## 4 Experiments
### Datasets and Experimental Setting  
**Datasets description:** To evaluate the performance of our proposed method, we selected several multi-label data sets in different scenarios in the real world for experiments. Table 1 summarizes the details of the selected multi-label data sets comprising multiple data containing multi-variable characteristics and labels. Therefore, they are a group of rather complex data, resulting in increased computational complexity in the learning process. * **Image** contains 2000 samples from the image domain, and these samples have 5 labels. * **Scene** contains 2407 samples from the image domain, and these samples have 6 labels. * **Yeast** contains 2417 samples from the biology domain, and these samples have 14 labels. * **Cal500** contains 502 samples from the music domain, and these samples have 174 labels. * **Rcv1s1** contains 6000 samples from the text domain, and these samples have 101 labels. * **Core116k4** contains 13,837 samples from the image domain, and these samples have 162 labels. **Evaluation metrics:** In evaluating the performance of multi-label classification learning methods, the correlation between multiple labels for each instance must be considered. This makes the evaluation of muti-label classification cumbersome compared to traditional single-label classification. The evaluation methods used in current classification learning tasks can be categorized into sample-based and label-based measurements. The label-based indicators are designed to calculate the metrics for each individual label and then aggregate them to obtain the overall label indicators using either macro or micro averaging techniques. In addition, in multi-label classification learning, the measure of evaluation by each instance is generally used. The multi-label classification algorithm mainly calculates the inconsistent ratio between the predicted label and the actual label of each instance. Then the evaluation is performed with metrics such as Hamming loss, accuracy, F1 measure, ranking loss, etc. In this paper, we used the following five evaluation metrics for the multi-label learning classification. Given a test set \(D=\{(X_{i},Y_{i}),1\leq i\leq m\}\), where \(Y\) represents the label datasets of dimension \(q\) and \(X\) represents the instance datasets of dimension \(p\). (1) Hamming loss quantifies the proportion of example-label pairs that are misclassified. \[\text{Hammingloss}=\frac{1}{m}\sum_{i=1}^{m}\frac{|h(X_{i})\Delta Y_{i}|}{q} \tag{42}\]  
where \(\Delta\) denotes the symmetric difference between two sets. \(h(X_{i})\) represents the trained predictive function that generates a set of predictive labels based on the value of \(X_{i}\). Therefore, a lower Hamming loss value indicates a higher degree of similarity between the predicted and actual values, signifying improved classifier performance. (2) Subset accuracy measures the fraction that the predicted label subset and the ground-truth label subset are the same. \[\text{Subset Accuracy}=\frac{1}{m}\sum_{i=1}^{m}\left[h(X_{i})=Y_{i}\right] \tag{43}\]  
(3) Example-F1 is the average F1 measure that is the harmonic mean of recall and precision over each instance. \[\text{Example-F1}=\frac{1}{m}\sum_{i=1}^{m}\frac{2|P_{i}^{+}\cap Y_{i}^{+}|}{ \left|P_{i}^{+}\right|+\left|Y_{i}^{+}\right|} \tag{44}\]  
where \(Y_{i}^{+}\)(or \(Y_{i}^{-}\)) represents the index set of the ground-truth relevant (or irrelevant) labels associated with \(X_{i}\), and \(P_{i}^{+}\)(or \(P_{i}^{-}\)) denotes the index set of the predicted relevant (or irrelevant) labels associated with \(X_{i}\). (4) Micro-F1 is an indicator used to measure the accuracy of multivariate classification learning. It first averages the element values corresponding to each confusion matrix, yields the TP, FP, TN, and FN, and then calculates the micro-precision and micro-recall.