## 4 Experiments
### Datasets and Experimental Setting
\[\text{Micro-F1}=B\left(\sum_{i=1}^{q}tp_{i},\sum_{i=1}^{q}fp_{i},\sum_{i=1}^{ q}tn_{i},\sum_{i=1}^{q}fn_{i}\right) \tag{45}\]  
where \(tp_{i}\) and \(fp_{i}\) represent each sample's true positive and false positive, respectively, and \(fn_{i}\) and \(tn_{i}\) represent the false negative and true negative. (5) Ranking loss measures the average fraction of the label pairs that an irrelevant label ranks higher than a relevant label over each instance. \[\text{Ranking Loss}=\frac{1}{m}\sum_{i=1}^{m}\frac{|SetR_{i}|}{\left|Y_{i}^ {+}\right|\left|Y_{i}^{-}\right|} \tag{46}\] \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Datasets** & **Examples** & **Features** & **Labels** & **Cardinality** & **Density** & **Domain** & **URL** \\ \hline Image & 2000 & 294 & 5 & 1.240 & 0.248 & image & URL 2 \\ Scene & 2407 & 294 & 6 & 1.074 & 0.179 & image & URL 1 \\ Yeast & 2417 & 103 & 14 & 4.237 & 0.303 & biology & URL 1 \\ Cal500 & 502 & 68 & 174 & 26.044 & 0.150 & Music & URL 1 \\ Rcv1s1 & 6000 & 944 & 101 & 2.880 & 0.029 & Text & URL 1 \\ Core116k4 & 13,837 & 500 & 162 & \(2.867\pm 0.033\) & \(0.018\pm 0.001\) & image & URL 1 \\ \hline \hline URL 1: [[http://mulan.sourceforge.net/datasets-mlc.html](http://mulan.sourceforge.net/datasets-mlc.html)]([http://mulan.sourceforge.net/datasets-mlc.html](http://mulan.sourceforge.net/datasets-mlc.html)), accessed on 8 July 2023. URL 2: [[http://palm.seu.edu.cn/zhangml](http://palm.seu.edu.cn/zhangml)]([http://palm.seu.edu.cn/zhangml](http://palm.seu.edu.cn/zhangml)), accessed on 8 July 2023. & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Statistics of the experimental datasets. (“Cardinality” indicates the average number of labels per example. “Density” normalizes the “Cardinality” by the number of possible labels. “URL” indicates the source URL of the dataset). where \(SetR_{i}=\big{\{}(p,q)\big{|}f_{p}(x_{i})\leq f_{q}(x_{i}),(p,q)\in Y_{i}^{+}\times Y _{i}^{-}\big{\}}\). Selecting the most suitable comparative algorithm based on the specific field of research and available resources can help demonstrate the effectiveness and advantages of the method proposed in this paper. We considered the most representative RANK-SVM algorithm from traditional multi label classification algorithms, and ML-KNN and CPNL algorithms from SVM's unique multi label extensions. We also looked at MLR and RBRL algorithms from the latest multi label methods. The evaluation performance of our proposed algorithm is compared with several excellent multi-label classification methods listed below. * **Rank-SVM**[19] is an adaption of the maximum margin strategy for MLC. * **ML-KNN**[20] is a multi-label delayed learning method based on the traditional K-nearest neighbor (KNN) algorithm. * **CPNL**[29] is a recent method proposed as a cost-sensitive loss function to address the issue of class imbalance and leverages correlations between negative and positive labels to improve performance. * **MLR**[30] converts MLC task into the pairwise label ranking problem. * **RBRL**[31] (robust low-rank learning) is a technique that integrates Rank-SVM and binary relevance. Additionally, the thresholding step is incorporated into the ranking learning component of Rank-SVM via binary relevance. This enables model training to occur in a single unified step, rather than sequentially.