# How To Overcome Richness Axiom Fallacy

arXiv: https://arxiv.org/abs/2210.15507 · HTML: https://mlsanity.com/paper/2210.15507/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 26 references that are in the map.
- First posted on arXiv 27 Oct 2022.

## Builds on (most cited first, 4 of 4)

- [Axioms for graph clustering quality functions](https://mlsanity.com/paper/1308.3383/) (2013)
- [Possibility results for graph clustering: A novel consistency axiom](https://mlsanity.com/paper/1806.06142/) (2018)
- [Towards Continuous Consistency Axiom](https://mlsanity.com/paper/2202.06015/) (2022)
- [A Clustering Preserving Transformation for k-Means Algorithm Output](https://mlsanity.com/paper/2202.10455/) (2022)

## Abstract (arXiv)

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.