Federated Learning Strategies for Enhancing Privacy-Preserving Euclidean Distance Matrix Computation

Numerous Machine Learning (ML) algorithms require pairwise Euclidean distance computations between all data points in horizontally partitioned datasets. To ensure data privacy, most existing solutions incorporate encryption or cryptographic techniques, allowing secure sharing and computation of data points. In this study, we propose two methodologies for generating Euclidean distance matrices: the Federated Euclidean Distance Matrix (FEDM) and the Predicted Euclidean Distance Matrix (PEDM), derived from the pairwise Euclidean distances of horizontally partitioned data to ensure privacy by design. The proposed approach has significant potential to transform the execution of ML algorithms that rely on Euclidean distance calculations and to eliminate the need for separate encryption methods, thereby potentially reducing communication and computation costs in a Federated Learning (FL) environment. The proposed methods achieve high accuracy and exhibit strong similarity to the actual Euclidean distance matrix. FL has gained prominence as a privacy-preserving ML solution that encapsulates data while appropriately sharing model parameters. To this end, we utilize artificial spike points for the creation of FEDM. We also elucidate the foundational workflows of the method and matrix construction and demonstrate their efficacy through comprehensive experimentation.