# Domain Discrimination Expert Weighted Network for Multi-Source Carotid Artery Plaque Classification
## 3 Materials and Methods
### Methods
#### 3.2.3 Training Steps  
Given the distinct nature of the multicenter issues compared to the common fully supervised models, this section details the training process, including the training and testing phases of the model. The training phase consists of two steps:  
Step A. The initial stage aims to build a foundational model that is better suited for the multicenter plaque classification. At this point, the model is trained using the plaque data from the source centers, with a particular focus on the source center with the largest  
Figure 4: The architecture of the expert discriminator. dataset. The main goal of this step is to minimize the cross-entropy loss to optimize the preliminary performance of the model, with the specific objectives described as follows:  
\[\min_{\theta_{FC},\theta_{G},\theta_{C}}\mathcal{L}_{CE} \tag{8}\]  
Step B. During this phase, the model is trained to include the data from the target center, and the detailed algorithmic process is displayed in Algorithm 1. Initially, a multicenter domain adaptation layer is implemented to reduce the gap between the target and source centers, and the Maximum Mean Discrepancy \(\mathcal{L}_{MMD}\) is calculated. Subsequently, the classification \(\mathcal{L}_{CLS}\) is calculated to independently train the expert classifiers corresponding to each source center. Additionally, the model involves training a domain discriminator expert, achieved by computing the \(\mathcal{L}_{D}\). The detailed parameter settings for each loss function will be elaborated upon in the experimental section. The goal of this section is shown in Equation (9). \[\min_{\theta_{FC},\theta_{D},\theta_{C}}(\mathcal{L}_{CLS}+\gamma\mathcal{L}_ {MMD}+\alpha\mathcal{L}_{D}) \tag{9}\]  
```
0: Data from source center 1 \(\{x_{s1},y_{s1}\}\) and source center 2 \(\{x_{s2},y_{s2}\}\); target center data \(\{x_{t}\}\) and the number of training epochs \(T\); feature extractor \(G\); expert classifiers \(\{C_{1},C_{2}\}\); multicenter domain adaptation layers \(\{FC_{1},FC_{2}\}\); domain discriminator expert \(D\). 1:for\(t=1\to T\)do
2: Extract features from multiple source domain centers and target domain images \(G(x_{s1}),\ G(x_{s2}),\ \text{and}\ G(x_{t})\) using the feature extractor \(G\). 3: Pass the common latent representations \(f_{x_{s1}}\) from the source center samples and \(f_{t}\) from the target center samples to the domain-specific feature extractor \(FC_{1}\). This process obtains the domain-specific representations for the source samples. Then, compute the \(\mathcal{L}_{MMD}\) using Equation (4) to measure the domain alignment. 4: Pass the common latent representations \(f_{x_{s2}}\) from the source center samples and \(f_{t}\) from the target center samples to the domain-specific feature extractor \(FC_{2}\). This process obtains the domain-specific representations for the source samples. Then, compute the \(\mathcal{L}_{MMD}\) using Equation (4) to measure the domain alignment. 5: Pass \(f_{x_{s1}}\) and \(f_{x_{s2}}\) through expert classifiers \(C_{1},C_{2}\), respectively, and compute \(\mathcal{L}_{cls}\) using Equation (5). 6: Pass \(f_{x_{s1}}\) and \(f_{x_{s2}}\) through expert classifier \(D\), respectively, and compute \(\mathcal{L}_{D}\) using Equation (6). 7: Minimize the loss and update the parameters of \(C_{1},C_{2},G,D,FC_{1},FC_{2}\) to optimize the model. 14:endfor Output: The label prediction \(y\)
```  
**Algorithm 1**The proposed WUCF  
In regard to the testing phase of the model, the schematic diagram is shown in Figure 2, and the testing algorithm process is presented in Algorithm 2. The plaque ultrasound images from the target center first pass through the feature extractor \(G\) to extract the deep features. The obtained feature \(f_{t}\) is then processed along three independent paths.