## 3 UA-BFET Sentiment Analysis Model
### Feature Enhancement Module
#### 3.2.2 Feature Enhancement Based on Canonical Correlation Analysis  
The feature enhancement technology based on CCA is used to enhance the correlation among the fusion features. Specifically, CCA is based on a linear combination of the two random variables. Firstly, the first pair of canonical variables \((u_{1},v_{1})\) are selected, and a group of correlation coefficients \(p(u_{1},v_{1})\) with the greatest correlation between \((u_{1},v_{1})\) is obtained. And then, the second pair of canonical variables \((u_{2},v_{2})\) in this group is selected to make the second pair of canonical variables uncorrelated with the first pair of canonical variables \((u_{1},v_{1})\). Thus, the second set of correlation coefficients \(p(u_{2},v_{2})\) with the second great correlation is calculated, and so on, until all the correlation coefficients are extracted to simplify the correlations between the original two sets of variables. As shown in Figure 3, on the basis of \(h_{t}\in R^{t_{1}\times d_{1}^{\prime}}\), \(h_{v}\in R^{t_{2}\times d_{2}^{\prime}}\) and \(h_{c}\in R^{t_{3}\times d_{3}}\) obtained in Section 3.2.1, the unimodal feature representations \(h_{t},h_{v}\) are first shared by a hard sharing strategy and combined with the obtained cross-modal fusion features \(h_{c}\). CNN is used to carry out the convolution reduction of the above three features in the time dimension to obtain the one-dimensional global features \(Vec\_h_{t}\), \(Vec\_h_{v}\), \(Vec\_h_{c}\). And then, three \(1\times 1\) convolution cores are adopted to convolve and reduce the temporal dimension of three modal features, where the input channels are \(t_{1}\), \(t_{2}\), and \(t_{3}\), respectively, and the output channel is 1, as shown in Equations (14)-(16). \[Vec\_h_{t}=Conv1D(h_{t})^{T}\in R^{t_{1}\times 1} \tag{14}\]  
\[Vec\_h_{v}=Conv1D(h_{v})^{T}\in R^{t_{2}\times 1} \tag{15}\]  
\[Vec\_h_{c}=Conv1D(h_{c})^{T}\in R^{t_{3}\times 1} \tag{16}\]  
where \(Vec\_h_{t}\), \(Vec\_h_{v}\), and \(Vec\_h_{c}\) are three one-dimensional feature vectors. Figure 3: Feature enhancement based on canonical correlation analysis. Next, the three feature vectors are cascaded into the fully connected layer for sentiment analysis, as shown in Equation (17). \[Vec\_all=Concat(Vec\_h_{t},Vec\_h_{v},Vec\_h_{c}) \tag{17}\]  
Subsequently, we calculate the canonical correlation coefficients of text features \(Vec\_h_{t}\in R^{b_{z}\times d}\) and video features \(Vec\_h_{v}\in R^{b_{z}\times d}\), where \(b_{z}\) represents the batch size during the training process. After the above two groups of features are given, two groups of neural networks \(f_{1}\), \(f_{2}\) are used to carry out nonlinear changes for \(Vec\_h_{t}\), \(Vec\_h_{v}\), respectively, as shown in Equations (18) and (19). \[Y_{h_{t}}=f_{1}(Vec\_h_{t};\theta_{1}) \tag{18}\]  
\[Y_{h_{v}}=f_{2}(Vec\_h_{v};\theta_{2}) \tag{19}\]  
where \(\theta_{1}\), \(\theta_{2}\) denotes the network parameters of \(f_{1}\), \(f_{2}\), respectively. In the following, the most suitable two groups of network parameters \(\theta_{1}\), \(\theta_{2}\) are found by training two sets of neural networks to make the network output \(Y_{h_{t}}\), \(Y_{h_{v}}\) in Equations (18) and (19) hold the maximum correlation, as shown in Equation (20). \[\theta_{1}^{*},\theta_{2}^{*}=\arg\max_{\theta_{1}\theta_{2}}\max CCA(Y_{h_{t} },Y_{h_{v}}) \tag{20}\]  
Typically, we use the backpropagation algorithm to update the network parameters of the above two networks. Assume \(M_{11}\), \(M_{22}\) is the covariance matrix of \(Y_{h_{t}}\), \(Y_{h_{v}}\), and \(M_{12}\) is the mutual covariance matrix of \(Y_{h_{t}}\), \(Y_{h_{v}}\), so the final loss function of \(CCA\) is shown in Equation (21). \[CCA\_Loss_{h_{t},h_{v}}=-trace(E^{T}E)^{\frac{1}{2}} \tag{21}\]  
where \(E=M_{11}-^{\frac{1}{2}}M_{12}M_{22}^{\frac{1}{2}}\), so that the above network parameters can update the above results and minimize the loss function.