Fuzzy rough discrimination and label weighting for multi-label feature selection

Abstract

Fuzzy rough set is a theoretical framework of fuzzy uncertainty management, and discernibility matrix offers a mathematical foundation for algorithm construction of feature learning. The approaches of fuzzy rough set and discernibility matrix have been successfully applied in single-label learning. However, few works have been done on investigating the foundation of fuzzy rough discernibility matrix on multi-label data. There will be two pivotal problems to be addressed when using fuzzy rough discernibility matrix for multi-label data analysis. One is how to extract sample-level and label-level correlations; and the other is how to utilize the discernibility matrix for algorithm construction. For this reason, in this paper the fuzzy rough discrimination matrix is introduced to deal with the problem of multi-label feature selection. First, the significance of labels in the label space is captured based on the label correlation. Labels with different significances contribute to different weights for measuring the similarity between samples. Hence, a sample similarity matrix in the label space is computed based on the label weighting strategy. Then, a framework of a fuzzy decision system is formalized, in which the discernibility matrix of fuzzy rough sets is introduced as a foundation to evaluate the sample discrimination ability of features. Under the discernibility matrix criterion, a multi-label learning algorithm is developed to select discriminative features from multi-label data. A series of experimental analysis verifies the effectiveness and efficiency of the proposed method.