## 3 Results
### Evaluation Metrics  
After generating the synthetic datasets, a quality assessment is conducted to evaluate the effectiveness of the UMAP-based approach. To establish a performance benchmark, we compare our results with the evaluation metrics obtained from synthetic datasets generated using CTGAN, CopulaGAN, and TVAE. These synthetic datasets have been created from the reference dataset in each case, with an output size matching the scale of the UMAP-based synthetic data (79,000 for prostate cancer, 17,000 for beast cancer, and 50,000 for cardiovascular diseases). The evaluation metrics encompass two key dimensions: fidelity and utility. Fidelity is assessed by comparing the cumulative distribution function (CDF) of real and synthetic data, measuring how well the synthetic data represent the distribution of the original dataset. Utility is evaluated based on the synthetic data's contribution to machine learning (ML) model performance, reflecting its practical applicability for data-driven healthcare tasks. The fidelity assessment of the synthetic data generation through CDF is performed both visually, as shown in Figure 10, and quantitatively, using the Kolmogorov-Smirnov statistic, which measures the maximum absolute difference between the synthetic and real data distributions. This K-S statistic, presented in Table 4, provides a robust metric for evaluating distributional similarity for each attribute. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Feature** & **Mean \(\mathbf{f_{\text{disp}}}\)** & \(\mathbf{\varepsilon}\) \\ \hline patient\_age & 1.18 & 1 \\ PSA & 3.77 & 4 \\ prostate volume & 5.67 & 6 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Mean feature dispercity for prostate cancer reference data (PI-CAI). Figure 10 shows the CDFs for various attributes across the datasets. For the prostate cancer data, the patient_age attribute is shown in Figure 10a. In the case of the breast \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Attribute** & **UMAP** & **CTGAN** & **CopulaGAN** & **TVAE** \\ \hline \multirow{3}{*}{Prostate Cancer} & patient\_age & 0.1587 & 0.3299 & **0.1554** & 0.1673 \\  & psa & 0.4103 & 0.4695 & 0.3583 & **0.1980** \\  & prostate\_volume & 0.3639 & 0.3557 & 0.1690 & **0.1327** \\ \hline \multirow{3}{*}{Breast Cancer} & age & **0.3262** & 0.3990 & 0.3289 & 0.5524 \\  & tumor-size & 0.1793 & **0.1344** & 0.2042 & 0.1410 \\  & inv-nodes & **0.6010** & 0.6942 & 0.6254 & 0.9477 \\ \cline{1-1}  & node-caps & **0.4254** & 0.7501 & 0.6662 & 0.8906 \\ \cline{1-1}  & tumor-size & 0.1793 & **0.1344** & 0.2042 & 0.1410 \\ \cline{1-1}  & deg-malig & **0.3756** & 0.4090 & 0.3876 & 0.5921 \\ \cline{1-1}  & irradiat & **0.3931** & 0.7118 & 0.6330 & 0.9448 \\ \hline \multirow{3}{*}{Cardiovascular Diseases} & chestpain & **0.3505** & 0.4443 & 0.3834 & 0.4865 \\  & restingBP & 0.1351 & **0.0382** & 0.1419 & 0.1478 \\ \cline{1-1}  & fastingbloodsougar & **0.5749** & 0.6689 & 0.6730 & 0.8934 \\ \cline{1-1}  & maxheartrate & 0.0568 & **0.0404** & 0.1919 & 0.3230 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: K-S statistic for CDFs. Lower K-S statistic for each attribute in bold. Figure 10: Cumulative distribution function per attribute for real data, UMAP, CTGAN, CopulaGAN, and TVAE synthetic data. cancer datasets, the CDF of the tumor-size attribute is illustrated in Figure 10b. In both plots, none of the synthetic datasets perfectly replicate the real data distribution at every point. However, the overall behavior of the four synthetic datasets is similar, with comparable deviations from the real CDF. This indicates that, while minor discrepancies exist, the general distributional properties are preserved across all methods. For the cardiovascular disease datasets, the CDF of restingBP is depicted in Figure 10c. In this case, the synthetic datasets generated by UMAP and CopulaGAN closely follow the real data distribution, demonstrating high fidelity.