Federated horizontally partitioned principal component analysis for biomedical applications.

Motivation: Federated learning enables privacy-preserving machine learning in the medical domain because the sensitive patient data remain with the owner and only parameters are exchanged between the data holders. The federated scenario introduces specific challenges related to the decentralized nature of the data, such as batch effects and differences in study population between the sites. Here, we investigate the challenges of moving classical analysis methods to the federated domain, specifically principal component analysis (PCA), a versatile and widely used tool, often serving as an initial step in machine learning and visualization workflows. We provide implementations of different federated PCA algorithms and evaluate them regarding their accuracy for high-dimensional biological data using realistic sample distributions over multiple data sites, and their ability to preserve downstream analyses. Results: Federated subspace iteration converges to the centralized solution even for unfavorable data distributions, while approximate methods introduce error. Larger sample sizes at the study sites lead to better accuracy of the approximate methods. Approximate methods may be sufficient for coarse data visualization, but are vulnerable to outliers and batch effects. Before the analysis, the PCA algorithm, as well as the number of eigenvectors should be considered carefully to avoid unnecessary communication overhead. Availability and implementation: Simulation code and notebooks for federated PCA can be found at https://gitlab.com/roettgerlab/federatedPCA; the code for the federated app is available at https://github.com/AnneHartebrodt/fc-federated-pca. Supplementary information: Supplementary data are available at