Closure operators: Complexity and applications to classification and decision-making

TL;DR

This paper introduces a complexity measure for closure operators, linking their theoretical properties to practical applications in machine learning classification, clustering, and decision-making processes involving utility functions.

Contribution

It formulates a novel notion of complexity for closure operators, connecting theoretical aspects to real-world ML and decision theory applications.

Findings

Closure operators are fundamental in data classification and clustering.

Complexity of closure operators correlates with classifier and utility function complexity.

The framework aids in understanding the computational aspects of classification and decision models.

Abstract

We study the complexity of closure operators, with applications to machine learning and decision theory. In machine learning, closure operators emerge naturally in data classification and clustering. In decision theory, they can model equivalence of choice menus, and therefore situations with a preference for flexibility. Our contribution is to formulate a notion of complexity of closure operators, which translate into the complexity of a classifier in ML, or of a utility function in decision theory.