Feature selection for classification with Spearman's rank correlation coefficient-based self-information in divergence-based fuzzy rough sets

Feature selection facilitates uncertainty disposal and information mining, and it has received widespread research interests. Divergence-based fuzzy rough sets (Div-FRSs), a new kind of fuzzy rough sets, have been applied to feature selection and induced two efficient algorithms, FS-AFS and FS-RFS. Nevertheless, FS-AFS and FS-RFS still have advancement space, because the dependency functions only focus on lower approximation and ignore the uncertainty in upper approximation, which will certainly undermine the algorithmic evaluation effects. To this end, this paper introduces the upper approximation and fuses it with lower approximation via class-specific pattern and Spearman coefficient to construct a new information measurement for metric perfection, called Spearman-based self-information. Relying on this new measurement, a novel feature selection algorithm SPESI is established to improve FS-AFS and FS-RFS. At first, Spearman coefficient is introduced and upper approximation is defined. Second, class-driven precision and roughness are built by incorporating Spearman coefficient-based class-specific weight vectors with class-driven lower and upper approximations. Meanwhile, the granulation monotonicity of newly-defined measurements is also explored. Then, the core measurement Spearman-based self-information is firstly given and its feature significance motivates a feature selection algorithm SPESI with heuristic search. Finally, data experiments are implemented to validate the effectiveness of SPESI, and a conclusion can be drawn that SPESI outperforms FS-AFS and FS-RFS to acquire better classification performances with fewer feature numbers and less running time.