## 3 UA-BFET Sentiment Analysis Model
### Unimodal Feature Extraction  
Although the data sequence in the unaligned data scenarios is longer and contains richer information, it is also accompanied by more redundant information. To represent unimodal features effectively, this model mainly analyzes text features and uses video features as the auxiliary for cross-modal sentiment analysis in unaligned data scenarios. As shown in the emotional feature extraction module in Figure 1, given the original text, video modalities (\(Ti\), \(Vi\)), for text modality \(Ti=(t_{i,1},\cdots,t_{i,k},\cdots,t_{i,n})\in R^{t_{1}\times d_{1}}\), where \(t_{i,k}\) represents the \(kth\) word of the article \(ith\) text. For video modality \(Vi=(v_{i,1},v_{i,2},\cdots,v_{i,k},\cdots v_{i,m})\in R^{t_{2}\times d_{2}}\), where \(v_{i,k}\) represents the \(kth\) image frame in the \(ith\) video fragment. In \(Ti\) and \(Vi\), \(t_{1}\), \(t_{2}\) represents the length of the text and video modality preprocessing features, respectively, \(d_{1}\), \(d_{2}\) represents the dimensions of the text and video modality preprocessing features, respectively, and \(R\) represents the set of real numbers. In this section, we will describe the unimodal feature extraction process, including text feature extraction and video feature extraction. (1) In the stage of text feature extraction, this model uses \(BERT\)[19] word embedding to obtain the specific vector representation of text information: \(T_{world}=BERT(Ti)\), for obtaining the different meanings of the same word in different contexts. Each word is embedded into a \(d\)-dimension word vector \(t_{world,k}\in R^{d}\), where \(d\) represents the feature dimensions of the word vector, so \(T_{world}=(t_{world,1},\cdots t_{world,k},\cdots t_{world,n})\). Then, each word embedding vector is input into the Bi-GRU to obtain a contextual text modality encoding. Both GRU and Long Short Memory (LSTM) networks can solve the problems of gradient vanishing and gradient explosion in traditional Recurrent Neural Networks (RNNs) when dealing with long sequence texts and can better capture dependencies with a larger time step distances in time series. However, the GRU has fewer tensor operations and trains faster in large data volumes [36]. Therefore, this paper selects the GRU deep learning model for text and video modality encoding. The GRU, as a variant of the LSTM, integrates input gates and forgetting gates into update gates and uses hidden states for achieving information transmission. The GRU module structure is shown in Figure 2, which only includes update gates and reset gates. Figure 2: GRU system structure. Specifically, the update process of the GRU model is shown in Equations (1)-(5). Assume that GRU accepts a word embedding vector \(t_{wordi,k}\) as input at time \(k\) and outputs a new hidden state vector \(h_{i,k}\). And the output at the previous time is denoted as \(h_{i,k-1}\). \[z_{i,k}=\sigma(W_{update}t_{wordi,k}+U_{update}h_{i,k-1}), \tag{1}\]  
\[r_{i,k}=\sigma(W_{reset}t_{wordi,k}+U_{reset}h_{i,k-1}), \tag{2}\]  
\[\widetilde{h}_{i,k}=\tanh(Wt_{wordi,k}+U_{text}(r_{i,k}\times h_{i,k-1})), \tag{3}\]  
\[h_{i,k}=(1-z_{i,k})\times h_{i,k-1}+z_{i,k}\times\widetilde{h}_{i,k}, \tag{4}\]  
\[h_{i,k}=GRU(t_{wordi,k},h_{i,k-1}) \tag{5}\]  
where \(z_{i,k}\) is the update gates and denotes whether the previous status needs to be updated; \(r_{i,k}\) is the reset gates and indicates whether the previous status needs to be reset. \(\widetilde{h}_{i,k}\) represents the hidden state vector to be selected, whose value is determined by \(r_{i,k}\). \(h_{i,k}\) is the updated hidden state calculated at the time \(i\). \(W_{update}\), \(U_{update}\), \(W_{reset}\), \(U_{reset}\), \(W\), \(U_{text}\) are the weight matrix of the corresponding feature, whose parameters are generated by the model training.