## 3 Results
### Hyperparameter Tuning for Synthetic Data Validation  
Hyperparameters, such as the density threshold for defining cluster areas and the \(\epsilon\) for assigning reliability scores, were tuned based on UMAP-transformed data distributions.  
The density threshold plays a key role in determining the cluster validation process. Cluster validation depends on the cluster area, which is directly affected by the selected density threshold. A lower density threshold expands the cluster area, allowing more samples to achieve cluster validation. Conversely, as the density threshold increases, the cluster area shrinks, reducing the number of validated samples.  
In order to determine the optimal density threshold, the percentage of cluster validated samples against the different density thresholds is considered, as shown in Figure 8. It can be observed how a high percentage of validated samples is achieved up to the elbow point, after which it decreases. Beyond this point, the cluster area becomes too small, resulting in fewer samples achieving validation. This trend highlights the importance of selecting a threshold that maximizes the inclusion of meaningful samples without compromising the accuracy of cluster validation. With this aim, the elbow point for each dataset has been computed, resulting in a chosen density threshold equal to 4 for prostate and breast cancer data and equal to 5 for cardiovascular disease data.  
As an example, Figure 9 illustrates cluster areas defined by different density thresholds in the breast cancer data. For thresholds above the selected value, the cluster area does not include all samples within the cluster. Conversely, lower density thresholds produce larger areas, resulting in validation of samples that deviate significantly from the cluster in UMAP space.  
The \(\epsilon\) hyperparameter for reliability scores is defined based on the average feature disparity among reference points, and serves as a threshold for assessing the reliability of the generated samples. A generated sample with a feature disparity close to or below \(\epsilon\) will receive a high reliability score, indicating that its feature values are consistent with those of reference points.  
Figure 7: Quantization process applied to the PSA values.  
To calculate \(\epsilon\), the feature disparity is computed by evaluating the mean difference between each reference point's feature value and the average feature value of its 10 nearest neighbors in the UMAP-transformed space. This mean feature disparity serves as the foundation for \(\epsilon\) adjustment, ensuring that the threshold is data-specific and reflective of the distribution of the reference dataset.  
Table 3 presents the computed mean feature disparity values for each feature in the prostate cancer dataset as an example of this process. It can be observed how \(\epsilon\) is the closest  
Figure 8: Percentage of cluster-validated samples for different density thresholds.  
Figure 9: UMAP visualization of breast cancer reference data (BC-MLR) and cluster areas for different density thresholds.  
integer to the mean feature disparity values. An analog procedure was applied to the other datasets analyzed in this study to ensure consistency and accuracy in defining the \(\epsilon\) values for each case.