## 4 Case Study and Experimental Implementation
### Hyperparameters Optimization  
The objective of this step is to identify the optimal hyperparameters that result in the highest performance, as indicated by low loss and high accuracy. In particular, the hyperparameters of the 1 dCNN-AE model architecture are calibrated using the David Bouldin Index (DBI) and a validation dataset. The DBI is a metric for evaluating the quality of clustering, whereby the mean distance between clusters is considered in relation to their respective sizes. In order to achieve this objective, a series of hyperparameters have been selected, encompassing the learning rate, optimizer, number of layers, kernel size, and filter size. Table 2 illustrates the range of hyperparameters under consideration and the optimal values selected. Figure 7 illustrates the impact of tuning the hyperparameters of the 1 dCNN-AE model on the clustering performance, as reflected in the DBI score. It was determined that the lower the DBI score, the more optimal the clustering performance. Figure 7a illustrates the impact of modifying the kernel size of the 1 dCNN-AE on the clustering performance across distinct epochs. It can be observed that an increase in kernel size allows the 1 dCNN-AE model to capture more global features, therefore improving the clustering results. The model was trained over different epochs, and the kernel size of 3 with 64 epochs demonstrated the optimal clustering performance with a DBI score of 0.493. It is noteworthy that a larger kernel size for the 1 dCNN-AE model correlates with a higher level of complexity and a higher DBI score, particularly when working with a smaller dataset. Similarly, an increase in the filter size allows for the expansion of the model's capacity, enabling the learning of more complex and varied features and the capture of diverse patterns. This resulted in an improvement in the clustering performance, as can be observed in Figure 7b, where filter size 8.8.16.64 was used with the model trained over 128 epochs. The learning rate and the utilized optimizer represent noteworthy hyperparameters that exerted a considerable influence on the model performance. Figure 7c illustrates the accuracy of the Adam optimizer in terms of low DBI (0.49) at a learning rate of 0.001, in \begin{table}
\begin{tabular}{l l l} \hline \hline
**Hyperparameter** & **Range** & **Optimized Value** \\ \hline Learning rate & [0.01–0.0005] & 0.0005 \\ Optimizer & Adam, AMSProp, and ADAgrade & Adam \\ Number of layers & [1–4] & 4 \\ Kernel size & [1–5] & 3 \\ Filter size & 8.8.8.8–16.64.128.128 & 8.8.32.64 \\ Epochs & [32–128] & 128 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Hyperparameters used in optimization process. comparison to the RMSprop and Adagrad optimizers, which exhibited DBI values of 0.64 and 0.69, respectively. Alongside the use of various optimizers, the 1 dCNN-AE model was trained using different learning rates. It can be demonstrated that a low learning rate was instrumental in enhancing the clustering performance, with a DBI of 0.46 at a learning rate of 0.0005. Nevertheless, the low learning rate necessitates a considerable computational expenditure in the form of training time. Figure 7d illustrates the impact of augmenting the 1 dCNN-AE architecture with additional hidden layers. As can be observed, the DBI score has been markedly reduced by augmenting the model layers, reaching a value of 0.533 with four layers. Despite the ability to learn a more complex, hierarchical representation of data, the more layers there are, the greater the complexity of the model. Once the optimal structure of 1 dCNN-AE has been determined, the developing clustering model is constructed using the k-mean algorithm. To ascertain the optimal number of clusters, the DBI score is employed as a metric for the inertia value, therefore enabling the selection of cluster numbers at the elbow point where the DBI exhibits a notable increase from its minimum values.