## 4 Results
### Clustering Validation Analysis
This pattern is divided into several clear or controversial scenarios that map the CVIs' voting process and the production of the final decision. Scenario 0: The decision is made by the CVIs' absolute majority. The absolute majority points to the correct \"true\" number of clusters. This scenario illustrates the consensus between CVIs in final decision-making. Moreover, Scenario 0 does not require additional verification by invasive methods. Figure 3: Simplified validation scheme of the non-invasive and invasive decision fusion methods. Scenario 1a: The decision is made by the relative majority of CVIs, and the nearest alternative (the second largest group of CVIs) has 50% fewer votes than half of the majority. The relative majority points to the correct \"true\" number of clusters. The situation is clear enough; however, an absolute majority is not obtained as in Scenario 0. Scenario 1b: The final decision is taken by the CVIs' relative majority, and the nearest alternative is 50% more votes than half of the majority. The relative majority points to the \"true\" number of clusters. This scenario shows the controversial situation where there is no clear-cut grouping structure. Scenarios 1a and 1b require additional verification by means of the invasive relative majority decision fusion method. Scenario 2: The relative majority of CVIs points to the incorrect number of clusters. The nearest alternative group of CVIs, in turn, shows the \"true\" number of clusters. The most critical of all the previous scenarios, it requires complete and precise verification by means of the invasive relative majority decision fusion method. Scenario 3: The data sets for which no majority prevails. Two of the largest equal groups of CVIs vote for different numbers of clusters; however, only one group of CVIs makes the \"true\" decision, and the other is misleading. This scenario requires complete and precise verification by means of the invasive parity majority decision fusion method. Figure 4 shows the study sample, which consists of 379 data points (without dividing the data into a particular educational mode) in the form of a three-dimensional scatter plot. To provide significant insights into clustering validation procedures, the clustering operation should first be applied. Figure 5 shows the results of the clustering operation, where three clear-cut globular-form clusters are identified. Figure 5 illustrates the result of the clustering process. The raw input data set is partitioned into three clusters. The clustering results could be extrapolated to the descriptive statistics, where the critical verdict could be made, namely, the blue cluster corresponds to the traditional educational mode, the green cluster corresponds to the STEM-based approach, and the orange cluster corresponds to the STEAM active learning approach. Even though the clustering algorithm with the dissimilarity measure identifies three clusters, the validation procedure should be applied. To verify the quality of clustering results and to justify that three is the \"true\" number of clusters, majority-based decision fusion methods are performed. The validation results of majority-based decision fusion methods with 24 CVIs engaged in the voting process are shown in Table 3. Critical values of CVIs are  
Figure 4: A scatter plot of a three-dimensional raw data set (379 data points). The \(x\)-axis corresponds to secondary school students’ learning outcomes toward general sensor-based knowledge; the \(y\)-axis corresponds to students’ creativity; and the \(z\)-axis corresponds to students’ intrinsic relevance. One data point correlates with one particular secondary school student. used to select the best number of clusters. This set of 24 CVIs has been chosen from the literature [105]. The majority-based decision fusion method with a non-invasive configuration reveals the absolute majority (13 CVIs) voted for three clusters to be the \"true\" ones.