# AU-Guided Unsupervised Domain-Adaptive Facial Expression Recognition
## 4 Experiments
### Ablation Studies  
We conduct ablation studies for the modules of our AdaFER and other hyper parameters. **The three types of label assignments**. In AGA, we introduce three kinds of assignment, namely, S-hard, T-hard, and T-soft. We explore individual types and their combination on the CK+, ExpW, FERPlus, and FER2013 datasets. The results are shown in Figure 5. For individual assignments, we observe that the T-soft strategy performs best on average, followed by the S-hard strategy. Combining the T-soft and S-hard strategies further boosts performance in most cases. We use this combination strategy by default in the following experiments. **Anchor images in AGT module**. In AU-guided triplet training, both the source and target data can be used as anchor images. We evaluate the effect of the anchor images in Table 2. As can be observed, using source data as anchor images largely outperforms the target anchor scheme on the CK+ dataset, which may be explained by the target CK+ dataset being too small to collect enough triplet samples. Both individual anchor schemes  
Figure 4: Visualizations of pseudo-labels from baseline method #3 and our AGA module. BSA represents baseline method #3. Figure 5: Evaluation of pseudo-assignment strategies. perform similarly on large-scale datasets, and combining both schemes consistently boosts performance on all datasets. **AU-guided annotating (AGA) and AU-guided triplet training (AGT)** are two crucial modules in AdaFER, which, respectively, leverages pseudo-labels for target domain images and constraints the distance structure of each triplet tuple. To explore the effectiveness of each module, we conduct the evaluation on the CK+, ExpW, FER2013, and FERPlus datasets. As shown in Table 3, both the AGA and AGT modules can individually improve the baseline by a large margin, and they perform similarly on most of the datasets. This may be explained by that both the AGA and AGT modules essentially resort to AU information, and the only difference is that AGA performs supervision on the classifier, while AGT does so on the feature mapping. Nevertheless, from the results of AGA+AGT, it is clear that they compliment each other on all the datasets. **The margin \(\gamma\) of the AGT module. \(\gamma\)** is a margin parameter to control the distance between the anchor-positive pair and the anchor-negative pair. Theoretically, it can be a learnable parameter in the end-to-end framework. We evaluate it with both a fixed mode and a learnable mode. The results are illustrated in Figure 6. For the fixed mode, we evaluate a margin from 0.25 to 1.5, with 0.25 as the interval. On all of the four FER datasets, our default margin \(\gamma=0.5\) achieves the highest performance. Larger margins make training harder, which degrades performance on the CK+ and ExpW datasets. For the learnable mode, \(\gamma\), respectively, converges to 0.62 (\(\pm\)0.034), 0.37 (\(\pm\)0.067), 0.71(\(\pm\)0.026), and 0.42(\(\pm\)0.033) on the CK+, ExpW, FERPlus, and FER2013 datasets. Meanwhile, the learnable \(\gamma\) also obtains competitive results. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Source** & **Target** & **CK+** & **ExpW** & **FER2013** & **FERPlus** \\ \hline \(\surd\) & \(\times\) & 80.62 & 69.90 & 54.36 & 77.61 \\ \(\times\) & \(\surd\) & 71.23 & 69.73 & 55.45 & 77.93 \\ \(\surd\) & \(\surd\) & **81.40** & **70.86** & **57.29** & **78.22** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Evaluation of the influences of anchor images on the AGA module. Figure 6: Evaluation of the margin parameter (\(\gamma\)), and the trade-off ratios \(\epsilon\) and \(\beta\). **The trade-off ratios \(\beta\) and \(\epsilon\). \(\beta\)** is the trade-off ratio between two loss values calculated by the pseudo-labels and ground truths in Equation (2). \(\epsilon\) is the trade-off ratio between \(L_{c}\) and \(L_{tri}\).