Multi-label feature selection via label relaxation

Multi-label feature selection (MFS) has emerged as a prevalent strategy to manage high-dimensional multi-label data. Most existing methods assume that the rigid binary label matrix can perfectly fit the pseudo-label matrix during the learning process, so as to preserve the structural information in raw data. However, the original label space with the limited freedom makes it challenging to accurately convert to the pseudo-label matrix. Additionally, most methods utilize different matrix to explore structural information, and ignore the connection of structural information. To tackle these problems, a novel method named multi-label feature selection via label relaxation (LRMFS) is proposed. LRMFS designs a label relaxation regression to transform the rigid binary label matrix into a slack variable matrix, allowing for a more flexible fitting relationship. By leveraging this flexible fitting, LRMFS decomposes the feature selection matrix to a structured subspace, which can learn the graph structures of both features and labels by graph Laplacian. These properties of LRMFS are converted to an objective function, and we further develop an alternative solution for the function optimization. Comparative experiments show that LRMFS exhibits superior performance than eight MFS methods on twelve multi-label data sets.