## 3 Results
### Second Evaluation of Trained Models
#### 3.4.2 Suspected Planetary Nebulae  
In addition to the previous tests, an additional analysis was conducted using a carefully selected set of 15 stars that are considered candidates for planetary nebulae. Following this careful selection process, this group of stars was evaluated using our previously trained models, as detailed in Table 21. This information was obtained from the Symbad database. The purpose of including this group of 15 candidate stars for planetary nebulae in the study was to further expand the understanding of the models and their ability to identify and classify specific celestial objects. The Figure 11 shows the spectral representation of the stars obtained previously from the article. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \multirow{2}{*}{**Suspected Symbiotic Stars**} & \multicolumn{3}{c}{**Trained Model (Balanced Data)**} & \multicolumn{3}{c}{**Trained Model (Unbalanced Data)**} \\ \cline{2-9}  & \multicolumn{2}{c}{**ANN**} & \multicolumn{2}{c}{**RF**} & \multicolumn{2}{c}{**ANN**} & \multicolumn{2}{c}{**RF**} \\ \cline{2-9}  & **SY** & **PN** & **RG** & **Class** & **SY** & **PN** & **RG** & **Class** \\ \hline V748 Cen & 1.0 & 0.0 & 0.0 & PN & 0.0222 & 0.9778 & 0.0 & PN \\ \hline WRAY 16-294 & 0.9134 & 0.0799 & 0.0067 & Sy & 0.8504 & 0.1486 & 0.001 & Sy \\ \hline DASCH J075731.1+201735 & 0.7153 & 0.0142 & 0.2704 & Sy & 0.7673 & 0.0485 & 0.1841 & RG \\ \hline ASAS J174600-2321.3 & 0.0642 & 0.1435 & 0.7923 & RG & 0.0091 & 0.091 & 0.8999 & RG \\ \hline IPHASJ201550.96+373004.2 & 0.2938 & 0.703 & 0.0032 & PN & 0.1461 & 0.8369 & 0.017 & PN \\ \hline IPHASJ202058.52+380949.8 & 0.9299 & 0.0687 & 0.0013 & Sy & 0.7117 & 0.2695 & 0.0188 & Sy \\ \hline IPHASJ202947.93+355926.5 & 0.9343 & 0.0654 & 0.0003 & Sy & 0.8125 & 0.1869 & 0.0005 & RG \\ \hline IPHASJ204713.69+463517.5 & 0.9189 & 0.0737 & 0.0075 & Sy & 0.8513 & 0.148 & 0.0006 & Sy \\ \hline IPHASJ215628.47+571445.5 & 0.972 & 0.028 & 0.0 & Sy & 0.82 & 0.1799 & 0.0001 & PN \\ \hline IPHASJ231735.92+634506.4 & 0.9772 & 0.0223 & 0.0006 & Sy & 0.8664 & 0.1307 & 0.0029 & Sy \\ \hline VPHASDR2J175320.4-295327.4 & 0.8999 & 0.0862 & 0.0139 & RG & 0.7163 & 0.2261 & 0.0577 & RG \\ \hline VPHASDR2J175346.2-284826.6 & 0.8452 & 0.1433 & 0.0116 & Sy & 0.8842 & 0.1157 & 0.0002 & Sy \\ \hline VPHASDR2J172830.6-292124.5 & 0.9833 & 0.0157 & 0.001 & Sy & 0.9507 & 0.0493 & 0.0 & Sy \\ \hline VPHASDR2J181154.5-243536.2 & 0.5373 & 0.2681 & 0.1946 & Sy & 0.7686 & 0.2258 & 0.0055 & Sy \\ \hline VPHASDR2J181333.6-245225.0 & 0.9604 & 0.0329 & 0.0067 & Sy & 0.879 & 0.1208 & 0.0001 & Sy \\ \hline VPHASDR2J181123.2-241430.0 & 0.9174 & 0.0714 & 0.0111 & Sy & 0.7778 & 0.2096 & 0.0126 & Sy \\ \hline VPHASDR2J141301.4-653320.1 & 0.9903 & 0.0094 & 0.0003 & Sy & 0.9544 & 0.0456 & 0.0 & Sy \\ \hline \end{tabular}
\end{table} 
Table 20: Results of the classification using ANN and Random Forest. Both algorithms were trained using both balanced and imbalanced datasets. The dataset of suspected symbiotic stars was obtained from the article “A machine learning approach for identification and classification of symbiotic stars using 2 MASS and WISE” [29]. The ANN model’s results are expressed as probabilities with four significant digits, whereas the Random Forest model only shows the resulting class.