Coordinate descent for top-k multi-label feature selection with pseudo-label learning and manifold learning

Multi-label learning plays an increasingly important role in handling complex problems where data instances are associated with multiple labels. However, current methods face significant limitations when dealing with high-dimensional feature spaces. They struggle to preserve the geometric structure among features while failing to fully exploit the latent correlations between labels. To address these key challenges, this paper proposes a novel feature selection method called coordinate descent for top-k multi-label feature selection with pseudo-label learning and manifold learning (CD-MPL), which integrates manifold learning with pseudo-label learning techniques. First, by constructing a feature graph Laplacian matrix, we establish a mathematical representation of the feature manifold structure, effectively preserving the local geometric properties of the feature space. Second, we introduce a pseudo-label learning mechanism, converting discrete binary labels into continuous representations to better model complex label correlations. Notably, to tackle the non-convex optimization problem caused by the ${\ell }_{2,0}$-norm constraint, we innovatively transform the original problem into the joint optimization of a continuous matrix and a discrete selection matrix. We then employ a coordinate descent (CD) method to efficiently solve the selection matrix, overcoming the non-convexity issue while enhancing model performance, interpretability, and practicality. Experimental results on ten multi-label datasets demonstrate that CD-MPL significantly outperforms existing methods across multiple key evaluation metrics, achieving an average performance improvement of 3.31 %. The algorithm maintains stable performance even with reduced feature subsets and exhibits rapid convergence within 10 iterations, fully validating its efficiency and effectiveness in multi-label classification tasks.