The rapid growth in feature dimension may introduce implicit associations between features and labels in multi-label datasets, making the relationships between features and labels increasingly complex. Moreover, existing methods often adopt low-dimensional linear decomposition to explore the associations between features and labels. However, linear decomposition struggles to capture complex nonlinear associations and may lead to misalignment between the feature space and the label space. To address these two critical challenges, we propose innovative solutions. First, we design a random walk graph that integrates feature-feature, label-label, and feature-label relationships to accurately capture nonlinear and implicit indirect associations, while optimizing the latent representations of associations between features and labels after low-rank decomposition. Second, we align the variable spaces by leveraging low-dimensional representation coefficients, while preserving the manifold structure between the original high-dimensional multi-label data and the low-dimensional representation space. Extensive experiments and ablation studies conducted on seven benchmark datasets and three representative datasets using various evaluation metrics demonstrate the superiority of the proposed method\footnote{Code: https://github.com/Heilong623/-GRW-}.

Multi-label learning poses significant challenges in extracting reliable supervisory signals from the label space. Existing approaches often employ continuous pseudo-labels to replace binary labels, improving supervisory information representation. However, these methods can introduce noise from irrelevant labels and lead to unreliable graph structures. To overcome these limitations, this study introduces a novel multi-label feature selection method called Binary Hashing and Dynamic Graph Constraint (BHDG), the first method to integrate binary hashing into multi-label learning. BHDG utilizes low-dimensional binary hashing codes as pseudo-labels to reduce noise and improve representation robustness. A dynamically constrained sample projection space is constructed based on the graph structure of these binary pseudo-labels, enhancing the reliability of the dynamic graph. To further enhance pseudo-label quality, BHDG incorporates label graph constraints and inner product minimization within the sample space. Additionally, an $l_{2,1}$-norm regularization term is added to the objective function to facilitate the feature selection process. The augmented Lagrangian multiplier (ALM) method is employed to optimize binary variables effectively. Comprehensive experiments on 10 benchmark datasets demonstrate that BHDG outperforms ten state-of-the-art methods across six evaluation metrics. BHDG achieves the highest overall performance ranking, surpassing the next-best method by an average of at least 2.7 ranks per metric, underscoring its effectiveness and robustness in multi-label feature selection.

In the last decade, embedded multi-label feature selection methods, incorporating the search for feature subsets into model optimization, have attracted considerable attention in accurately evaluating the importance of features in multi-label classification tasks. Nevertheless, the state-of-the-art embedded multi-label feature selection algorithms based on least square regression usually cannot preserve sufficient discriminative information in multi-label data. To tackle the aforementioned challenge, a novel embedded multi-label feature selection method, termed global redundancy and relevance optimization in orthogonal regression (GRROOR), is proposed to facilitate the multi-label feature selection. The method employs orthogonal regression with feature weighting to retain sufficient statistical and structural information related to local label correlations of the multi-label data in the feature learning process. Additionally, both global feature redundancy and global label relevancy information have been considered in the orthogonal regression model, which could contribute to the search for discriminative and non-redundant feature subsets in the multi-label data. The cost function of GRROOR is an unbalanced orthogonal Procrustes problem on the Stiefel manifold. A simple yet effective scheme is utilized to obtain an optimal solution. Extensive experimental results on ten multi-label data sets demonstrate the effectiveness of GRROOR.