Hierarchical Clustering With Confidence

2025-12-06

AI Summary

Hierarchical clustering is highly sensitive to data perturbations due to its greedy merging strategy, resulting in unstable outputs and ambiguity in distinguishing true from spurious cluster structures. To address this, we propose a robust evaluation framework integrating randomization with selective inference: it constructs valid p-values for each merge step—controlling Type I error at a user-specified level—without requiring derivation tailored to specific linkage criteria. Furthermore, we design an adaptive α-spending procedure to consistently estimate the optimal number of clusters. Extensive experiments on simulated and real-world datasets demonstrate that our method significantly improves statistical power, accurately recovers ground-truth cluster structures, mitigates over-segmentation, and quantifies clustering stability across multiple runs. The core contribution lies in the first systematic application of selective inference to hierarchical clustering, enabling interpretable, tunable, and statistically rigorous reliability assessment.

Technology Category

• Machine Learning: Clustering
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Data transparency and provenance

Abstract

Agglomerative hierarchical clustering is one of the most widely used approaches for exploring how observations in a dataset relate to each other. However, its greedy nature makes it highly sensitive to small perturbations in the data, often producing different clustering results and making it difficult to separate genuine structure from spurious patterns. In this paper, we show how randomizing hierarchical clustering can be useful not just for measuring stability but also for designing valid hypothesis testing procedures based on the clustering results. We propose a simple randomization scheme together with a method for constructing a valid p-value at each node of the hierarchical clustering dendrogram that quantifies evidence against performing the greedy merge. Our test controls the Type I error rate, works with any hierarchical linkage without case-specific derivations, and simulations show it is substantially more powerful than existing selective inference approaches. To demonstrate the practical utility of our p-values, we develop an adaptive $α$-spending procedure that estimates the number of clusters, with a probabilistic guarantee on overestimation. Experiments on simulated and real data show that this estimate yields powerful clustering and can be used, for example, to assess clustering stability across multiple runs of the randomized algorithm.

Problem

• Develops a hypothesis testing method for hierarchical clustering merges
• Proposes a randomization scheme to quantify evidence against greedy merges
• Introduces an adaptive procedure to estimate cluster count with guarantees

Innovation

• Randomized hierarchical clustering for stability measurement
• Valid p-value construction at dendrogram nodes
• Adaptive alpha-spending for cluster number estimation