Feature selection for multilabel classification with missing labels via multi-scale fusion fuzzy uncertainty measures

Numerous high-dimension multilabel data are generated, posing a challenge for multilabel learning. Building effective learning models with discriminative features is essential to improve the performance of multilabel learning. Multilabel feature selection can filter out the discriminative features according to their contribution to classification. However, ambiguity, uncertainty, and missing labels coexist in real-life multilabel data, which brings adverse effects to multilabel feature selection. The multi-scale fuzzy rough set gives an effective way to mine intrinsic knowledge hidden in uncertain data. This paper first extends the multi-scale learning to multilabel data with missing labels and proposes a feature selection method for multilabel classification with missing labels via multi-scale fusion fuzzy uncertainty measures called FSMML. The missing label space construction and feature evaluation metric are carefully investigated in the framework of multi-scale learning. A multilabel multi-scale learning strategy is formalized with the fuzzy granularity cognitive mechanism as the core, and the multi-scale fusion fuzzy label learning is given to reconstruct the missing label space. Then, a novel multilabel multi-scale fuzzy rough sets with missing labels is developed, and the significance of each scale is quantified. Moreover, some multi-scale fusion fuzzy uncertainty measures are defined by capturing the sample fuzzy similarity in the feature and reconstructed label spaces. Accordingly, the relevance between features and label set and the interactivity and redundancy between features in feature evaluation are discussed. Finally, FSMML chooses high-quality features to maximize relevance and interactivity and minimize redundancy. Extensive experiments demonstrate the effectiveness of FSMML on fifteen datasets with missing labels.