# FedCO: Communication-Efficient Federated Learning via Clustering Optimization +
## 4 Proposed Approach
Figure 9: Learning accuracy versus number of communication rounds for CelebA data. The top plot presents the results produced in the case of the IID data distribution scenario, while the bottom plot depicts the results generated in case of the Non-IID data distribution scenario. (**a**) IID; (**b**) Non-IID. The communication cost savings for algorithm \(X\) (\(X\) = FedProx, CMFL, or FedCO) is computed as

\[1-\frac{Communication\_overhead\_X}{Communication\_overhead\_FedAvg}.\]

As can be seen in Figure 10,b, the FedCO costs on the CIFAR-10 IID data are 1 MB for 20 workers, which is a reduction in communication costs by 83% in comparison with FedAvg, while FedProx and CMFL are allowed to save only 12% and 36% in communication costs, respectively. In an experiment involving 100 workers on the CIFAR-10 dataset, FedAvg, FedProx, and CMFL exchange 32.5, 31.04, and 20 MB of data, while the proposed FedCO consumes only 5.4 MB, which means that FedCO reduces the communication overhead by 84% with respect to FedAvg, and CMFL reduces the communication overhead by 38%, while FedProx saves only 3% in communication costs. Figure 11,b report the communication costs under the MINIST IID and Non-IID data distribution scenarios, respectively. The trend is similar to the results of the CIFAR-10 data experiments. Both the IID and Non-IID data distribution settings confirm that our FedCO algorithm ensures a significantly smaller communication overhead in comparison with FedAvg, FedProx, and CMFL, by substantially reducing the required number of bytes exchanged. As can be noticed, FedCO allows a saving of between 80% and 85% with respect to FedAvg. In Figures 10 and 11, the communication costs increase linearly with the increasing number of workers for all of the compared algorithms. It is obvious that FedCO consistently outperforms FedAvg, FedProx, and CMFL in terms of reducing communication costs. Figure 11: The communication overhead for 100 rounds for the MNIST data. The top plot presents the results produced in the case of the IID data distribution scenario, while the bottom plot depicts the results generated in the case of the Non-IID data distribution scenario. (**a**) IID. (**b**) Non-IID. Figure 10: The communication overhead for 100 rounds for the CIFAR-10 data. The top plot presents the results produced in the case of the IID data distribution scenario, while the bottom plot depicts the results generated in the case of the Non-IID data distribution scenario. (**a**) IID. (**b**) Non-IID. ### Threshold-Based Worker Selection

We also study scenarios in which we use an accuracy threshold to select the number of workers. The threshold is the specified cut-off of accuracy value for the selection of representatives of a cluster of workers. We select any worker where the local update ensures an accuracy of greater than or equal to the predefined threshold as a representative of a cluster. In this section, we report the results produced by testing four different threshold values for FedCO, namely 70%, 75%, 80%, and 85%. The network threshold for the selection of workers varies from bandwidth, transmission speed, or packet loss [48]. Table 6 reports the number of the top-ranked workers that the FedCO algorithm has selected to communicate with the server when the predefined threshold is met within 100 communication rounds. In the case of the CelebA data, the highest number of representatives has been selected when the accuracy of the local models is equal to or above 70%, namely 853 and 826 workers under IID and Non-IID, respectively. In the experiments conducted on the FEMNIST data, when the threshold of the local models was greater than or equal to 70%, 912 workers were selected as representatives for the IID scenario, and 844 workers for the Non-IID one. Similarly, these two values represent the highest numbers of selected workers. It is obvious from the number of representatives reported in Table 6 that the low threshold value implies the greater number of representatives to be selected for global training in FL and vice versa.