SMT-DL: A semi-supervised multi-task learning framework based on dictionary learning for robust feature sharing

Multi-task learning (MTL) leverages shared representations across related tasks, facilitating the utilization of latent data information and enhancing classification performance. In complex learning scenarios, two major challenges frequently arise: limited labeled data and inefficient cross-task knowledge transfer. To address these issues, we propose a semi-supervised multi-task learning (SMT-DL) method based on dictionary learning. Specifically, we establish a dual dictionary architecture by innovatively combining dictionary learning with a multi-task coordination mechanism: (1) a semi-supervised synthetic dictionary that jointly reconstructs labeled and unlabeled data to capture potential cross-task features, and (2) an analytical dictionary that aligns sparse representations with discriminative decision boundaries. The framework incorporates three technical innovations: a block sparse regularization scheme that enforces feature sharing across tasks, a dual-space reconstruction mechanism that separates task-specific and shared representations, and a cross-task support vector synchronization strategy. In addition, we rigorously demonstrate the convergence of the proposed optimization algorithm. Extensive experimental results validate that the proposed SMT-DL approach outperforms existing methods in terms of robustness and classification performance.