# High-Dimensional Wide Gap k-Means Versus Clustering Axioms

arXiv: https://arxiv.org/abs/2211.17036 · HTML: https://mlsanity.com/paper/2211.17036/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 23 references that are in the map.
- First posted on arXiv 30 Nov 2022.

## Builds on (most cited first, 7 of 7)

- [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)
- [An Aposteriorical Clusterability Criterion for k-Means++ and Simplicity of Clustering](https://mlsanity.com/paper/1704.07139/) (2017)
- [Computational Feasibility of Clustering under Clusterability Assumptions](https://mlsanity.com/paper/1501.00437/) (2015)
- [An Effective and Efficient Approach for Clusterability Evaluation](https://mlsanity.com/paper/1602.06687/) (2016)

## Abstract (arXiv)

Kleinberg's axioms for distance based clustering proved to be contradictory. Various efforts have been made to overcome this problem. Here we make an attempt to handle the issue by embedding in high-dimensional space and granting wide gaps between clusters.