Pattern Recognition on Oriented Matroids

1.4Graphs Related to Tope Committees

In this section we consider two “extremal” committee constructs for simple oriented matroids: on the one hand, these are the critical committees (which we have already dealt with in the previous Section 1.3) with the topes that belong to the vertex sets of the symmetric cycles in the tope graph and, on the other hand, the committees whose topes have inclusion-maximal (among all topes) positive parts. In the rank 2 case these committee constructs coincide.

The committees whose topes have inclusion-maximal positive parts are arguably the best-quality building blocks of decision rules in the two-class pattern recognition problem.

Although critical committees can be regarded as worst-quality prerequisites for ...