CHIRA-Convex Hull Based Iterative Algorithm of Rules Aggregation

In the paper we present CHIRA, an algorithm performing decision rules aggregation. New elementary conditions, which are linear combinations of attributes may appear in rule premises during the aggregation, leading to so-called oblique rules. The algorithm merges rules iteratively, in pairs, according to a certain order specified in advance. It applies the procedure of determining convex hulls for regions in a feature space which are covered by aggregated rules. CHIRA can be treated as the generalization of rule shortening and joining algorithms which, unlike them, allows a rule representation language to be changed. Application of presented algorithm allows one to decrease a number of rules, especially in the case of data in which decision classes are separated by hyperplanes not perpendicular to the attribute axes. Efficiency of CHIRA has been verified on rules obtained by two known rule induction algorithms, RIPPER and q-ModLEM, run on 18 benchmark data sets. Additionally, the algorithm has been applied on synthetic data as well as on a real-life set concerning classification of natural hazards in hard-coal mines.