# On a Framework for Federated Cluster Analysis
## 4 Discussion  
In this work, we introduce a federated clustering framework (Section 2.2) that solves three challenges: determine the number of global clusters in a federated dataset, obtain a global clustering via a federated fuzzy \(c\)-means algorithm (Section 2.2.1), and validate the clustering through a federated cluster validation metric (Section 2.2.2). To the best of our knowledge, there exists no other similar federated cluster analysis framework. Instead, previous works mostly focus on the clustering method itself. The lack does not stem from the lack of necessity, as we show with our motivational example (Section 1.1): There exist situations where global clusters remain hidden behind local clients' optima.  
The complete framework is evaluated through numerical experiments on different datasets (Section 3). We find that the framework identifies global cluster structures (correct number of clusters and data partitions) that are hidden in non-i.i.d. data (Section 3.2.1). We also find that the framework performs reliably if the data have certain properties, but fails if they do not (Section 3.2.2). In particular, it struggles with sparse data as well as with high cluster overlap. This is consistent with the equivalent nonfederated setting. In our last set of experiments, we outline how the framework can be applied in practice. It shows a good consistency with nonfederated clustering, and can even find better data partitions than in the centralized case (as measured by the Davies-Bouldin index).  
Lastly, we see multiple interesting research directions for future works. One direction is to better understand the theoretical properties of the federated fuzzy \(c\)-means algorithm with \(k\)-means averaging. Moreover, the calculation of the federated fuzzy Davies-Bouldin index potentially creates a privacy risk. We suggest simple prevention mechanisms, but an in-depth analysis could lead to more sophisticated mechanisms. Furthermore, the cluster determination method still needs an initial range for the number of clusters, which can be hard to obtain. We provide a rule of thumb, but a better understanding of when and how federated clusters form could help to make this initial guess more accurate or even automate the choice. Moreover, FedFuzzDB can be extended to a federated crisp clustering or can be applied in combination with other clustering algorithms. Finally, the framework can be extended to include more steps in cluster analysis, such as federated preprocessing or feature selection.  
Figure 7: (**a**) Local-only clustering results for \(K=4\) of the clients in one plot. Each color corresponds to one client. (**b**) Federated and centralized cluster centers for \(K=4\). The darker points are the federated cluster centers and the brighter points are the central cluster centers.  
Overall, we propose the first federated cluster validation metric, a new federated clustering approach based on existing works in the field, propose a comprehensive federated cluster analysis framework, and demonstrate how it can be applied. In comprehensive experiments, we observe promising results and identify shortcomings. Topics such as theoretical properties of the clustering algorithm and privacy evaluation of the framework have only been briefly discussed and can be addressed in more detail in future works.  
Conceptualization, methodology, validation, analysis: M.S. and A.W.; software: M.S.; writing--original draft preparation: M.S.; writing--review and editing: A.W.; visualization: M.S.; supervision: A.W. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The analyzed data can be retrieved from online repositories as referenced in the article. Online repositories are referenced in the paper.  
The authors declare no conflict of interest.