# Deep-Learning-Based Identification of Broad-Absorption Line Quasars
## 4 Results and Discussion  
To evaluate the performance of the classification model, we used _accuracy_, _precision_, _recall_, and _F1_ scores to evaluate the classification performance of the model. The following formulas were calculated:  
\[Accuracy=\frac{TP+TN}{TP+TN+FP+FN}, \tag{2}\]  
\[Precision=\frac{TP}{TP+FP}, \tag{3}\]  
\[Recall=\frac{TP}{TP+FN},\text{ and} \tag{4}\]  
\[F1=\frac{2\cdot Precision\cdot Recall}{Precision+Recall} \tag{5}\]  
where _TP_ (true positive) is the number of cases where the sample was truly positive (BAL quasars) and the model's predictions were correct, _TN_ (true negative) is the number of cases where the sample was actually negative (non-BAL quasars) and the model correctly predicted that it was negative, _FP_ (False Positive) indicates a situation where the sample was actually negative and the model incorrectly predicted it as positive, and _FN_ (false negative) indicates a situation where the sample was actually positive and the model incorrectly predicted it as negative. In this paper, we used PCA, t-SNE, LLE, and ISOMAP, respectively, to extract features from original data. These features were applied to the deep learning model (Figure 3), and the classification results were evaluated using the _accuracy_, _precision_, _recall_, and _F1_ scores mentioned above. The results indicated that the deep learning model with feature extraction using the PCA method was the best-performing model on both the training (Table 2) and test (Table 3) datasets. During our classification experiments, we found that the performance of the deep learning models varied considerably depending on the dimension reduction algorithm used to extract the features. Among the four algorithms--PCA, LLE, ISOMAP, and t-SNE--PCA performed the best on the training and test datasets. Specifically, the models using PCA achieved impressive accuracy rates of 99.7% and 99.1% on the training and test datasets, respectively. In addition, the recall, precision, and F1 results for the combined PCA model were all greater than 99.0%, indicating that it was able to accurately classify the vast majority of BAL and non-BAL quasars with minimal error. This excellent performance \begin{table}
\begin{tabular}{c c c c c} \hline
**Algorithm** & **Accuracy (\%)** & **Precision (\%)** & **Recall (\%)** & **F1 Score (\%)** \\ \hline PCA & 99.7 & 99.9 & 99.5 & 99.7 \\ t-SNE & 91.1 & 95.2 & 86.4 & 90.6 \\ LLE & 98.5 & 99.2 & 97.9 & 98.5 \\ ISOMAP & 94.2 & 96.7 & 91.6 & 94.1 \\ \hline \end{tabular}
\end{table} 
Table 2: Summary of the accuracy, precision, recall, and F1 scores for the training dataset. \begin{table}
\begin{tabular}{c c c c c} \hline
**Algorithm** & **Accuracy (\%)** & **Precision (\%)** & **Recall (\%)** & **F1 Score (\%)** \\ \hline PCA & 99.1 & 99.5 & 98.8 & 99.1 \\ t-SNE & 90.6 & 92.5 & 88.3 & 90.4 \\ LLE & 98.9 & 99.1 & 98.7 & 98.9 \\ ISOMAP & 94.5 & 95.8 & 93.0 & 94.4 \\ \hline \end{tabular}
\end{table} 
Table 3: Summary of the accuracy, precision, recall, and F1 scores for the test dataset. shows that PCA effectively captured the key data features while reducing the size of the data. In doing so, it promoted the ability of the deep learning model to generalize unseen data, highlighting the robustness of the approach in distinguishing types of quasars. In the contrast, the model using LLE also performed well, although it was slightly behind the model that was based on PCA. It had an accuracy of 98.5% for the training set and 98.9% for the testing set. The performance indicators (the _recall_, _accuracy_, and \(F1\) scores) were almost comparable to PCA, with a value of approximately 99% for all test data. The emphasis was on maintaining local relationships in the data, which allowed it to obtain strong classification results. However, its performance was slightly lower than that of PCA, likely due to the emphasis on local rather than global structures, which may have led to a less complete understanding of the global feature space of the data.