## 2 Federated Learning Systems  
The key idea of the FL consists of training local models directly on clients that generate or own data, then their parameters are aggregated to produce a global model that is distributed across all collaborating clients [1]. Thus, it is possible to outline three main components of the FL:  
1. Clients that own data and train local model;
2. Server that coordinates the whole training process and computes the global model;
3. Communication environment. FL systems are characterized by three important properties:
1. Communication scheme or FL topology [18];
2. Computational and network resources available to collaborating clients;
3. Type of the data partition. The communication scheme defines how the federated learning process is orchestrated. The role of the coordinating server could be implemented by a designated server that is often represented by a trusted entity. This case corresponds to the centralized architecture of the FL systems. In the case of a decentralized FL system, the functions of the aggregating server are implemented by collaborating clients [6]. Figure 1 shows the communication schemes of the federated learning process. It is necessary to mention that there are also hybrid communication schemes that are represented either by a hierarchy of the decentralized federations or by a peer-to-peer network of federations with a centralized communication scheme [18]. Depending on the client's computational and memory resources, and their network bandwidth characteristics, it is possible to outline cross-device and cross-silo settings. In cross-device settings, the clients have limited computational resources and low network bandwidth, their behavior is not stable, and they could drop out from the learning process. In contrast to the cross-device settings, the clients in cross-silo settings are characterized by a stable behavior and powerful computational and networking resources. Type of the data partition defines how data are distributed across the clients. This notion is quite semantically similar to the notion of data partition commonly used in the distributed warehouses [32]. Usually, a dataset is characterized by two dimensions: (1) number of attributes and (2) number of samples. If the clients have similar sets of the  
Figure 1: Overview of the communication scheme in FL systems: centralized communication topology (**a**), decentralized communication topology (**b**). attributes then the data are horizontally partitioned. In the case of vertically partitioned data, the clients have different data attributes for the same set of samples. This type of data partition is natural to many situations, for example, communication organization may have data about person's contacts, while the financial organization may have information about their financial state, and mining such data may give interesting insights into fraud detection activity. Figure 2 shows the schema of these data partition types. In the real world cases, the data could be partitioned across the clients partly vertically, partly horizontally--this case corresponds to the most complex type of the data partition, a hybrid one. These FL properties define different types of the FL systems as well as the requirements to the throughput of the training process, choice of the aggregation function, etc. FL paradigm is considered as a privacy-preserving computational paradigm because data are processed locally; they are not transferred to some entity in order to perform their processing. FL clients exchange model parameters only that are needed to form a global aggregated model. Thus, this reduces the risks of unauthorized access to the data when they are transmitted via communication channels or processed by the party. However, it was shown that there are theoretical FL-specific attacks that enable attackers to make inference on dataset characteristics and even recreate samples from it [29; 30].