## 5 Simulation Results and Discussions
### Simulation Results and Analysis
#### 5.2.4 The Influence of the Uncertainty in the Number of Categories on NTC Performance  
For unsupervised clustering, there is an inevitable disadvantage, that is, it is difficult to determine the appropriate number of clusters in advance, resulting in a low clustering quality. The key to obtain a good clustering effect is to determine the optimal number of clusters. Therefore, this paper used the elbow method and the silhouette coefficient method to determine the optimal number of clusters. As a low-complexity linear dimensionality reduction method, the PCA algorithm is suitable for quickly determining the range of the optimal number of clusters in this paper. The objective function of k-means clustering is the squared sum of the distance between the sample and the center point, also known as the distortion. For a cluster, the lower the distortion, the closer the samples in the cluster are. The higher the distortion, the farther the samples in the cluster are. The distortion of samples decreases with the increase in clustering categories. However, if the data of each class of samples are very different, when the clustering class is close to the real class, the distortion is greatly reduced, and then tend to be flat. This turning point is considered as a point with good clustering performance. Based on this indicator, multiple k-means models were trained, and different \(k\)-values (cluster center) were selected for comparison, as shown in Figure 8.  
Figure 8: The change in average distortion at different cluster centers.  
Figure 7: t-SNE feature visualizations for different clustering algorithms. (**a**) CAE; (**b**) CVAE; (**c**) CAAE; (**d**) DC-CAE; (**e**) DC-CVAE; (**f**) DC-CAAE.  
When \(k=20\), the distortion is greatly improved, and the maximum curvature value appears. For a sample set, its silhouette coefficient is the average value of all sample silhouette coefficients. The closer the distance between samples of the same category, the farther the distance between samples of different categories, and the higher the score, the better the classification effect. As can be seen from Figure 9, when \(k=18\) and \(k=20\), the silhouette coefficient has a high peak value. Combined with the elbow method diagram, when \(k=20\), the average distortion is relatively small, and the trend is gentle. Therefore, \(k=20\) can be considered as the best number of clusters.  
After roughly determining the number of clusters, we verified the reliability of the proposed method. When \(k=\{5,10,15,20,25\}\), the DC-CAAE model proposed in this paper was used for training. It can be seen from Figure 10 that when \(k=20\), the accuracy of the model tends to be stable and the highest, which is consistent with the guess above. To further determine the specific values of the cluster, on the basis of Figure 10, we expanded the analysis to around \(k=20\). Five points, \(k=\{18,19,20,21,22\}\), were chosen for the demonstration. The experimental results are shown in Figure 11.  
When \(k=22\), the accuracy of the clustering is slightly improved compared to when \(k=20\). The reasons for this situation are as follows: when the number of clusters is smaller than the real sample category, the number of cluster centers is small; hence, the samples of the additional categories will inevitably converge to other categories, resulting in too large a distance between the same category of samples. When the number of clusters is greater than the real sample category, the number of cluster centers is large, hence the same type of samples will be divided into multiple categories. However, this does not affect the evaluation of the clustering accuracy, and even the accuracy will be improved compared  
Figure 10: Performance of the DC-CAAE model at \(k=\{5,10,15,20,25\}\).  
Figure 9: The change in silhouette coefficient at different cluster centers.  
with the actual number of clusters. However, on the whole, when the cluster category is 20, the five evaluation indexes are relatively stable, and \(k=20\) has the best performance.