# Hybrid Uncertainty Metrics-Based Privacy-Preserving Alternating Multimodal Representation Learning
## 4 Results and Discussion
### Experimental
#### 4.1.3 Evaluation Metrics  
For the multimodal multi-class classification task, we used the following metrics to evaluate the overall classification performance of the model:  
1. Accuracy (ACC): Accuracy measures the proportion of correctly classified samples out of the total samples. It is calculated as \[ACC=\frac{\sum_{i=1}^{N}1(\hat{y}_{i}=y_{i})}{N}\] where \(N\) is the total number of samples, \(\hat{y}_{i}\) is the predicted class for sample \(i\), \(y_{i}\) is the true class, and \(1(\cdot)\) is the indicator function (1 if \(\hat{y}_{i}=y_{i}\), 0 otherwise).  
2. Precision: Precision measures the proportion of samples predicted as positive that are actually positive, reflecting the model's prediction precision. It is calculated as \[Precision=\sum_{c=1}^{C}w_{c}\cdot\frac{TP_{c}}{TP_{c}+FP_{c}}\] where \(C\) is the number of classes, \(w_{c}\) is the proportion of samples in class \(c\), \(TP_{c}\) is the number of true positives for class \(c\), and \(FP_{c}\) is the number of false positives for class \(c\).
3. Recall: Recall measures the proportion of actual positive samples correctly identified by the model, reflecting the model's coverage ability. The weighted average recall is calculated as \[Recall=\sum_{c=1}^{C}w_{c}\cdot\frac{TP_{c}}{TP_{c}+FN_{c}}\] where \(FN_{c}\) is the number of false negatives for class \(c\).
4. F1 score: The F1 score is the harmonic mean of precision and recall, providing a balanced measure of model performance. The weighted average F1 score is calculated as \[F1=\sum_{c=1}^{C}w_{c}\cdot\frac{2\cdot Precision_{c}\cdot Recall_{c}}{Precision_{c}+ Recall_{c}}\] where \(Precision_{c}\) and \(Recall_{c}\) are the precision and recall for class \(c\), respectively.
5. Expected Calibration Error (ECE): ECE measures the difference between the model's predicted confidence and its actual accuracy, reflecting the model's calibration quality. ECE divides the predicted confidences into \(M\) bins (typically \(M=10\)) and computes the weighted average of the absolute difference between accuracy and confidence in each bin: \[ECE=\sum_{m=1}^{M}\frac{|B_{m}|}{N}\cdot|acc(B_{m})-\textit{conf}(B_{m})|\] where \(B_{m}\) is the set of samples in the \(m\)-th confidence bin, \(|B_{m}|\) is the number of samples in bin \(B_{m}\), \(N\) is the total number of samples, \(\text{acc}(B_{m})\) is the accuracy in bin \(B_{m}\), and \(\text{conf}(B_{m})\) is the average confidence in bin \(B_{m}\). A lower \(ECE\) indicates better calibration.
6. Confidence-Stratified Accuracy Low (ConfAcc_Low): ConfAcc_Low measures the model's accuracy in the low-confidence interval (confidence range [0, 0.5]), reflecting the reliability of low-confidence predictions. It is calculated as \[\textit{ConfAcc\_Low}=\frac{\sum_{i\in S_{\textit{low}}}(\hat{y}_{i}=y_{i})}{| S_{\textit{low}}|}\] where \(S_{\textit{low}}\) is the set of samples with confidence in [0, 0.5], \(\hat{y}_{i}\) is the predicted class for sample \(i\), \(y_{i}\) is the true class, \(1(\cdot)\) is the indicator function (1 if \(\hat{y}_{1}=y_{i}\), 0 otherwise), and \(|S_{\textit{low}}|\) is the number of samples in \(S_{\textit{low}}\).  
These metrics collectively provide a comprehensive evaluation of the model's performance. ACC offers a straightforward measure of overall classification performance; precision, recall, and F1 score complement ACC by addressing class imbalance; ECE and ConfAcc_Low provide insights into the model's confidence calibration and reliability, enhancing the analysis of prediction robustness.