Three-way fusion measures and three-level feature selections based on neighborhood decision systems

Uncertainty measures exhibit algebraic and informational perspectives, and the two-view measure integration facilitates feature selections in classification learning. According to neighborhood decision systems (NDSs), two basic algorithms of feature selections (called JE-FS and DE-FS) already exist by using joint and decisional entropies, respectively, but they have advancement space for informationally fusing algebraic measures. In this paper on NDSs, three-way fusion measures are systematically constructed by combining three-way algebraic and informational measures, and thus three-level feature selections are hierarchically investigated by using corresponding monotonic and nonmonotonic measures and strategies. At first, the accuracy, granularity, and composite granularity-accuracy constitute three-way algebraic measures, while the joint, conditional, and decisional entropies (JE, CE, DE) formulate three-way informational measures. Then, three-way algebraic and informational measures are combined via normalization and multiplication, so three-way fusion measures based on JE, CE, DE are established. These new measures acquire granulation monotonicity and nonmonotonicity. Furthermore by relevant measures and monotonicity/nonmonotonicity, three-level feature selections (with null, single, and double fusion levels) related to JE, CE, DE are proposed, and corresponding heuristic algorithms are designed by monotonic and nonmonotonic principles. 4×3=12 selection algorithms comprehensively emerge, and they extend and improve current JE-FS and DE-FS. Finally by data experiments, related uncertainty measures and granulation properties are validated, and all 12 selection algorithms are compared in classification learning. As a result, new algorithms outperform JE-FS and DE-FS for classification performance, and the algorithmic improvements accord with the fusion-hierarchical deepening and entropy-systematic development of uncertainty measures.