# Anomaly Detection in Automotive Industry Using Clustering Methods--A Case Study
## 4 Case Study, Results, and Discussions
### Computational Results  
In this section, we present the results achieved by the nine algorithms described in Section 2 [71]. We present the results separated by an evaluation metric. For the stochastic methods, we present the best of 30 independent simulations. Figure 6 presents the SSE index evolution throughout a different quantity of groups formed. Graphical analysis shows a clear disadvantage of the DBSCAN algorithm. It is because of the input parameters, which cannot be translated as noise. For this purpose, even isolated data from the predefined radius must be considered as a group. Due to the distribution of the data in the dimensional space, many items fell into this situation. In the analysis of the groups, the large number of single items within several clusters generated by DBSCAN was precise. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Algorithm** & **(a)** & **(b)** & **(c)** \\ \hline
**GA** & 89.78\% & 92.00\% & 88.67\% \\ \hline
**FCM** & 89.78\% & 89.33\% & 91.33\% \\ \hline
**K-Medoids** & 89.78\% & 89.33\% & 91.33\% \\ \hline
**K-Means** & 89.78\% & 89.33\% & 91.33\% \\ \hline
**Hierarchical** & 89.78\% & 89.33\% & 90.00\% \\ \hline
**PSO** & 89.11\% & 90.00\% & 88.67\% \\ \hline
**DE** & 89.11\% & 90.00\% & 88.67\% \\ \hline
**SOM** & 85.33\% & 85.33\% & 85.33\% \\ \hline
**DBSCAN** & 67.78\% & 68.00\% & 67.33\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Clustering algorithm performances considering the use of PCA on the Iris dataset. Figure 6: SSE index evaluation over a different number of groups considering nine clustering methods. It is possible to observe that the FCM algorithm did not perform better than the others. Again, this result can be attributed to the input data distribution, which caused the algorithm to fall to a local minimum, harming the result. Another point to highlight is the positive result of the curves for the K-Medoids, Hierarchical, and K-Means algorithms with a distance from the other curves and the corresponding proximity. In Figure 7 is plotted the SSW index. In the same way as it was observed in the SSE, for the SSW index, there is a clear advantage to the K-Medoids, Hierarchical, and K-Means algorithms, and a disadvantage to the DBSCAN and FCM algorithms, for the reasons already discussed. Figure 8 presents the results for the SSB index. Figure 8: SSB index evaluation over different group amounts considering nine clustering methods. Figure 7: SSW index evaluation over different group amounts considering nine clustering methods. It is essential to point out that the SSB goal is to maximize the distance between centroids. This means that better distinct groups are formed, as the centroids are far apart. The same reason explains the advantage of DBSCAN as the disadvantage found in the SSW for this algorithm. Many centroids ended up being formed with unique elements, which increased the sum of the Euclidean distances between the centroids of the groups included. At the other end of the exact Figure, there is a disadvantage in the design of the groups formed in applying SOM and FCM algorithms. The performance highlights K-Medoids, Hierarchical, and K-Means. Figure 9 presents the results for the CH index. Remembering that the higher the CH, the better the quality of the clusters, or else, the more cohesive and outlined are the groups formed. This metric is calculated by Equation (18), representing a relationship between SSB, SSW, amount of data (\(n\)), and the number of centroids (\(k\)). In this way, equating the correlation at once to maximizes the SSB and minimizes the SSW. Once again, we observe the same tendency regarding the previous metrics. Figure 10 shows the results for the WB index. Figure 10: WB index evaluation over different group amounts considering nine clustering methods. Figure 9: CH index evaluation over different group amounts considering nine clustering methods. From Figure 10, we observe that the evolution curve of the WB index decreases significantly from the 360 groups formed for the different algorithms.