Optimization of inner and general rules

The subject of the paper concerns the problem of deriving decision rules from distributed data. The paper examines issues of learning general and inner decision rules from a set of decision trees. Inner rules refer to the routes within decision trees from the root to leaf nodes, while general rules are arbitrary rules derived from attributes found in the set of decision trees. The paper illustrates that the optimization of general decision rules is NP-hard problem, so the authors propose heuristics $H_1$ and $H_2$ for this issue. Taking into account induction and optimization of inner decision rules an algorithm $A$ is employed. Additionally, an approach based on global optimization relative to length, support, and sequential optimization is proposed. The presented algorithms were studied considering two perspectives (i) knowledge discovery from data and (ii) knowledge representation. In the first case, it is possible to discover patterns from the data and verify the induced model, in the second case, it is possible to represent knowledge in a comprehensible and explainable way. These elements are important in an era of heterogeneous, distributed data sources. Experiments were carried out on selected datasets from UCI ML and Kaggle repositories. In order to create a distributed data structure, an approach based on reducts induced by a genetic algorithm was employed. Obtained results show that there are cases where the global rule-based classifiers built in the framework of optimization of inner decision rules perform better in terms of accuracy than that of local models induced directly from subtables. In the case of algorithms $H_1$ and $H_2$, the low complexity of models based on decision rules induced from a set of decision trees is noted.