# Establishing Two-Dimensional Dependencies for Multi-Label Image Classification
## 4 Experiments
### Experimental Results
#### 4.4.2 Statistical Significance Experiment  
To demonstrate that our data were significantly superior to the other groups, we first used the Wilcoxon signed-rank test to check if there was a significant statistical difference between our data and the other groups. The Wilcoxon signed-rank test is a non-parametric method thaat is used to compare two related samples. It involves calculating the differences between data pairs, ranking the absolute differences, assigning signs based on the direction, and then calculating the positive and negative rank sums. The \(p\)-value is derived from comparing the rank sums, and if it is below the significance level (typically 0.05), a significant difference is indicated. The PASCAL VOC 2007 dataset was utilized for validation, wherein the results of 13 comparison methods were assessed for significance against those of the method. The Wilcoxon signed-rank test was employed to analyze the significance, with the results depicted in Table 4. Notably, all \(p\)-values were found to be less than the significance threshold (a = 0.05). This indicates that the results of our model showed a significant difference compared to the results of the other 13 models. Secondly, we further compared the mean values (i.e., mAP) of each group to determine which group performed better in terms of numerical value. It was clear that our model had a higher mAP compared to the other 13 models (see Table 1), indicating that the performance of our model is superior to the other groups. Taken together, these two points demonstrate that our method is statistically superior to other methods, and the advantages over different comparison methods are not coincidental, but rather stable and consistent. In addition, we calculated the 95% confidence intervals for the mean differences. The calcul  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Methods**} & \multicolumn{8}{c}{**ALL**} & \multicolumn{8}{c}{**TOP-3**} \\ \cline{2-13}  & **mAP** & **CP** & **CR** & **CF1** & **OP** & **OR** & **OF1** & **CP** & **CR** & **CF1** & **OP** & **OR** & **OF1** \\ \hline CNN-RNN [39] & 61.2 & - & - & - & - & - & - & 66.0 & 55.6 & 66.4 & 69.2 & 66.4 & 67.8 \\ SRN [40] & 77.1 & 81.6 & 65.4 & 71.2 & 82.7 & 69.9 & 75.8 & 85.2 & 58.8 & 67.4 & 87.4 & 62.5 & 72.9 \\ ResNet-101 [26] & 77.3 & 80.2 & 66.7 & 72.8 & 83.9 & 70.8 & 76.8 & 84.1 & 59.4 & 69.7 & 89.1 & 62.8 & 73.6 \\ ML-GCN [12] & 83.0 & 85.1 & 72.0 & 78.0 & 85.8 & 75.4 & 80.3 & 89.2 & 64.1 & 74.6 & 90.5 & 66.5 & 76.7 \\ GCN-MS-SGA [13] & 83.4 & 85.1 & 71.6 & 77.8 & 84.0 & 75.0 & 79.3 & 88.8 & 63.4 & 75.7 & 88.8 & 66.0 & 75.7 \\ MCAR [10] & 83.8 & 85.0 & 72.1 & 78.0 & 88.0 & 73.9 & 80.3 & 88.1 & 65.5 & 75.1 & **91.0** & 66.3 & 76.7 \\ CFMIC [18] & 83.8 & **85.8** & 72.7 & 78.7 & 86.3 & 76.3 & 81.0 & **89.7** & 64.5 & 75.0 & 90.7 & 67.3 & 77.3 \\ LGR [49] & 83.9 & 85.0 & 73.3 & 78.7 & 86.2 & 76.4 & 81.0 & 89.0 & 64.8 & 75.0 & 90.7 & 67.0 & 77.1 \\ FLNet [53] & 84.1 & 84.9 & 73.9 & 79.0 & 85.5 & 77.4 & 81.1 & 89.0 & 65.2 & 75.2 & 90.4 & 67.5 & 77.3 \\ LGLM [56] & 84.2 & 85.7 & 72.8 & 78.7 & 86.6 & 76.7 & 81.3 & 89.4 & 64.7 & 75.0 & 90.7 & 67.4 & 77.3 \\ STMG [57] & 84.3 & **85.8** & 72.7 & 78.7 & **86.7** & 76.8 & 81.5 & 89.3 & 64.8 & 75.1 & 90.8 & 67.4 & 77.4 \\ Ours & **85.2** & 84.1 & **75.9** & **79.8** & 85.2 & **78.7** & **81.8** & 88.7 & **66.5** & **76.0** & 90.5 & **68.1** & **77.7** \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparisons with state-of-the-art methods on the MS-COCO dataset.  
intervals was based on the results of multiple independent experiments, which can more comprehensively reflect the stability of the model's performance. The experimental results indicate that the differences were statistically significant, and the estimation precision was high. By introducing confidence intervals, we were able to more intuitively assess the variability of the model's performance, thereby enhancing the credibility and scientific rigor of the conclusions.