# Effective Attention-Based Feature Decomposition for Cross-Age Face Recognition
## 4 Experiments
### Ablation Studies  
In this subsection, we describe an experiment performed to investigate the efficacy of the proposed model with the CACD-VS, CALFW, and AgeDB-30 datasets. Then, we analyze the effect of taking different values for the hyperparameters, \(\lambda_{1}\) and \(\lambda_{2}\) in Equation (7), and \(K\) in Equation (3). In the end, we compare the time complexity with that of state-of-the-art methods.  
**Efficacy of the proposed method.** To investigate the efficacy of the proposed decomposition module and direct sum loss in our method, we considered the following variants of our method for ablative comparison based on three benchmark datasets for CAFR: (1) Baseline: the baseline model was pre-trained only on IResNet-101; (2) Baseline + EFDM: the model was trained by the EFDM; (3) Baseline + EFDM + direct sum: our proposed model, which was trained simultaneously by the EFDM and direct sum module. As reported in Table 1, our model had the best performance on CALFW, CACD-VS, and AgeDB, demonstrating the efficacy of the proposed method.  
**Settings of the hyperparameters.** As mentioned in our description of the whole loss function, we use hyperparameters \(\lambda_{1}\) and \(\lambda_{2}\) to balance the three losses. We conducted experiments to observe the effects of \(\lambda_{1}\) and \(\lambda_{2}\). We, respectively, set \(\lambda_{1}\) as {1, 0.1, 0.01, 0.001} while \(\lambda_{2}\) = 0.01, and then set \(\lambda_{2}\) as {1, 0.1, 0.01, 0.001} while \(\lambda_{1}\) = 0.01 to test the face verification accuracy with the CACD-VS dataset. The verification rates under different values of \(\lambda_{1}\) and \(\lambda_{2}\) are shown in Figure 9, which indicates that the best performance was obtained when \(\lambda_{1}\) = 0.01 and \(\lambda_{2}\) = 0.01.  
Parameter \(K\) is the number of basis vectors, as explained above in the direct sum loss section. We constructed face verification experiments using four values (\(K\) = 25, 50, 75, and 100). The evaluation results are tabulated in Table 2 and show that increasing \(K\) can improve face verification accuracy. That is understandable because a larger \(K\) leads to a more powerful nonlinear transformation. The best performance was obtained when \(K\) = 75. Further increases in \(K\) led to more noise vectors, which produced a drop in accuracy. Therefore, we set parameter \(K\) to 75.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**EFDM** & **Direct Sum** & **CALFW** & **CACD-VS** & **AgeDB-30** \\ \hline  & & 96.03 & 99.33 & 98.37 \\ \(\surd\) & & 96.06 & 99.40 & 98.38 \\ \(\surd\) & \(\surd\) & 96.10 & 99.63 & 98.38 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Evaluation results (%) by different methods.  
Figure 8: Trend of training and validation loss.  
**Exploration of identity loss.** The Arcface loss is also an effective method for generating discriminative identity features. Therefore, we compared the performance of Arcface and CurricularFace loss on the CACD-VS dataset by replacing the CurricularFace loss in Equation (7) with the Arcface loss. Table 3 shows the results of CurricularFace and Arcface on CACD-VS. CurricularFace loss performed better than Arcface loss.  
**Time complexity.** We used a well pre-trained general FR network to save resources and reduce the time required to train the network from scratch. With fewer training images and training parameters (in Table 4) than MTLFace [19] and DAL [30], the proposed method achieves a comparable and stable performance. Compared with the age-invariant representations learning method under the same environment and batch size, DAL [30] costs 0.963 s for each iteration on the Nvidia Titan X Pascal GPUs, whereas our method costs only 0.416 s. Therefore, our method reduces the complexity and computational power required for CAFR.