# Class Imbalanced Medical Image Classification Based on Semi-Supervised Federated Learning
## 3 Results
### Comparison with Advanced Methods  
We set up controlled experiments including (1) a FedAvg [22] model using only 20% of the central client with labeled data and using it as a baseline criterion; (2) FedIRM [12] using a new inter-client matching relationship to obtain similar information about labeled client diseases to constrain unlabeled clients and reduce task loss; and (3) imFed-Semi [18] used to build a dynamic class library, filter out high confidence samples, re-estimate the client class distribution, subdivide it into sub-banks with different pseudo-labels, and construct a priori transformation functions through Bayesian criteria to transform the task into classification of the sub-banks, thus avoiding the impact caused by the majority class of the central client. Due to the limitations of the experimental equipment, the upper limit of our method batches was 10, which is also the optimal batch that our method can achieve. We performed two sets of control experiments for the state-of-the-art method separately: One set of models effects under 10 batches of data training (fixed variables, let the state-of-the-art method be compared with our method under the same batches). The other set shows the effect of the model trained with the optimal batch (greater than 10) (fixed upper limit to allow the state-of-the-art method to be compared with our method at the optimal effect that can be achieved). A comparison of the results of our method and the state-of-the-art method is shown in Table 1.  
Among them, the FedIRM [12] and imFed-Semi [18] methods produce a degradation in model performance due to the reliance on inter-data relationship-driven representation and the need for sub-base-alike redistribution of data in small batches of data. This leads to insufficient information on class relationships during a single training session, resulting in the loss of a few class decision boundaries in the aggregated and broadcast models. When increasing the batch size, there is a significant improvement in model performance beyond the baseline level as more information on class relationships can be obtained from the labeled data and there is a greater probability of reassigning a few classes, indicating that the additional unlabeled information is beneficial for federated learning through the integration algorithm. Our combination of regularization constraints and pseudo-label construction solves these problems well. In contrast to FedIRM [12], which can only find limited relational \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{3}{c}{**Client Num**} & \multicolumn{5}{c}{**Metrics**} & \multirow{2}{*}{**Precision**} \\  & **Label** & **Unlabel** & **AUC** & **Accuracy** & **Sensitivity** & **Specificity** & **Precision** & **F1** \\ \hline FedAvg [22] & 2 & 0 & 88.27 & 92.34 & 61.43 & 92.28 & 66.50 & 62.53 \\ FedIRM(10) [12] & 2 & 8 & 88.17 & 89.87 & 40.76 & 91.66 & 34.38 & 37.02 \\ FedIRM(best) [12] & 2 & 8 & 90.38 & 90.30 & 67.86 & 92.87 & 61.20 & 62.02 \\ imFed-Semi(10) [18] & 2 & 8 & 92.40 & 93.30 & 58.29 & 92.10 & 76.87 & 63.10 \\ imFed-Semi(best) [18] & 2 & 8 & 88.40 & 94.75 & 67.75 & 94.04 & 79.12 & 71.77 \\ our & 2 & 8 & 95.75 & 95.58 & 72.92 & 95.47 & 73.88 & 72.90 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison with state-of-the-art methods on the same task. matches from each batch of labeled image data, our imbalance factors extracted from the labeled data are global and unique, and thus are not affected by the size of the data training batches. Relying only on regularized relational matches between clients in FedIRM [12] greatly reduces the learning ability of the model for fewer classes in the face of small batches of imbalanced data, while our regularized class balancing aid, constructed using imbalance factors, significantly improves the learning ability of the model.