# DualCascadeTSF-MobileNetV2: A Lightweight Violence Behavior Recognition Model
## 3 Methods
### DualCascadeTSF Module  
Based on the concept mentioned above, this paper proposes a module, the Dual Cascade Temporal Shift and Fusion (DualCascadeTSF) module. As shown in Figure 3, this is the structural diagram of the Dual Cascade TSF module. The design of this module inherits the core idea of the TSM, which involves shifting the temporal positions of video frame channels to alter the manner of convolution operations, thereby improving computational efficiency. Building on this foundation, the DualCascadeTSF module further introduces a feature fusion mechanism that merges feature maps at the same temporal position during each temporal shift. This enhances the model's ability to extract longer-term information. As shown in Figure 4, the working principle of the DualCascadeTSF module is illustrated. Stage 1 represents the original input video stream, where each column corresponds to a channel, and each row represents a frame. In this figure, we assume that it has four frames and six channels. Stage 2 involves the first temporal shift, where one channel is shifted forward in time while another channel is shifted backward. Stage 3 shows the feature fusion of the original input video stream with the shifted video stream after the first temporal shift. Stage 4 involves a second temporal shift after the first feature fusion. Stage 5 shows the feature fusion of the original input video stream with the shifted video stream after the second temporal shift. At this point, the DualCascadeTSF module completes its entire operation. It can be seen from the figure that the working principle of the DualCascadeTSF module is very simple and does not introduce significant additional parameters. Figure 3: The structure of the DualCascadeTSF module. After intuitively presenting the working principle of the module in the form of diagrams, this paper further explains the ingenuity of the module's design from a mathematical perspective. Suppose that there are a \(1\times 3\) convolution kernel \(W=(\omega_{1},\omega_{2},\omega_{3})\) and a 3-channel infinitely long video stream \(X^{k}_{n\times 3}=(X_{i-k,j},X_{i,j},X_{i+k,j})\in\mathbb{R}^{n\times 3},(n=\infty)\), where \(k\) represents the number of temporal shifts, \(i\) represents the position of the time step in the video stream, \(j\) represents the position of the channel in the video stream, and \(n\) represents the number of frames in the input video stream. After one temporal shift, the video stream becomes \(X^{1}_{n\times 3}=(X_{i-1,j},X_{i2},X_{i+1,j})\in\mathbb{R}^{n\times 3},(n=\infty)\), and then the convolution operation is performed:  
\[y^{1}_{i}=\omega_{1}x_{i-1,1}+\omega_{2}x_{i,2}+\omega_{3}x_{i+1,3} \tag{4}\]  
\[Y^{1}=\sum_{j=1}^{3}(\omega_{j}x_{i-1,j},\omega_{j}x_{i,j},\omega_{j}x_{i+1,j}) \tag{5}\]  
where \(y^{1}_{i}\) represents the process of the first convolution operation, and \(Y^{1}\) represents the calculation result. After the first temporal shift, feature fusion is performed:  
\[X^{1^{\prime}}=X^{0}\pm X^{1}M \tag{6}\]  
where \(X^{1^{\prime}}\) represents the feature values of the infinitely long video stream after the first feature fusion, \(M\) is the \( \begin{bmatrix}1&1&1\\ 0&0&0\\ 0&0&0\end{bmatrix} \) matrix, which is used to extract the columns that have undergone temporal shifting in \(X^{1}\), namely the feature values in columns 1 and 3. At this point, \(X^{1^{\prime}}\) is  
\[X^{1^{\prime}}=(x_{i,1}\pm\omega_{1}x_{i-1,1},x_{i,2},x_{i,3}\pm\omega_{3}x_{i -1,3})_{n\times 3} \tag{7}\]  
After completing the first temporal shift and feature fusion, the second temporal shift is then performed:  
\[y^{2}_{i}=\omega_{1}(x_{i-1,1}\pm\omega_{1}x_{i-2,1})+\omega_{2}x_{i,2}+\omega _{3}(x_{i+1,3}\pm\omega_{3}x_{i+2,3}) \tag{8}\]  
\[Y^{2}=\sum_{j=1}^{3}\bigl{[}\omega_{j}(x_{i-1,j}\pm\omega_{j}x_{i-2,j})+\omega _{j}x_{i,j}+\omega_{j}(x_{i+1,j}\pm\omega_{j}x_{i+2,j})\bigr{]} \tag{9}\]  
Figure 4: The working principle of the DualCascadeTSF module.