mlsanityData to 14 Oct 2026

Adjusting for Chance Clustering Comparison Measures

arXiv 1512.01286 ↗First posted 3 Dec 2015stat.MLcited by 27

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Abstract (arXiv)

Adjusted for chance measures are widely used to compare partitions/clusterings of the same data set. In particular, the Adjusted Rand Index (ARI) based on pair-counting, and the Adjusted Mutual Information (AMI) based on Shannon information theory are very popular in the clustering community. Nonetheless it is an open problem as to what are the best application scenarios for each measure and guidelines in the literature for their usage are sparse, with the result that users often resort to using both. Generalized Information Theoretic (IT) measures based on the Tsallis entropy have been shown to link pair-counting and Shannon IT measures. In this paper, we aim to bridge the gap between adjustment of measures based on pair-counting and measures based on information theory. We solve the key technical challenge of analytically computing the expected value and variance of generalized IT measures. This allows us to propose adjustments of generalized IT measures, which reduce to well known adjusted clustering comparison measures as special cases. Using the theory of generalized IT measures, we are able to propose the following guidelines for using ARI and AMI as external validation indices: ARI should be used when the reference clustering has large equal sized clusters; AMI should be used when the reference clustering is unbalanced and there exist small clusters.

Key facts. Cited by 27 papers in the map (data through 14 Oct 2026). First posted on arXiv 3 Dec 2015.

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Citing papers per year: 2021: 7; 2022: 3; 2023: 5; 2024: 7; 2025: 2; 2026: 3.

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  2. 2022Boosting Object Representation Learning via Motion and Object Continuitycited by 17
  3. 2021Characterizing and comparing external measures for the assessment of cluster analysis and community detectioncited by 6
  4. 2022Tensor-based Multi-view Spectral Clustering via Shared Latent Spacecited by 5
  5. 2024An Empirical Study into Clustering of Unseen Datasets with Self-Supervised Encoderscited by 5
  6. 2021Pairwise Adjusted Mutual Informationcited by 3
  7. 2024AuToMATo: An Out-Of-The-Box Persistence-Based Clustering Algorithmcited by 3
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  10. 2021SOMTimeS: Self Organizing Maps for Time Series Clustering and its Application to Serious Illness Conversationscited by 2
  11. 2024Multivariate Beta Mixture Model: Probabilistic Clustering With Flexible Cluster Shapescited by 2
  12. 2023FastAMI -- a Monte Carlo Approach to the Adjustment for Chance in Clustering Comparison Metricscited by 1
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  3. 2021The Hyperspherical Geometry of Community Detection: Modularity as a Distancecited by 0
  4. 2022Dictionary learning for clustering on hyperspectral imagescited by 0
  5. 2023Impact of Event Encoding and Dissimilarity Measures on Traffic Crash Characterization Based on Sequence of Eventscited by 0
  6. 20232D Floor Plan Segmentation Based on Down-samplingcited by 0
  7. 2023Disentangled Latent Spaces Facilitate Data-Driven Auxiliary Learningcited by 0
  8. 2024Making Multi-Axis Gaussian Graphical Models Scalable to Millions of Cellscited by 0
  9. 2024Automatic Die Studies for Ancient Numismaticscited by 0
  10. 2024Multimodal Structure Preservation Learningcited by 0
  11. 2025Flexible Bivariate Beta Mixture Model: A Probabilistic Approach for Clustering Complex Data Structurescited by 0
  12. 2025Unifying Information-Theoretic and Pair-Counting Clustering Similaritycited by 0
  13. 2026Adjusted Similarity Measures and a Violation of Expectationscited by 0
  14. 2026MultiST: A Cross-Attention-Based Multimodal Model for Spatial Transcriptomiccited by 0
  15. 2026Bridging Maximum Likelihood and Optimal Transport for Efficient Inference and Model Selection in Stochastic Block Modelscited by 0