Logical Classification of Partially Ordered Data

TL;DR

This paper introduces a logical classification scheme for partially ordered data in machine learning, highlighting the complexity of learning such classifiers and demonstrating its effectiveness on various datasets.

Contribution

It proposes a novel logical classification framework for partial orders and analyzes the intractability of learning these classifiers, supported by matrix formulation and empirical results.

Findings

Logical classifiers based on partial orders are effective.

Learning these classifiers involves solving an intractable dualization problem.

The approach is validated on model and real-life data.

Abstract

Issues concerning intelligent data analysis occurring in machine learning are investigated. A scheme for synthesizing correct supervised classification procedures is proposed. These procedures are focused on specifying partial order relations on sets of feature values; they are based on a generalization of the classical concepts of logical classification. It is shown that learning the correct logical classifier requires an intractable discrete problem to be solved. This is the dualization problem over products of partially ordered sets. The matrix formulation of this problem is given. The effectiveness of the proposed approach to the supervised classification problem is illustrated on model and real-life data.