## 3 UA-BFET Sentiment Analysis Model
### Feature Enhancement Module
#### 3.2.1 Cyclic Memory Enhancement Network across Time Steps  
In the feature enhancement module, this study designs a cyclic memory enhancement network across time steps. The basic idea is to use the Bi-GRU system to encode unimodal so that the unimodal features can constantly approach the important words over time. At the time step \(t\), \(h_{m}^{[t-1,t]}(m\in\{t,v\})\) denotes the receiving text and video features across two consecutive time steps. First, text features \(h_{i}^{[t-1,t]}\) and video features \(h_{v}^{[t-1,t]}\) across two continuous time steps obtained by the Bi-GRU system are used as the inputs of the cross-modal hierarchical attention module to obtain the gradually enhanced cross-modal fusion features \(h_{c}\in R^{l_{3}\times d_{3}}\) between text and video features, where \(d_{3}\) is the feature dimensions of the cross-modal fusion features. Second, the cross-modal fusion features are input into the _Bi-GRU_ system at the next time step to update unimodal feature representation. The calculation process is shown in Equation (8):  
\[\alpha_{word}^{[t+1]}=Bi-GRU_{update}(h_{c};\alpha_{word}^{[1:t]}) \tag{8}\]  
where \([t+1]\) and [1:\(t\)] represent time \(t+1\) from the initial time to time t, respectively. \(\alpha_{word}^{[t+1]}\) represents the attention weight of the word obtained from the cross-modal fusion feature \(h_{c}\) at the next time step, \(t+1\), which is inferred from the attention weight \(\alpha_{word}^{[1:t]}\) previously assigned from the initial time to the time \(t\). This denotes that the attention weight of the word at the next time step depends on the influence of the previous cross-modal fusion features on the word. To fully encapsulate these dependencies, the process of attention allocation is executed in a cyclic manner by using the Bi-GRU. And \(m_{t}\), \(m_{v}\) represent the memory of the Bi-GRU system for text and video modalities, respectively. When \(t=0\), the initial memory of the Bi-GRU system for text modality is expressed as \(h_{t}^{[0]}\), and the network \(M\) is used to map \(h_{t}\) to the Bi-GRU memory space, as shown in Equation (9):  
\[h_{t}^{[0]}=M(h_{t};\Theta) \tag{9}\]  
The specific intra-modal representation \(h_{t}\) can be dynamically adjusted by the Bi-GRU's memory mechanism. Since the emotional information and intensity of each word in a sentence are not equal, the model added an additive attention mechanism to highlight the emotional weight of words with different levels of importance in the text. It results that the cross-modal fusion features of different time steps output by the Bi-GRU system are activated by the Softmax function. An attention weight of each word \(\alpha_{word}^{[t+1]}\) contained in the sentence is produced, as shown in Equation (11):  
\[c_{i,k}=U_{hidden}^{T}\tan\ h(W_{hidden}h_{c}^{[1:t]}+b_{hidden}) \tag{10}\]  
\[\alpha_{word}^{[t+1]}=\frac{\exp(c_{i,k})}{\sum\limits_{j=0}^{n}\exp(c_{i,k})} \tag{11}\]  
where \(c_{ijk}\) is the attention value calculated by the model and represents the emotional weight of cross-modal fusion features \(h_{c}^{[1-t]}\) in the sentence from the beginning time to time \(t\). The weight matrix \(W_{hidden}\) and bias vector \(b_{hidden}\) are used to map \(h_{c}^{[1:t]}\) to the attention space and then multiply the projection with the context vector \(U_{hidden}\). Next, the importance of the word at time \(t+1\) in the text is denoted by multiplying the attention weight \(\alpha_{word}^{[t+1]}\) with the cascaded intra-modality representation \(h_{t}\) element by element, as shown in Equation (12):  
\[\widetilde{h}_{t}^{[t+1]}=h_{ijk}^{word}\odot\alpha_{word}^{[t+1]} \tag{12}\]  
where \(\odot\) represents the Hadamard product and \(\widetilde{h}_{t}^{[t+1]}\) denotes the text features participating in the cyclic memory enhancement network across time steps at time \(t+1\). After obtaining the text features with weights at time \(t+1\), it is integrated with the text features \(h_{t}\) cascaded at previous moments.