## 5 Results and Discussion
### Third Experiment  
Succeeding the two new equivalent variables to deploy from the application of the PCA, the graph in Figure 7 was plotted, as mentioned in [1].  
From the analysis of the centers of each cluster, it is possible to understand the features that separate and organize each cluster from the others. The majority of the features are common so it was decided to resample the initial data containing just the features where it is possible to see big oscillations in the coordinates of the centers of the cluster. Furthermore, the silhouette score was only 0.043, which even if it is higher than 0, is still poor. The reason it is that low could be related to the number of features in common in the analysis of the centers.  
The new subset contains all the variables related to the SMSs and the variable _principal_, which is the amount of money requested by the user.  
Therefore, the modeling process was repeated and a new graph of the clusters was plotted. The graph is shown in Figure 8[1].  
Note that since the K-means model was redone, the legend from Figure 8 is different as the new number labeled is settled randomly, so Cluster 1 from Figure 7 is not the same as Cluster 1 from Figure 8. The comparison between both representations will be based on the size and the position of the points in each cluster.  
Consequently, there are minimal differences between the previous graphic and this new one, which can verify that these features are the ones that impact the cluster formation. Furthermore, the silhouette score also reflected it, with an improvement to 0.194. Since this score varies between \(-1\) and \(1\), in practice 0.194 would mean trust in the model.  
From a business perspective, for the company case, created three criteria were created to define which clusters would have the loans that require higher prioritization. These criteria can be described, with the order mattering, as:  
Figure 7: Visual representation by the PCA method of the three clusters present in this data [1].  
1. **Percentage of loans recovered per cluster:** To check where the amount of paid loans is the highest, and consequently with more probability of a return;
2. **Amount of defaulting money per cluster:** To show where the biggest amount of money can be lost is. This results from the sum of the variable _principal_;
3. **Average from a particular SMS feature:** This criterion will not be described in detail to protect the business side of this MFI.  
After setting these criteria, a table was built, Table 5, where the results for each cluster can be consulted. Furthermore, these were analyzed following the importance of each criterion (shown by the order enumerated).  
For the first criterion, Cluster 2 has the highest percentage whereas Cluster 0 and Cluster 1 are similar. So, there is now some advantage for Cluster 2 in the prioritization scale.  
For the second criterion, Cluster 0 represents a higher amount of possible defaulting money, but Cluster 2 shows high values as well. For this reason, Cluster 2 keeps the advantage of being the most prioritized (since the first criterion has more weight on the decision), but Cluster 0 is now settled to be the second in the prioritization scale.  
For the third and last criteria, the results came to confirm that Cluster 0 has more potential than Cluster 1.  
To sum up, the prioritization for the loans should be in the following order:  
1. Cluster 2
2. Cluster 0
3. Cluster 1