# Communication-Efficient Vertical Federated Learning
## 1 Introduction  
As organizations seek to modernize and optimize business processes, machine learning (ML) has emerged as a powerful tool for driving automation. It has aided in the enhancement of business scalability and the improvement of business operations for companies all over the globe by extracting meaningful insights from raw data to quickly solve complex, data-rich business problems. Furthermore, in healthcare, machine learning (ML) applied to electronic health records (EHRs) can yield actionable insights, ranging from improving patient risk score systems to predicting disease onset and streamlining hospital operations [1]. ML has also made a significant contribution to the agriculture sector by assisting farmers in reducing farming losses by providing rich recommendations and insights into crops [2]. There is virtually no application domain that could not benefit from using ML techniques for decision support. Although organizations benefit from using machine learning approaches on their data, using data from other similar organizations for the same purpose could result in significant improvements to the existing organizational processes. Recognizing the importance of collaboration, a significant emphasis has been placed on integrating data from multiple organizations in order to design sophisticated machine learning models for improving customer service and acquisition. However, at present, data sharing among organizations has become critical due to concerns of privacy, maintaining competitive advantages, and/or other constraints. Although significant research has been conducted related to distributed learning [3], which aims at performing tasks on data distributed across multiple servers, it mainly focuses on reducing the time required to perform tasks by parallelizing computation power. On the other hand, federated learning (FL) focuses on data locality [4] and is seen as a promising technology approach that enables a network of autonomous organizations that face the same machine learning task to collaboratively learn a global model that offers better predictive performance for all participants without the need to share sensitive data. Generally, FLcan be divided into different scenarios based on how the data are partitioned or distributed among the data owners, i.e., horizontally or vertically. Horizontal federated learning (HFL), also known as Homogeneous FL, is used in scenarios where data owners possess data with the same characteristics or features, but differ in the number of samples they possess in their data. An example of HFL is a group of hospitals collaborating to build a model that can predict a health risk for their patients, based on agreed data. However, this is not the only possibility. Imagine a scenario in which multiple data owners or clients wish to collaborate in the training of ML models having common samples of data, but not the same features, for instance, a telecom company collaborating with a home entertainment company (cable TV provider), or an airline collaborating with a car rental agency. As the data are vertically partitioned rather than horizontally, HFL does not fit in such cases. Vertical federated learning (VFL) can overcome client data heterogeneity (same samples with different features). It can be referred to as the process of aggregating different features and computing the training loss and gradients in a privacy-preserving manner to build a model with data from both parties collaboratively. Although FL comes with a lot of advantages, one of the major challenges of this approach is the communication overhead, which is discussed further in Section 2. Our key contribution in this paper is the introduction of a communication-efficient vertical federated approach that uses a feature extraction technique to compress local data of clients. The compressed data from the clients are then aggregated to train the final machine learning model.