## 4 Experimental Analysis
### Parameter Analysis  
For the multi-channel self-attention mechanism module described in this paper, the channel dimension N of the multi-channel self-attention feature map is a key parameter. When the number of self-attention weight channels is low, it may be difficult to provide enough attention information, affecting the results of fine-grained image recognition. When there are many self-attention weight channels, the network parameters increase and so does the complexity of the network. Simultaneously, the dimension of the image representation vector output after attention increases. It is difficult to obtain a compact image representation. We analyzed the Kappa coefficient of fine-grained image recognition obtained by training in dataset 1 when the number of channels in the self-attention weight map increased as follows: 4, 8, 16, 32 and 64. The analysis results are shown in Table 1.  
It shows in Table 1 that there was a huge difference in the Kappa coefficient when the number of attention channels was 4 and 8. This suggests that the self-attention weight feature did not provide enough information, which had a great impact on the accuracy of fine-grained image recognition. When the number of channels of the self-attention weight map was greater than 16, the Kappa coefficients were relatively close, which means that, after the number of channels of the self-attention weight map exceeded 16, the multi-channel self-attention mechanism model in this method contained sufficient self-attention information; therefore, it can improve the precision of fine-grained image recognition. The experimental results also suggest that a good balance between the recognition accuracy and model complexity could be achieved when the number of attention weight map channels was 16 or 32. When designing the AM-softmax loss function, this method includes two superparameters \(\gamma\) and \(\epsilon\). In this paper, we conducted a superparameter sensitivity experiment on dataset 1, and used the Kappa coefficient as the evaluation criterion. The specific steps are described as follows:  
(1) Train softmax classifier \(L_{1,l}\) on the training set using the extracted feature vectors and corresponding labels. (2) As needed, the center loss \(L_{2}\) and attention weakening loss function \(L_{3}\) can be added to the overall loss function \(L_{1}^{\prime}\) to increase the similarity between features and class centers. (3) Set the hyperparameter range: set the hyperparameter to an equidistant value between 0.1 and 1 in the experiment. (4) Set up training and validation process: Divide dataset 1 into training and validation sets. During the training process, the AM-softmax loss function is used as the optimization objective, and the values of hyperparameters are adjusted. In each training iteration, calculate the loss function based on the current hyperparameter settings and update the parameters. (5) Evaluation indicator selection: use the Kappa coefficient as the evaluation criterion to measure the performance of fine-grained image recognition. (6) Conduct hyperparameter sensitivity experiments: Train and validate each combination based on the set hyperparameter range, and record the \begin{table}
\begin{tabular}{c c c} \hline \hline
**Number of Channels** & **Kappa Coefficient** & **Computational Cost/ms** \\ \hline
4 & 0.75 & 15 \\
8 & 0.95 & 32 \\
16 & 0.96 & 58 \\
32 & 0.97 & 77 \\
64 & 0.98 & 103 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Results of Kappa coefficient analysis for fine-grained image recognition with different channel number of self-attention weight graph. corresponding Kappa coefficients. Repeat multiple experiments to obtain multiple sets of Kappa coefficients with different combinations of hyperparameters. (7) Draw hyperparameter sensitivity analysis curve: Based on the experimental results, draw a hyperparameter sensitivity analysis graph (i.e., Figure 1). The horizontal axis represents the values of hyperparameters and the vertical axis represents the corresponding Kappa coefficients.