## 5 Results
### Confusion Matrix and Statistics for Overall Authorization  
The confusion matrix and statistics for the whole authentication to authorization process are displayed in Figure 5 where the confusion matrix, the Kappa Score, and [PERSON]'s test are shown in order.  
As can be seen, the model accurately classified every instance in the dataset, with a 95% confidence interval indicating a 100% accuracy. The model's low \(p\)-value suggested superior performance compared to the baseline, with a true accuracy of at least 98.44%. The No Information Rate indicated that an estimate about the most prevalent class could be accurate 51.06% of the time. When taken as a whole, these metrics offered strong proof that the model performed extremely well on the given data, correctly classifying each event with no mistakes. Other metrics used included balanced accuracy, prevalence, detection rate, positive predictive value (PPV), negative predictive value (NPV), specificity, and sensitivity. The specificity and sensitivity were both one, indicating that the model correctly detected true negatives and positives. Similar functionality in both groups was indicated by thedataset's balanced accuracy of one, with equal prevalence, detection rate, and detection prevalence matching the real class distribution. Verifying the model's performance using untested test data is essential to ensure that it generalizes well and does not overfit the training set.  
Our model, which had an Area Under the ROC Curve (AUC) value of one, showed excellent discrimination ability between the positive and negative classes. For randomly chosen positive and negative instances, the model consistently gave positive occurrences a higher score than negative instances. Figure 6 shows the ROC curve for authentication and authorization with the Area Under the Curve (AUC) of one with control = 0 and cases = 1.  
The results of combining the AUC with additional performance indicators derived from Figure 1 are shown in Table 2.  
The adaptive authentication model, with no false positives or negatives, accurately recognized all positive and negative classifications, predicting data distributions. The model accurately predicted the dataset's class distributions and consistently ranked positive examples higher than negative ones, demonstrating a flawless AUC. However, since these results  
\begin{table}
\begin{tabular}{l c} \hline \hline
**Metric** & **Value** \\ \hline Accuracy & 1 \\ Sensitivity (recall) & 1 \\ Specificity & 1 \\ Precision (PPV) & 1 \\ NPV & 1 \\ Balanced accuracy & 1 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Combination of AUC with other performance metrics.  
Figure 5: Overall confusion matrix and statistics.  
Figure 6: ROC curve for authentication and authorization.  
may indicate overfitting, we further performed cross-validation. Since perfect performance is uncommon, overfitting is the only explanation for these findings. Normalization and more thorough testing with a wider variety of datasets (real-world data) are needed to make sure the model performs well outside of a controlled environment. However, since there are not many studies that directly connect to our work, real-world deployment was carried out to acquire a dataset, which was evaluated. The results of the calculations for the False Positive Rate (FPR) and False Negative Rate (FNR) were zero for each. The FPR and FNR values of zero for the provided dataset supported the accuracy and reliability of the model.