Partial Multi-label Learning Based on Shared Subspace Representation

Partial Multi-Label Learning (PML) is a weakly supervised learning framework in which each instance is associated with a set of candidate labels, among which only a subset are correct. The presence of noisy labels in the candidate set poses significant challenges for accurate classification and effective feature selection. Existing methods often overlook either the noise in the feature space or the structural relationships within the label space, limiting their robustness and generalizability. In this paper, we propose a novel PML approach based on Shared Subspace Representation, which jointly learns a low-dimensional latent space for both feature and label information. Our method decomposes the noisy candidate label matrix into a low-rank ground-truth label component and a sparse noise component, leveraging the inherent structure and sparsity of label noise. Simultaneously, a feature correlation matrix maps original features into a compact subspace, enhancing discriminative power while mitigating the impact of feature noise. To preserve the geometric structure of the data, manifold regularization is incorporated via a graph Laplacian constructed from the feature space, enforcing local consistency between similar instances. We formulate the overall objective as a unified optimization problem, which is efficiently solved using block coordinate descent and gradient-based methods. Extensive experiments on benchmark datasets demonstrate that our approach outperforms state-of-the-art methods in both label recovery and feature selection, confirming the effectiveness of shared subspace modeling in partial multi-label learning.