Statistical Significance for Hierarchical Clustering

TL;DR

This paper introduces a Monte Carlo-based method for testing the statistical significance of clusters identified by hierarchical clustering, controlling for false positives in complex nested structures.

Contribution

It presents a novel sequential testing procedure with theoretical guarantees for significance testing in hierarchical clustering, addressing a key challenge in high-dimensional data analysis.

Findings

Method controls family-wise error rate in hierarchical clustering

Simulation studies demonstrate high power in detecting true clusters

Applications to cancer gene expression data validate practical utility

Abstract

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.