  Federated learning (FL) offers a privacy-preserving approach to machine
learning for multiple collaborators without sharing raw data. However, the
existence of non-independent and non-identically distributed (non-IID) datasets
across different clients presents a significant challenge to FL, leading to a
sharp drop in accuracy, reduced efficiency, and hindered implementation. To
address the non-IID problem, various methods have been proposed, including
clustering and personalized FL frameworks. Nevertheless, to date, a formal
quantitative definition of the non-IID degree between different clients'
datasets is still missing, hindering the clients from comparing and obtaining
an overview of their data distributions with other clients. For the first time,
this paper proposes a quantitative definition of the non-IID degree in the
federated environment by employing the cumulative distribution function (CDF),
called Fully Homomorphic Encryption-based Federated Cumulative Distribution
Function (FHE-FCDF). This method utilizes cryptographic primitive fully
homomorphic encryption to enable clients to estimate the non-IID degree while
ensuring privacy preservation. The experiments conducted on the CIFAR-100
non-IID dataset validate the effectiveness of our proposed method.
