How To Overcome Richness Axiom Fallacy
Mieczys{\l}aw A. K{\l}opotek, Robert A. K{\l}opotek
TL;DR
This paper addresses issues caused by the richness axiom in Kleinberg's clustering axioms, proposing solutions to improve learnability and consistency in clustering algorithms.
Contribution
It introduces learnability constraints and domain restrictions as novel resolutions to the conflicts caused by the richness axiom.
Findings
Identifies conflicts between richness and consistency axioms
Proposes centric consistency as a resolution
Suggests restricting clustering domain to super-ball-clusterings
Abstract
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.
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Taxonomy
TopicsMachine Learning and Algorithms · Bayesian Modeling and Causal Inference · Advanced Clustering Algorithms Research