Feature selections based on uncertainty measurements from dual-quantitative improvement and double-hierarchical fusion

Abstract

Feature selections promote classification learning, and rough set theory offers effective mathematical methods; in practice, the performance enhancement of feature selection algorithms formulates a research target and challenge, and the corresponding problem solving usually resorts to improvement constructions of uncertainty measures. By fitting fuzzy rough sets (FFRSs), the relative dependency complement mutual information (FDCIE) motivates a recent algorithm of feature selection, called FNRDCI; however, FDCIE has improvement space of quantification view and fusion hierarchy, so the corresponding feature selection and heuristic algorithm can be advanced. In this paper, the dependency is improved by information localization, while the mutual information is enriched by information fuzzification and decision-class combination, so improved fusion measures and robuster feature selections are established by double-hierarchical fusion on decision classification and class. At first, the correctional dependency is proposed by fuzzy decision localization, and it induces a classification fusion measure (i.e. FCDCIE); based on two types of fuzzy decisions, two types of mutual information (i.e. FRCEmI and FRCFmI) are established by information fuzzification and class combination. Then, two types of dependency and two types of mutual information combinedly generate \(2\times 2=4\) classification fusion measures (i.e. IFRDCEmI, IFRDCFmI, IFRCDCEmI, IFRCDCFmI) by pursuing class-level priority fusion; these new measures acquire semantics uncertainty, system equations, and granulation monotonicity/nonmonotonicity. Furthermore, \(1+2\times 2=5\) fusion measures yield 5 novel feature selections with heuristic algorithms. Finally, experimental comparisons demonstrate the effectiveness and efficiency of the proposed novel methods of uncertainty measures and selection algorithms.