## 3 Method
### Proposed Federated Learning Algorithm  
Existing FL algorithms aggregate local models from multiple clients using simple averaging, random sampling, or by adding regularization terms, and then update the global model. These approaches have several inherent issues in terms of efficiency and practicality [46]. Simple averaging, which aggregates under the assumption that all clients are equally important, can be inefficient for model optimization as it does not consider the quality, quantity, and distribution of data. Additionally, random sampling is reliant on chance and cannot eliminate the possibility that some inefficient local models might adversely affect the global model. The method of adding regularization terms can also \begin{table}
\begin{tabular}{c c c} \hline \hline
**Characteristics** & **Description** & **Details** \\ \hline \multirow{2}{*}{Emergency Room (ER) ID} & Classification number for each ER & \multirow{2}{*}{Composed of 172 hospitals in total} \\ \hline \multirow{2}{*}{Basic Information} & Patient’s basic demographic information & \multirow{2}{*}{Gender, Age} \\ \hline \multirow{2}{*}{Time of Symptom Onset} & Time from onset of symptoms to arrival at the ER & \multirow{2}{*}{Distributed from 1 h to more than 30 days} \\ \hline \multirow{4}{*}{Early Biosignals} & Initial vital signs information measured in the ER & \multirow{2}{*}{Blood Pressure (Systolic, Diastolic), Heart rate, Respiration rate, Body Temperature, Oxygen Saturation rate} \\ \hline \multirow{2}{*}{Response Upon Visit} & Patient’s initial reaction seen in the emergency room & \multirow{2}{*}{Alert, Reacting to voice, Reacting to pain, Unresponsive} \\ \hline \multirow{2}{*}{Main Symptoms} & Main symptoms of patients who came to the ER & \multirow{2}{*}{Pain, Fever, Dizziness, etc.} \\ \hline \multirow{2}{*}{KTAS Severe Index} & Korean emergency patient classification information & \multirow{2}{*}{Resuscitation, Urgent, Emergency, Semi-emergency, non-emergency} \\ \hline \multirow{2}{*}{Outcomes} & Patient final status outcome in the ER & \multirow{2}{*}{Return Home, Transfer, Hospitalization (General, ICU), Death} \\ \cline{1-1} \cline{4-4}  & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Data characteristics information. increase the complexity of the model, and finding the appropriate regularization term can be challenging. To solve these issues, this paper proposes a client selection algorithm based on local model evaluation. The proposed algorithm flexibly selects clients according to various evaluation metrics that determine the model's performance. This dynamic selection mechanism evaluates and compares each client's local model using metrics such as loss, accuracy, AUC, or other custom metrics. To express the LMECS algorithm mathematically, it is necessary first to define the process of evaluating each client's local model and the criteria for their selection. The LMECS algorithm is as follows. The method for evaluating a client's local model is as follows: Si represents the score of client's local model. E evaluates how well the local model performs on the dataset Ci using the global model parameters \(W_{t}\). \[S_{i}=E\Big{(}C^{i},W_{t}\Big{)} \tag{5}\]  
A set of clients \(C_{s}\) that meet a user-defined criterion \(\theta\) is defined. A client \(i\) is selected when its score \(S_{i}\) is equal to or exceeds the threshold \(\theta\). \[C_{s}=\{\;i\;|\;S_{i}\;\geq\;\theta\;\} \tag{6}\]  
The local model parameters of the selected clients are aggregated to update the global model. Each client updates its model based on its local data and sends these updated model parameters \(W_{t+1}^{i}\) to the central server. The FL server aggregates these updates, applying weights divided by the number of selected clients \(|C_{s}|\). Consequently, this formula updates the global model using the parameters of the selected local models, creating a new model \(\mathcal{W}_{t+1}\) to be used in the next round of training.