Pattern Recognition on Oriented Matroids: The Existence of a Tope Committee

TL;DR

This paper generalizes committee techniques in pattern recognition to oriented matroids, showing that their rich structure allows for constructing committees using maximal chains in tope posets, aiding decision-making processes.

Contribution

It introduces a novel approach to pattern recognition using oriented matroids and demonstrates how their structure facilitates committee construction for decision-making.

Findings

Rich committee structures in many oriented matroids

Maximal chains in tope posets can be used to construct committees

Applicable to modeling collective decision-making in contradictory problems

Abstract

Oriented matroids can serve as a tool of modeling of collective decision-making processes in contradictory problems of pattern recognition. We present a generalization of the committee techniques of pattern recognition to oriented matroids. A tope committee for an oriented matroid is a subset of its maximal covectors such that every positive halfspace contains more than half of the maximal covectors from this subset. For a large subfamily of oriented matroids their committee structure is quite rich; for example, any maximal chains in their tope posets provide one with information sufficient to construct a committee.