Partial multi-label feature selection based on label matrix decomposition

In practice, each instance may be labeled with a candidate label set that contains all relevant labels and some noisy labels, which is known as the partial multi-label learning problem. Since it is difficult for existing multi-label feature selection methods to select the most discriminative features in a data set containing noisy labels, this paper proposes a partial multi-label feature selection method based on label matrix decomposition. Specifically, the method first decomposes the label matrix into two parts: the ground-truth label matrix and the noisy label matrix. Next, a low-rank restriction is applied to the ground-truth label matrix to utilize the correlation information among the ground-truth labels more efficiently; the noisy label matrix is constrained to be sparse, assuming that noise is typically sparse in practical applications. Second, graph Laplacian regularization is introduced to capture the local relevance information of the instances, thereby enabling more accurate identification of the ground-truth labels and allowing the most discriminative features to be selected. Third, a robust \(\sigma\) $\sigma$ -norm is introduced to suppress noise, thus utilizing the available label information more efficiently and improving model performance. Finally, a more flexible \(l_{2,p}\) $l_{2,p}$ -norm is chosen, which helps in better feature selection. Experiments performed on three real-world partial multi-label data sets and six synthetic multi-label data sets show the superiority of our proposed algorithm over several state-of-the-art multi-label feature selection algorithms.