# FedCO: Communication-Efficient Federated Learning via Clustering Optimization +
## 4 Proposed Approach
Therefore, if there are more workers with poor data quality, the convergence will be reached at a slower rate than when much fewer workers with high data quality are used. However, at each global round, FedCO may have selected a different set of workers. Those, however, are not selected randomly, but each one is a representative of a cluster of workers having modeled similar parameters, and in addition, it achieves the highest accuracy among the cluster members. Let \(T_{FedAvg}\) and \(T_{FedCO}\) represent the number of global rounds for which convergence has been reached by FedAvg and FedCO, respectively. Then, Tables 4 and 5 demonstrate that the inequality \(T_{FedCO}<T_{FedAvg}\) is valid in the experiments aiming to reach the same accuracy using the two algorithms. ### Communication Rounds versus Accuracy

In this subsection, we present the results related to the evaluation of the accuracy of our distributed deep learning (DL) model. Figures 5-7 show how the compared FL (FedAvg, FedProx, CMFL, and FedCO) algorithms perform in terms of Accuracy versus the Number of Communication Rounds. For the MNIST dataset (see Figure 5), we can observe that the FedCO algorithm converges faster than with the state-of-the-art approaches. As is shown in Figure 5a (IID data distribution setting), FedAvg and FedProx use 100 rounds to obtain an accuracy of 85%. The CMFL reaches the same accuracy in 30 rounds, while our FedCO algorithm achieves this result with only 10 rounds. Furthermore, in Figure 5b, FedCO dramatically decreases the communication rounds with respect to FedAvg, FedProx, and CMFL. Indeed, in Non-IID data, a learning accuracy of 90% is achieved by FedCO in 40 rounds, FedAvg has conducted 160 rounds, FedProx requires 200 rounds, and CMFL needs 60. In Figure 6a, we compare the accuracy of the four FL approaches in the case of the IID data distribution scenario of FashionMNIST. The FedCO outperforms FedAvg, FedProx, and CMFL in this experimental setting. Within 25 communication rounds, CMFL, FedAvg, and FedProx reach 81%, 69%, and 74% accuracy, respectively, while our FedCO algorithm achieves an accuracy of 90% with the same number of communication rounds. Notice that under the Non-IID data distribution setting, our FedCO algorithm outperforms the other, reaching an accuracy of nearly 79% with only 11 rounds; this costs 100 communication \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline  & \multicolumn{4}{c}{**IID**} \\  & \multicolumn{2}{c}{**MNIST**} & \multicolumn{2}{c}{**FashionMNIST**} & \multicolumn{2}{c}{**CIFAR-10**} \\ \cline{2-7}  & **Rounds** & **Saving** & **Rounds** & **Saving** & **Rounds** & **Saving** \\ \hline FedAvg & 190 & (ref) & 200 & (ref) & 200 & (ref) \\ FedProx & 185 & 26\% & 190 & 5\% & 188 & 6\% \\ CMFL & 50 & 73\% & 60 & 70\% & 80 & 60\% \\ FedCO & 25 & 86\% & 50 & 75\% & 30 & 85\% \\ \hline \hline  & \multicolumn{4}{c}{**Non-IID**} \\  & \multicolumn{2}{c}{**MNIST**} & \multicolumn{2}{c}{**FashionMNIST**} & \multicolumn{2}{c}{**CIFAR-10**} \\ \cline{2-7}  & **Rounds** & **Saving** & **Rounds** & **Saving** & **Rounds** & **Saving** \\ \hline FedAvg & 170 & (ref) & 200 & (ref) & 200 & (ref) \\ FedProx & 167 & 17\% & 186 & 7\% & \(>\)200 & - \\ CMFL & 60 & 64\% & 150 & 25\% & 160 & 20\% \\ FedCO & 30 & 82\% & 70 & 65\% & 60 & 70\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The number of communication rounds to reach a target accuracy for the three compared FL algorithms. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**IID**} \\  & \multicolumn{2}{c}{**FEMNIST**} & \multicolumn{2}{c}{**CelebA**} \\ \cline{2-5}  & **Rounds** & **Saving** & **Rounds** & **Saving** \\ \hline FedAvg & 140 & (ref) & 110 & (ref) \\ FedCO & 12 & 91\% & 30 & 72\% \\ \hline \hline  & \multicolumn{4}{c}{**Non-IID**} \\  & \multicolumn{2}{c}{**FEMNIST**} & \multicolumn{2}{c}{**CelebA**} \\ \cline{2-5}  & **Rounds** & **Saving** & **Rounds** & **Saving** \\ \hline FedAvg & 100 & (ref) & 150 & (ref) \\ FedCO & 14 & 86\% & 10 & 93\% \\ \hline \hline \end{tabular}
\end{table}