# Element-centric clustering comparison unifies overlaps and hierarchy

arXiv: https://arxiv.org/abs/1706.06136 · HTML: https://mlsanity.com/paper/1706.06136/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jun 2017.

## Built on by (most cited first, 17 of 17)

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- [Evaluating lightweight unsupervised online IDS for masquerade attacks in CAN](https://mlsanity.com/paper/2406.13778/) (2024)
- [Normalised clustering accuracy: An asymmetric external cluster validity measure](https://mlsanity.com/paper/2209.02935/) (2022)
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- [Community detection robustness of graph neural networks](https://mlsanity.com/paper/2509.24662/) (2025)
- [A Pragmatic Method for Comparing Clusterings with Overlaps and Outliers](https://mlsanity.com/paper/2602.14855/) (2026)
- [A Spectral Framework for Tracking Communities in Evolving Networks](https://mlsanity.com/paper/2412.07378/) (2024)
- [Robust Markov stability for community detection at a scale learned based on the structure](https://mlsanity.com/paper/2504.11621/) (2025)
- [Unifying Information-Theoretic and Pair-Counting Clustering Similarity](https://mlsanity.com/paper/2511.03000/) (2025)
- [Community Concealment from Graph Neural Networks](https://mlsanity.com/paper/2602.12250/) (2026)

## Abstract (arXiv)

Clustering is one of the most universal approaches for understanding complex data. A pivotal aspect of clustering analysis is quantitatively comparing clusterings; clustering comparison is the basis for many tasks such as clustering evaluation, consensus clustering, and tracking the temporal evolution of clusters. In particular, the extrinsic evaluation of clustering methods requires comparing the uncovered clusterings to planted clusterings or known metadata. Yet, as we demonstrate, existing clustering comparison measures have critical biases which undermine their usefulness, and no measure accommodates both overlapping and hierarchical clusterings. Here we unify the comparison of disjoint, overlapping, and hierarchically structured clusterings by proposing a new element-centric framework: elements are compared based on the relationships induced by the cluster structure, as opposed to the traditional cluster-centric philosophy. We demonstrate that, in contrast to standard clustering similarity measures, our framework does not suffer from critical biases and naturally provides unique insights into how the clusterings differ. We illustrate the strengths of our framework by revealing new insights into the organization of clusters in two applications: the improved classification of schizophrenia based on the overlapping and hierarchical community structure of fMRI brain networks, and the disentanglement of various social homophily factors in Facebook social networks. The universality of clustering suggests far-reaching impact of our framework throughout all areas of science.