# Concept of Virtual Reality Training of Facility Management Employees Using Eye Tracking
## 5 Clustering for Fast and Slow Learners  
Subsequent research aimed to divide the training participants into fast and slow learners. The clustering algorithm was based on the results of each participant's skills tests conducted after training in all VR modules. The scores for each test were normalized by dividing the test score by the value of the maximum possible score. Thus, the clustering algorithm was based on three values representing the relative (percentage) evaluation of the skills acquired after training in each VR module (Figure 6). \begin{table}
\begin{tabular}{c c c} \hline \hline
**VR Module** & **Result** & **Percent** \\ \hline Fire pump station & Pass & 72\% \\  & Fail & 28\% \\ HVAC roof station & Pass & 62\% \\  & Fail & 38\% \\ Air conditioning unit & Pass & 67\% \\  & Fail & 33\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Evaluation of the results of skills tests performed in VR modules. Figure 5: Examples of using an interactive tablet to guide and supervise participants during training. Figure 6: Histograms of the obtained results for specific VR modules. The Ward method was used to carry out the clustering, and the distances were determined based on the Euclidean metric. The number of clusters was chosen by silhouette coefficient agglomerative clustering analysis. [PERSON]'s method starts with a cluster number equal to the number of observations with only one observation assigned. It successively merges the most similar clusters, which minimally increases within-cluster variance until all the observations are included in one cluster. The results confirmed the correctness of grouping training participants into two classes (Figure 7). The highest value was obtained for the division into two clusters and slightly lower for the division into three. The analysis of the results related to passing the tests and the timely execution of the FM tasks allows dividing the participants into two groups: fast learners, i.e., those who may need less training before taking the skills test, and slow learners, who may need more training to be able to pass the skills test. The possible subsequent division was in the group of slow learners, resulting in three classes (Figure 8). However, the created new cluster of participants between fast and slow learners is small and constitutes less than 10% of all participants. Additionally, the participants who were classified as fast learners passed at least two VR scenarios and thus achieved the basic learning goal. As a result, an additional division was no longer needed. The aim was to determine clusters with more different average values and thus group participants into two more distinguished groups. The K-means method was used to divide the training participants into two clusters representing fast and slow learners (Figure 9). Initial cluster centers were determined using the k-means++ algorithm. As a result, a more significant number of participants assigned to the class of fast learners was distinguished, and their percentage share increased from 57% for the Ward method to 74% for the K-means method. The criteria for classifying into the group of fast learners decreased, and the percentage of fast learner training participants is more like the percentage of people who passed each VR scenario (Table 2). The results indicate that only those participants who score above 90% on the test of skills acquired during the training with the use of the fire pump station VR module and above 70% on the test of skills acquired during the training with the use of the HVAC roof station VR module will be classified as fast learners. The test results of skills acquired during the training using the air conditioning unit module are relatively low in evaluating the employee's learning speed. The air conditioning unit module contained the most elements of low technical complexity, such as checking the correctness of machine operations, checking for dirt, checking if cables are connected, and so on.