  Federated learning (FL) is a decentralized machine learning approach where
independent learners process data privately. Its goal is to create a robust and
accurate model by aggregating and retraining local models over multiple rounds.
However, FL faces challenges regarding data heterogeneity and model aggregation
effectiveness. In order to simulate real-world data, researchers use methods
for data partitioning that transform a dataset designated for centralized
learning into a group of sub-datasets suitable for distributed machine learning
with different data heterogeneity. In this paper, we study the currently
popular data partitioning techniques and visualize their main disadvantages:
the lack of precision in the data diversity, which leads to unreliable
heterogeneity indexes, and the inability to incrementally challenge the FL
algorithms. To resolve this problem, we propose a method that leverages entropy
and symmetry to construct 'the most challenging' and controllable data
distributions with gradual difficulty. We introduce a metric to measure data
heterogeneity among the learning agents and a transformation technique that
divides any dataset into splits with precise data diversity. Through a
comparative study, we demonstrate the superiority of our method over existing
FL data partitioning approaches, showcasing its potential to challenge model
aggregation algorithms. Experimental results indicate that our approach
gradually challenges the FL strategies, and the models trained on FedSym
distributions are more distinct.
