# Statistical Significance for Hierarchical Clustering

arXiv: https://arxiv.org/abs/1411.5259 · HTML: https://mlsanity.com/paper/1411.5259/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Nov 2014.

## Built on by (most cited first, 9 of 9)

- [Selective inference for k-means clustering](https://mlsanity.com/paper/2203.15267/) (2022)
- [LCS-DIVE: An Automated Rule-based Machine Learning Visualization Pipeline for Characterizing Complex Associations in Classification](https://mlsanity.com/paper/2104.12844/) (2021)
- [Significance-Based Categorical Data Clustering](https://mlsanity.com/paper/2211.03956/) (2022)
- [Weighted Conformal Clustering](https://mlsanity.com/paper/2606.00436/) (2026)
- [Mapping Hymns and Organizing Concepts in the Rigveda: Quantitatively Connecting the Vedic Suktas](https://mlsanity.com/paper/2503.18226/) (2025)
- [Interpretable Clustering with the Distinguishability Criterion](https://mlsanity.com/paper/2404.15967/) (2024)
- [Statistical Framework for Clustering MU-MIMO Wireless via Second Order Statistics](https://mlsanity.com/paper/2408.04484/) (2024)
- [The elbow statistic: Multiscale clustering statistical significance](https://mlsanity.com/paper/2603.03235/) (2026)
- [Selective Inference for Clustering Under Unknown Covariance](https://mlsanity.com/paper/2610.17458/) (2026)

## Abstract (arXiv)

Cluster analysis has proved to be an invaluable tool for the exploratory and unsupervised analysis of high dimensional datasets. Among methods for clustering, hierarchical approaches have enjoyed substantial popularity in genomics and other fields for their ability to simultaneously uncover multiple layers of clustering structure. A critical and challenging question in cluster analysis is whether the identified clusters represent important underlying structure or are artifacts of natural sampling variation. Few approaches have been proposed for addressing this problem in the context of hierarchical clustering, for which the problem is further complicated by the natural tree structure of the partition, and the multiplicity of tests required to parse the layers of nested clusters. In this paper, we propose a Monte Carlo based approach for testing statistical significance in hierarchical clustering which addresses these issues. The approach is implemented as a sequential testing procedure guaranteeing control of the family-wise error rate. Theoretical justification is provided for our approach, and its power to detect true clustering structure is illustrated through several simulation studies and applications to two cancer gene expression datasets.