## 4 Experiments
### Results under Different Noises  
To evaluate the effectiveness of our proposed approach on noisy datasets, we introduced manifold regularization matrix factorization. This enhancement enables our method to handle multi-label classification tasks even when the dataset is affected by noise interference. Figure 3: Performance of each kernel on the datasets. (**a**) Example-F1, (**b**) Micro-F1, (**c**) Hamming loss. Figure 4 presents the performance of our proposed method as well as the other comparative multi-label classification methods on salt and pepper noise induced image, scene, yeast, Rcv1s1 and Core116k4 datasets with respect to Example-F1, Micro-F1 and Hamming loss evaluation metrics. In the noise induced image and scene datasets, the proposed algorithm obtained a better performance compared to the relatively good performance achieved by RBRL and MLR algorithms. This may be attributed to the fact that, RBRL algorithm combines sorting support vector machines and binary correlation with robust low-order learning, which can achieve the effect of resisting noise to a certain extent. The MLR algorithm is systematically studied from two complementary perspectives: the consistency of learning algorithm and the generalized error bound. It can also solve the error problem caused by data corruption to a certain extent. CPNL, ML-KNN and Rank-SVM algorithms showed poor performance in image datasets with noise because they focus too much on label space and ignore the impact of noise on classifiers. In the case of the Yeast dataset without the noise, the difference in performance between the proposed method and other algorithms is not significant. This is because, these methods can still learn prominent or relevant features of the Yeast image. However, as the noise level increases, the effectiveness of our proposed method becomes increasingly obvious. Likewise, with low noise level in the Rcv1s1 and Core116k4 datasets, the evaluation performance of the proposed method compared to RBRL and MLR algorithms is not obvious, but in the case of at least 20% noise pollution, the proposed method demonstrates superior performance than other algorithms with respect to the three evaluation indicators of Example-F1, Micro-F1 and Hamming loss. This is due to the introduction of the manifold regularization matrix factorization in the proposed method, capable of finding robust low-rank subspaces in the input space to demonstrate strong robustness on high-noise datasets. Figure 5 shows the corresponding changes in the Gaussian noise on the Image, Scene, Yeast, Rcv1s1, and Core116k4 datasets with respect to the performance of Example-F1, Micro-F1, and Hamming loss evaluation metrics. In the case of the Image dataset, a trend similar to salt and pepper noise scenario was observed. Thus, the proposed algorithm, RBRL, and MLR, performed appreciably in noisy environments because all three methods consider the error problem caused by data corruption. Furthermore, due to the introduction of matrix decomposition in the algorithm proposed in this article, robust low-rank subspaces are considered in the input space. As a result, the proposed algorithm is less susceptible to Gaussian noise, hence the superior results. In the Scene and Yeast datasets, the CPNL algorithm also achieved good results, which may be attributed to its extension of BR to solve the problems of category imbalance and label correlation, making the model more robust. However, under different noise levels, our proposed algorithm still have the lowest reduction rate. The algorithm significantly decreases with increasing noise density in the Rcv1s1 and Core116k7 datasets. However, our method achieved better results than the other algorithms with respect to the evaluation metrics. This is indicative of the fact that, our proposed method has been tested on datasets with Gaussian noise and exhibits good robustness. The experimental results further demonstrate that this method can effectively improve the performance of multi label classifiers.