Exploiting feature multi-correlations for multilabel feature selection in robust multi-neighborhood fuzzy β covering space

Multilabel data contains rich label semantic information, and its data structure conforms to the cognitive laws of the actual world. However, these data usually involve many irrelevant, redundant, and noisy features, challenging constructing effective learning models. It is necessary to design a feature selection strategy to select valid information in multilabel data. Generally, constructing a robust granular space is essential for building learning methods that can capture the intrinsic information contained in data. In addition, carefully investigating the complex relationship between features facilitates the evaluation of features. However, the interactivity and complementarity between features are rarely studied for multilabel data. Fuzzy β covering constructs granular space flexibly and excavates potential uncertainty information. The concept of fuzzy β covering theory is extended to multilabel data to reasonably construct the granular space of multilabel data and effectively quantify the uncertainty of multilabel data. Concretely, a parameterized multilabel fuzzy β covering relation is proposed to resist the negative effect of ambiguity, uncertainty, and noise in multilabel data, and a robust multi-neighborhood fuzzy β covering granular space is constructed. Besides, the concept of multilabel fuzzy β covering decision is explored to improve the accuracy and robustness of multilabel learning. The above concepts build the basis of multilabel fuzzy β covering uncertainty measures, and a series of fuzzy β covering entropy measures are then defined. Consequently, feature multi-correlations are presented, including relevance, redundancy, interactivity, and complementarity between features. Finally, following the principle of correlation maximization, a robust multilabel feature selection considering feature multi-correlations (RMSMC) is designed. Extensive experiments illustrate the superiority of RMSMC over nine representative algorithms.