# From A-to-Z Review of Clustering Validation Indices

arXiv: https://arxiv.org/abs/2407.20246 · HTML: https://mlsanity.com/paper/2407.20246/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 113 references that are in the map.
- First posted on arXiv 18 Jul 2024.

## Builds on (most cited first, 17 of 17)

- [Hierarchical Clustering: Objective Functions and Algorithms](https://mlsanity.com/paper/1704.02147/) (2017)
- [Clustering Algorithms: A Comparative Approach](https://mlsanity.com/paper/1612.08388/) (2016)
- [Ground Truth Bias in External Cluster Validity Indices](https://mlsanity.com/paper/1606.05596/) (2016)
- [CSCF: a chaotic sine cosine firefly Algorithm for practical application problems](https://mlsanity.com/paper/2011.10283/) (2020)
- [Operational Framework for Recent Advances in Backtracking Search Optimisation Algorithm: A Systematic Review and Performance Evaluation](https://mlsanity.com/paper/1911.13011/) (2019)
- [A Multi-disciplinary Ensemble Algorithm for Clustering Heterogeneous Datasets](https://mlsanity.com/paper/2102.08361/) (2021)
- [An Optimized Framework to Adopt Computer Laboratory Administrations for Operating System and Application Installations](https://mlsanity.com/paper/2105.02147/) (2021)
- [Evaluating e-Government Services in Kurdistan Institution for Strategic Studies and Scientific Research Using the EGOVSAT Model](https://mlsanity.com/paper/2105.02697/) (2021)
- [Performance evaluation results of evolutionary clustering algorithm star for clustering heterogeneous datasets](https://mlsanity.com/paper/2105.02810/) (2021)
- [A New Framework to Adopt Multidimensional Databases for Organizational Information System Strategies](https://mlsanity.com/paper/2105.08131/) (2021)
- [A Novel Cluster Detection of COVID-19 Patients and Medical Disease Conditions Using Improved Evolutionary Clustering Algorithm Star](https://mlsanity.com/paper/2109.09492/) (2021)
- [Towards Semantic Web: Challenges and Needs](https://mlsanity.com/paper/2105.02708/) (2021)
- [Analysis for the Overwhelming Success of the Web Compared to Microcosm and Hyper-G Systems](https://mlsanity.com/paper/2105.08057/) (2021)
- [Formal context reduction in deriving concept hierarchies from corpora using adaptive evolutionary clustering algorithm star](https://mlsanity.com/paper/2107.04781/) (2021)
- [Next word prediction based on the N-gram model for Kurdish Sorani and Kurmanji](https://mlsanity.com/paper/2008.01546/) (2020)
- [Current Studies and Applications of Shuffled Frog Leaping Algorithm: A Review](https://mlsanity.com/paper/2202.03477/) (2022)
- [Cluster validity index based on Jeffrey divergence](https://mlsanity.com/paper/1812.08891/) (2018)

## Built on by (most cited first, 11 of 11)

- [Measuring the Validity of Clustering Validation Datasets](https://mlsanity.com/paper/2503.01097/) (2025)
- [Cluster Analysis with Resampling for Validation and Exploration (CARVE)](https://mlsanity.com/paper/2606.00327/) (2026)
- [Comparative Analysis of AES, Blowfish, Twofish, Salsa20, and ChaCha20 for Image Encryption](https://mlsanity.com/paper/2407.16274/) (2024)
- [Exploring Gaze Pattern Differences Between Autistic and Neurotypical Children: Clustering, Visualisation, and Prediction](https://mlsanity.com/paper/2409.11744/) (2024)
- [Out-of-Distribution Detection via Channelwise Feature Aggregation in Neural Network-Based Receivers](https://mlsanity.com/paper/2505.15570/) (2025)
- [ClustRecNet: A Novel End-to-End Deep Learning Framework for Clustering Algorithm Recommendation](https://mlsanity.com/paper/2509.25289/) (2025)
- [IPBC: An Interactive Projection-Based Framework for Human-in-the-Loop Semi-Supervised Clustering of High-Dimensional Data](https://mlsanity.com/paper/2601.18828/) (2026)
- [Explainable cluster analysis: a bagging approach](https://mlsanity.com/paper/2603.19840/) (2026)
- [Composite Silhouette: A Subsampling-based Aggregation Strategy](https://mlsanity.com/paper/2604.13816/) (2026)
- [Central Description Length (CDL) Clustering Validation Index](https://mlsanity.com/paper/2606.05230/) (2026)
- [Scalable and Distributed Silhouette Approximation](https://mlsanity.com/paper/2607.01993/) (2026)

## Abstract (arXiv)

Data clustering involves identifying latent similarities within a dataset and organizing them into clusters or groups. The outcomes of various clustering algorithms differ as they are susceptible to the intrinsic characteristics of the original dataset, including noise and dimensionality. The effectiveness of such clustering procedures directly impacts the homogeneity of clusters, underscoring the significance of evaluating algorithmic outcomes. Consequently, the assessment of clustering quality presents a significant and complex endeavor. A pivotal aspect affecting clustering validation is the cluster validity metric, which aids in determining the optimal number of clusters. The main goal of this study is to comprehensively review and explain the mathematical operation of internal and external cluster validity indices, but not all, to categorize these indices and to brainstorm suggestions for future advancement of clustering validation research. In addition, we review and evaluate the performance of internal and external clustering validation indices on the most common clustering algorithms, such as the evolutionary clustering algorithm star (ECA*). Finally, we suggest a classification framework for examining the functionality of both internal and external clustering validation measures regarding their ideal values, user-friendliness, responsiveness to input data, and appropriateness across various fields. This classification aids researchers in selecting the appropriate clustering validation measure to suit their specific requirements.