Robust Ranking Kernel Support Vector Machine via Manifold Regularized Matrix Factorization for Multi-Label Classification  
Hepping [PERSON]  
1 School of Computer Science and Communication Engineering, Jiangsu University, Zhenjiang 212013, China; [EMAIL_ADDRESS] (H.S.) [PERSON]  
1 School of Computer Science and Communication Engineering, Jiangsu University, Zhenjiang 212013, China; [EMAIL_ADDRESS] (H.S.) [PERSON]  
1 School of Computer Science and Communication Engineering, Jiangsu University, Zhenjiang 212013, China; [EMAIL_ADDRESS] (H.S.) [PERSON]  
1 School of Computer Science and Communication Engineering, Jiangsu University, Zhenjiang 212013, China; [EMAIL_ADDRESS] (H.S.) [PERSON]  
1 School of Computer Science and Communication Engineering, Jiangsu University, Zhenjiang 212013, China; [EMAIL_ADDRESS] (H.S.) Footnote 1: [[https://www.mdpi.com/journal/applsci](https://www.mdpi.com/journal/applsci)]([https://www.mdpi.com/journal/applsci](https://www.mdpi.com/journal/applsci))  
Footnote 2: [[https://www.mdpi.com/journals/](https://www.mdpi.com/journals/)]([https://www.mdpi.com/journals/](https://www.mdpi.com/journals/))  
machine (Rank-SVM) minimizes the pairwise approximate ranking loss, thereby addressing the second aspect of the class-imbalance issue in multi-label classification. This approach effectively mitigates the negative impact of class imbalance. However, apart from the class imbalance problem, there are additional challenges related to noise in multi-label classification. Data corruption and loss in high-dimensional datasets often lead to noise, which can significantly degrade the performance of multi-label classifiers. Consequently, several studies have proposed effective noise reduction methods. For instance, [PERSON] et al. [13] addressed missing labels in image annotation by improving the consistency between predicted and provided labels to enhance the model. Similarly, [PERSON] et al. [14] utilized a ramp loss to mitigate extreme penalties from incorrect-labels and learned a more resilient loss function. However, majority of multi-label classification methods primarily focus on noise within the label space, neglecting the presence of noise in the input feature space. Manifold regularization matrix factorization is a technique employed to address noise in the input space. Though matrix factorization [15] can effectively solve the problem of image noise, its extensive focus on the global structure of the data while ignoring the local structural features between samples negatively affect its robustness when dealing with complex data. Manifold learning [16] is introduced to adaptively learn local structural features within samples from low rank representations obtained from matrix factorization, ultimately obtaining the most robust low rank representation. This robust low order representation has better robustness when dealing with complex data. However, the features and classifiers selected through manifold regularization matrix factorization are independent of each other, resulting in suboptimal low-rank representation for multi-label classifiers. Additionally, most of these low-rank methods are linear models, limiting their ability to capture the intricate nonlinear relationship between input and output. To address these challenges, we present a novel multi-label classification model that integrates manifold regularization matrix factorization and a multi-label classifier within a unified framework. We adopt a joint learning approach to simultaneously learn feature selection and classifier parameters. Through joint optimization, optimal features are selected, resulting in a superior joint learning framework that outperforms individual model predictions. This joint framework effectively determines the optimal low-rank representation, leading to improved classification performance in high-noise data scenarios. Furthermore, the proposed unified framework is transformed via kernel function to incorporate a nonlinear multi-label classifier.