How To Overcome Richness Axiom Fallacy
This work tackles foundational issues in clustering theory for researchers, but it appears incremental as it builds on existing axiomatic frameworks.
The paper addresses the learnability problems and conflicts with the consistency axiom caused by the richness axiom in Kleinberg's axiomatic system, proposing resolutions such as learnability constraints, centric consistency, or restricting the domain to super-ball-clusterings.
The paper points at the grieving problems implied by the richness axiom in the Kleinberg's axiomatic system and suggests resolutions. The richness induces learnability problem in general and leads to conflicts with consistency axiom. As a resolution, learnability constraints and usage of centric consistency or restriction of the domain of considered clusterings to super-ball-clusterings is proposed.