aggregates the local models and organises the communications between the clients;
* communication and computing infrastructure.  
Two types of the federation are outlined depending on the computational resources of client nodes and their availability during the training process: a federation of organisations (cross-silo) and a federation of the devices (cross-device). For cross-silo federated learning settings, the small number of clients is typical. These clients are usually represented by organisations or/and data centers that are characterized by high computational resources, wide network bandwidth, and a high availability level during the training process. On the contrary, the cross-device federated learning settings are characterised by a large number of clients with limited computational, energy resources. These devices can drop out from the training process at any moment and appear again.  
Federated learning systems can implement two communication schemes between their components: centralised and decentralised [10; 11]. The centralised scheme includes the main server used to organise different stages of the federated learning process and to coordinate the clients. This scheme is typical for the federation of the devices of the Internet of Things. In the decentralised scheme, the clients can coordinate their actions to obtain the global model, and the role of the aggregating server could be assigned to any client at any round of aggregation. Such a training scheme is also known as swarm learning [12]. It is more common for the federation of organisations where the clients have sufficiently high computing resources.  
Another important feature of federated learning is the way data are distributed across the clients. In federated learning, this characteristic is referred to as data partition. There are two main types of data partition between the clients: horizontal and vertical ones. Let us consider them in detail. The data set usually contains information about some set of samples (or objects) that is presented by a set of attributes (or features). In the case of the horizontally partitioned data, the clients have datasets that describe different objects using the same set of attributes. In the case of the vertically partitioned data, the clients store the data that describe the same set of objects but in different attributes. Figure 2 shows the difference between horizontally partitioned data and vertically partitioned data. In real world cases, there is also a hybrid data partition when part of the data are partitioned partly horizontally and partly vertically.  
Figure 1: The scheme of federated learning.