# Part-Treatment Efficacy Prediction Using a CMA-ES-Based Dendritic Neuron Model
## 4 Experimental Studies
### Optimization Performance of CMA-ES  
The DNM has three hyperparameters: the constant parameter \(k\), the number of dendritic branches \(B\), and the threshold \(\gamma\). In the experiments, the standard \(L_{16}(4^{3})\) orthogonal array of [PERSON]'s method [48] was used to select the appropriate hyperparameters. Each hyperparameter has four different values, which are listed in Table 4. According to the orthogonal array, there were 16 parameter combinations. Each parameter combination was repeated 30 times to verify its stability, and in each experiment, the optimization algorithm underwent 100 iterations. The hyperparameters with the best classification results were selected based on the accuracy of the data obtained from the validation experiments. The results of the tuned hyperparameters are shown in Table 5.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Hyperparameter** & **Value 1** & **Value 2** & **Value 3** & **Value 4** \\ \hline \(k\) & 2 & 5 & 8 & 10 \\ \(B\) & \(N_{faa}^{~{}*}\) & \(N_{faa}\) +2 & \(N_{faa}\) +4 & \(N_{faa}\) +6 \\ \(\gamma\) & 0.2 & 0.4 & 0.6 & 0.8 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Values of the hyperparameters of the DNM.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Predicted** & **Actual** & **Treatment Success** & **Treatment Failure** \\ \hline Treatment success & TP & FP \\ Treatment failure & FN & TN \\ \hline \hline \end{tabular}
\end{table}
Table 3: Confusion matrix.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Hyperparameter** & **Value 1** & **Value 2** & **Value 3** & **Value 4** \\ \hline \(k\) & 2 & 5 & 8 & 10 \\ \(B\) & \(N_{faa}^{~{}*}\) & \(N_{faa}\) +2 & \(N_{faa}\) +4 & \(N_{faa}\) +6 \\ \(\gamma\) & 0.2 & 0.4 & 0.6 & 0.8 \\ \hline \hline \end{tabular}
\end{table}
Table 5: The hyperparameter settings of the DNM.  
In this study, we attempted to improve the performance of the dendritic neuron model using the CMA-ES. Based on the above tuning results, the performance of the CMA-ES, differential evolution (DE), particle swarm optimization (PSO), genetic algorithm (GA), Harris hawks optimization (HHO) [49], and backpropagation (BP) in training the DNM were compared. To be as fair as possible in the comparisons, the number of iterations of these heuristic algorithms was set to 100 and the epoch of BP was set to 2000. With this configuration, the training time required for the BP algorithm was longer. The convergence curves of the optimization algorithms generated using the MSE function and the FL function are shown in Figures 5  
Based on the convergence curves shown in Figures 5a and 6a, the cryotherapy dataset exhibited the fastest convergence rate in terms of both the MSE function and the FL function when using the CMA-ES. For the immunotherapy dataset, as illustrated in Figure 5b, PSO exhibited the fastest convergence rate among all the algorithms. Additionally, Figure 6b demonstrates that the CMA-ES was nearly as fast as the fastest converging DE on the FL function. The convergence results for each algorithm are summarized in Table 6. The CMA-ES achieved the minimum value for the MSE and FL functions on the cryotherapy dataset. For the immunotherapy dataset, PSO reached the minimum convergence value of the MSE function, whereas the CMA-ES almost reached the minimum convergence value of the FL function. These findings indicate that the CMA-ES exhibited powerful optimization performance in training the DNM.  
According to the comparison of the classification accuracies of these training algorithms shown in Table 7, the CMA-ES was the best-performing algorithm among the six algorithms because it achieved the highest classification accuracy. In addition, incorporating the FL further improved the prediction accuracy of the CMA-ES, indicating that incorporating the FL as the loss function was necessary.