System ADReD for discovering rules based on hyperplanes

Decision table describing n objects in terms of k classification attributes and one decision attribute can be seen as a collection of n points in k-dimensional space. Each point is classified either as positive or negative. The goal of this paper is to present an efficient strategy for constructing possibly the smallest number of hyperplanes so each area surrounded by them contains a group of points, mostly of the same type (either positive or negative). A threshold value given by user, uniquely defines what we mean by mostly. The strategy presented in [3] shows how to construct a possibly smallest number of pairs of hyperplanes, surrounding any dense cluster of objects, which intersection is a line orthogonal to and intersecting with one of the axes. In this paper that constraint is softened and these hyperplanes are built more independently. The main procedure starts with partitioning all negative objects into dense clusters. The same step is repeated for all positive objects also dividing them into dense clusters. To learn a negative rule, we take all objects in one of this negative clusters jointly with all positive objects. The algorithm, presented in this paper, constructs a minimal number of hyperplanes needed to build classification part of a rule describing this negative cluster. The same procedure is repeated for all the remaining negative clusters. Rules describing positive clusters are constructed the same way. Taking the Wisconsin Breast Cancer Database with 699 instances, as an example, we show that the overall support and confidence of rules, extracted from that database, using our strategy is much higher than the confidence and support of rules obtained using methods based on hyperplanes parallel to axes (See5, Rosetta).