Double-quantitative feature selection using bidirectional three-level dependency measurements in divergence-based fuzzy rough sets

Abstract

Feature selection benefits machine learning and knowledge acquisition, and it usually resorts to various intelligent methodologies. Fuzzy rough sets act as a powerful platform of intelligent processing, and they have introduced divergence measures to generate an effective method of feature selection, called FS-DD. However, Algorithm FS-DD still has advancement space, because its underlying dependency degree with absoluteness lacks decision-categorical manifestations and exhibits loose informatization. Within the framework of divergence-based fuzzy rough sets (Div-FRSs), we implement bidirectional three-level dependency measurements to establish double-quantitative feature selection, and two novel approaches of feature selection (i.e., Algorithms FS-AFS and FS-RFS) are designed to reconstruct and improve current Algorithm FS-DD. Based on divergence and lower-approximation matrices, we first make three-level measurements in vertical and horizontal directions, and correspondingly generate absolute and relative dependency degrees. Then, double-quantitative dependency degrees naturally induce double-quantitative feature significances, and the two types of uncertainty measures respectively exhibit granulation monotonicity and non-monotonicity. Furthermore, double-quantitative feature significances are utilized to motivate double-quantitative selection algorithms, i.e., absolute FS-AFS and relative FS-RFS. Finally, measurement properties and selection algorithms are fully validated by table examples and data experiments. This study systematically reveals hierarchical constructions and quantitative characteristics of dependency measurements in Div-FRSs, and the relative measures effectively extract class-specific and condensed information. For related selection algorithms, FS-AFS interprets existing FS-DD, while new FS-RFS outperforms the two to acquire better classification performances, as experimentally verified.