# Domain Discrimination Expert Weighted Network for Multi-Source Carotid Artery Plaque Classification
## 3 Materials and Methods
### Methods
#### 3.2.2 Multi-Source Domain Adaptation Module with a Domain Discrimination Expert  
In ultrasound examinations, plaque ultrasound images can be viewed in both transverse and longitudinal cuts, which necessitates special handling to unify the features from the multiple source centers in multi-source scenarios. Furthermore, plaque ultrasounds face challenges such as the imaging differences and low resolution between different centers. Inspired by MFSAN [27], this paper proposes a multi-source domain adaptation module that constructs independent classifier experts for each source domain and uses a domain discriminator to integrate the knowledge from various domain experts. The schematic diagram of the module is shown in Figure 3. This module is divided into three parts: two stages of domain alignment and a final stage of target label weighted  
Figure 2: The proposed WUCF framework. prediction. The first stage consists of two fully connected layers (FC), the second stage is composed of expert classifiers corresponding to the centers, and the third stage is formed by a domain discriminator. (1) Distribution alignment phase for specific centers  
The MADE includes two fully connected layers (FC), where the features from both the source center \(i\) and the target center are input into these layers. The distance between them is calculated to further quantify the differences. To better achieve the feature alignment in the first stage, the MADE employs the Maximum Mean Discrepancy (MMD) [28] distance as an estimate of the feature distance between different centers. MMD is a kernel two-sample test that rejects or accepts the null hypothesis \(p=q\) based on the observed samples. The fundamental idea of MMD is that if the generating distributions are the same, all the statistics are identical. Formally, MMD defines the following difference measure. The correction of noise labels is as follows:  
\[D_{\mathcal{H}}(p,q)\triangleq\parallel\mathrm{E}_{p}[\phi(\mathbf{x}^{s})]- \mathrm{E}_{q}[\phi(\mathbf{x}^{t})]\parallel\hat{\mathcal{H}} \tag{2}\]  
Here, \(\mathcal{H}\) is the reproducing kernel Hilbert space endowed with the feature kernel \(k\). The function \(\phi\) represents the feature map that projects the original samples into the reproducing kernel Hilbert space. \[\hat{D}_{\mathcal{H}}(p,q)=\left|\left|\frac{1}{n_{s}}\sum\limits_{\mathbf{x}_ {i}\in\mathcal{D}_{s}}\phi(\mathbf{x}_{i})-\frac{1}{n_{t}}\sum\limits_{ \mathbf{x}_{j}\in\mathcal{D}_{t}}\phi\big{(}\mathbf{x}_{j}\big{)}\right|\right| _{\mathcal{H}}^{2} \tag{3}\]  
where \(\hat{D}_{\mathcal{H}}(p,q)\). ishe unbiased estimate of \(D_{\mathcal{H}}(p,q)\), using Equation (3) to estimate the discrepancy between each source domain and target domain. The MMD loss is reformulated as shown in Equation (4). \[\mathcal{L}_{mmd} =\frac{1}{N}\sum\limits_{j=1}^{N}\hat{D}\big{(}H_{j}\big{(}F\big{(} X_{sj}\big{)}\big{)},H_{j}(F(X_{t}))\big{)} \tag{4}\]  
Each specific feature extractor can learn a domain-invariant representation for a particular source domain center and the target domain by minimizing Equation (4). (2) Training of expert classifiers for specific centers  
\(C\) is a multi-output network composed of expert classifiers for \(N\) specific centers, denoted as \(\big{\{}C_{j}\big{\}}_{j=1}^{N}\). Each predictor \(C_{j}\) is a softmax classifier that receives domain-invariant features processed by the feature extractor \(FC_{j}\Big{(}G\big{(}X_{i}^{j}\big{)}\Big{)}\) specific to the j-th source domain. The softmax classifier is a commonly used method that outputs the probabilities associated with each category, facilitating effective classification. Additionally, to optimize the performance of the predictors and enhance the classification accuracy, each classifier  
Figure 3: MADE module schematic diagram: (**a**) distribution alignment phase for specific centers; (**b**) training of expert classifiers for specific centers; (**c**) domain discrimination expert. employs a classification loss function based on cross-entropy.