Instance-Dependent Incomplete Multi-Label Feature Selection by Fuzzy Tolerance Relation and Fuzzy Mutual Implication Granularity

Multi-label feature selection is an effective approach to mitigate the high-dimensional feature problem in multi-label learning. Most existing multi-label feature selection methods either assume that the data is complete, or that either the features or the labels are incomplete. So far, there are few studies on multi-label data with missing features and labels. In many cases, missing features in instances of multi-label data often lead to missing labels, which is ignored by existing studies. We define this type of data as instance-dependent incomplete multi-label data. In this paper, we propose a feature selection method for instance-dependent incomplete multi-label data. Firstly, we use the positive correlations between features to reconstruct the feature space, thereby recovering missing values and enhancing non-missing values. Secondly, we use fuzzy tolerance relation to guide label recovery, and utilize fuzzy mutual implication granularity to impose structural constraint on the projection matrix. Thirdly, we achieve feature selection by eliminating the impact of incomplete instances and imposing sparse regularization on the projection matrix. Finally, we provide a convergent solution for the proposed feature selection framework. Comparative experiments with existing multi-label feature selection methods show that our method can perform effective feature selection on instance-dependent incomplete multi-label data.