# Effective Attention-Based Feature Decomposition for Cross-Age Face Recognition
## 3 Proposed Method
### Feature Decomposition Module  
As the face features extracted from the backbone are severely entangled with age-related information, such as texture changes, it is difficult to recognize two face images of the same person with a large age gap [19]. A CNN extracts the feature vector \(x\) from an input image. The linear factorization can be defined in Equation (1).  
\[x=x_{id}+x_{age} \tag{1}\]  
where \(x_{id}\) and \(x_{age}\) denote the identity-dependent factor and age-dependent factor of the facial feature vector, respectively. The identity-related factor, \(x_{id}\), can work as the age-invariant feature for CAFR. However, it has a drawback: this decomposition acts on a one-dimensional feature vector. The final identity-related factor lacks semantic feature  
Figure 2: Overall framework of the proposed AFEN and its training process.  
information about the aging face, such as beards and wrinkles. To resolve that issue, we propose a feature decomposition module (the EFDM) that uses ECA to decompose the feature map instead of a feature vector.  
Channel attention is a crucial component for improving the generalization capabilities of a deep CNN architecture. The channels are the result of convolutional filters that derive different features from the input, and they might not all have the same representative importance. As some channels are more important than others, it makes sense to apply a weight to the channels based on their importance before they propagate to the next layer. In this paper, we adopt channel-wise attention to highlight age-related information at the channel level. As the parameter and FLOPs overhead of the ECA block [39] are much smaller than the squeeze and excitation block [40], we use the ECA block to compute and apply attention weights to the channels of the input feature map.  
The ECA block is an extremely lightweight channel attention module for deep CNNs. The ECA block first uses global average pooling (GAP) for each channel independently to aggregate the feature map \(\chi\epsilon\mathbb{R}^{C\times H\times W}\), where \(C\), \(H\), \(W\) denote the channel, height, width, respectively. Then, the ECA generates channel weights by performing a fast 1D convolution of size k and a sigmoid function, where k represents how many neighbors participate in the attention prediction for one channel. Next, the age-specific feature map, \(\chi^{age}\in\mathbb{R}^{C\times H\times W}\), is obtained by channel-wise multiplication between the channel weights and the feature map \(\chi\). As illustrated in Figure 3, after channel-wise global average pooling without dimensionality reduction, the ECA module efficiently captures cross-channel interactions by considering every channel and its k neighbors. The ECA generates channel weights by performing a fast 1D convolution of size k, where kernel size k represents the coverage of the local cross-channel interaction, i.e., how many neighbors participate in the attention prediction for one channel.  
In Figure 3, the backbone is used to extract a face feature map, \(\chi\epsilon\mathbb{R}^{C\times H\times W}\), from the input image. In the decomposition module, we use the ECA block to transform the face feature map, \(\chi\), into an age-specific feature map, \(\chi_{age}\). The decomposition process can be defined in Equation (2).  
\[\chi_{id}=\chi-\chi_{age} \tag{2}\]  
By subtracting the age-specific feature map from the face feature map \(\chi\), we obtain the identity-specific feature map \(\chi_{id}\).  
The feature decomposition module based on the ECA block is built to obtain the identity-specific feature and age-specific feature. To achieve a significant separation of the identity-specific and age-specific features, the direct sum loss is proposed, which is introduced in the following section.  
Figure 3: Diagram of the ECA block.