Closure operators: Complexity and applications to classification and decision-making
This work addresses the complexity analysis of closure operators for researchers in machine learning and decision theory, but appears incremental as it builds on existing applications without introducing new methods or data.
The paper tackles the problem of quantifying the complexity of closure operators, which arise in machine learning for classification and clustering and in decision theory for modeling preferences. It formulates a notion of complexity that translates to classifier or utility function complexity, but does not provide concrete numerical results.
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.