Matrix factorization algorithm for multi-label learning with missing labels based on fuzzy rough set

In multi-label learning, samples of practical classification task may associated with multiple labels, it is challenging to acquire all labels of the training samples, the rapid expansion of the label space and the significant increase in annotation costs have exacerbated the issue of missing labels in multi-label learning. By utilizing the low rank structure of the label matrix, missing labels can be effectively recovered with matrix factorization technique. Nevertheless, current approaches disregard the potential correlation between the feature space and the multi-dimensional label data. In this paper, key features associated to different labels are extracted and then a non-negative matrix factorization algorithm is proposed for recover missing labels. Firstly, the fuzzy rough set theory is used to analyze the consistency between label matrix and feature space, potential feature information is employed to determine the latent variable dimension in non-negative matrix decomposition and the symbolic label matrix is also converted to a numerical one by means of the lower approximation operator. Then, feature-based manifold regularization and local label correlations are used to model the multi-label completion algorithm. In order to verify the effectiveness in dealing incomplete label data, comparison experiments with varying levels of missing values are designed, the experiments show that compared with the state-of-the-art algorithm, the proposed algorithm is effective in the completion of missing labels. In addition, the sensitivity analysis experiments also show that the proposed method has good stability.