# Stop using the elbow criterion for k-means and how to choose the number of clusters instead

arXiv: https://arxiv.org/abs/2212.12189 · HTML: https://mlsanity.com/paper/2212.12189/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 43 references that are in the map.
- First posted on arXiv 23 Dec 2022.

## Builds on (most cited first, 4 of 4)

- [Faster k-Medoids Clustering: Improving the PAM, CLARA, and CLARANS Algorithms](https://mlsanity.com/paper/1810.05691/) (2018)
- [Fast and Eager k-Medoids Clustering: O(k) Runtime Improvement of the PAM, CLARA, and CLARANS Algorithms](https://mlsanity.com/paper/2008.05171/) (2020)
- [Accelerating Spherical k-Means](https://mlsanity.com/paper/2107.04074/) (2021)
- [Clustering by Direct Optimization of the Medoid Silhouette](https://mlsanity.com/paper/2209.12553/) (2022)

## Built on by (most cited first, 25 of 25)

- [LSEnet: Lorentz Structural Entropy Neural Network for Deep Graph Clustering](https://mlsanity.com/paper/2405.11801/) (2024)
- [CARL-G: Clustering-Accelerated Representation Learning on Graphs](https://mlsanity.com/paper/2306.06936/) (2023)
- [More of the Same: Persistent Representational Harms Under Increased Representation](https://mlsanity.com/paper/2503.00333/) (2025)
- [Medoid Silhouette clustering with automatic cluster number selection](https://mlsanity.com/paper/2309.03751/) (2023)
- [Revisiting Silhouette Aggregation](https://mlsanity.com/paper/2401.05831/) (2024)
- [Neural empirical interpolation method for nonlinear model reduction](https://mlsanity.com/paper/2406.03562/) (2024)
- [Dying Clusters Is All You Need -- Deep Clustering With an Unknown Number of Clusters](https://mlsanity.com/paper/2410.09491/) (2024)
- [ASIL: Augmented Structural Information Learning for Deep Graph Clustering in Hyperbolic Space](https://mlsanity.com/paper/2504.09970/) (2025)
- [Influence of various text embeddings on clustering performance in NLP](https://mlsanity.com/paper/2305.03144/) (2023)
- [A Multivariate Unimodality Test Harnessing the Dip Statistic of Mahalanobis Distances Over Random Projections](https://mlsanity.com/paper/2311.16614/) (2023)
- [Detecting Novelties with Empty Classes](https://mlsanity.com/paper/2305.00983/) (2023)
- [Accelerating k-Means Clustering with Cover Trees](https://mlsanity.com/paper/2410.15117/) (2024)
- [AI-in-the-Loop: Privacy Preserving Real-Time Scam Detection and Conversational Scambaiting by Leveraging LLMs and Federated Learning](https://mlsanity.com/paper/2509.05362/) (2025)
- [Multivariate Time Series Clustering for Environmental State Characterization of Ground-Based Gravitational-Wave Detectors](https://mlsanity.com/paper/2412.09832/) (2024)
- [SurfPatch: Enabling Patch Matching for Exploratory Stream Surface Visualization](https://mlsanity.com/paper/2501.02003/) (2025)
- [Anomalous Agreement: How to find the Ideal Number of Anomaly Classes in Correlated, Multivariate Time Series Data](https://mlsanity.com/paper/2501.07172/) (2025)
- [A Tutorial on Discriminative Clustering and Mutual Information](https://mlsanity.com/paper/2505.04484/) (2025)
- [ADAM: Autonomous Discovery and Annotation Model using LLMs for Context-Aware Annotations](https://mlsanity.com/paper/2506.08968/) (2025)
- [TopoMap: A Feature-based Semantic Discriminator of the Topographical Regions in the Test Input Space](https://mlsanity.com/paper/2509.03242/) (2025)
- [Parameter-Free Clustering via Self-Supervised Consensus Maximization (Extended Version)](https://mlsanity.com/paper/2511.09211/) (2025)
- [Discovering Operational Patterns Using Image-Based Convolutional Clustering and Composite Evaluation: A Case Study in Foundry Melting Processes](https://mlsanity.com/paper/2511.13444/) (2025)
- [K-Means as a Radial Basis function Network: a Variational and Gradient-based Equivalence](https://mlsanity.com/paper/2603.04625/) (2026)
- [Amortized Neural Clustering of Time Series based on Statistical Features](https://mlsanity.com/paper/2605.13128/) (2026)
- [Learning Diachronic Representations of Ancient Greek Letterforms](https://mlsanity.com/paper/2606.24984/) (2026)
- [Scalable and Distributed Silhouette Approximation](https://mlsanity.com/paper/2607.01993/) (2026)

## Abstract (arXiv)

A major challenge when using k-means clustering often is how to choose the parameter k, the number of clusters. In this letter, we want to point out that it is very easy to draw poor conclusions from a common heuristic, the "elbow method". Better alternatives have been known in literature for a long time, and we want to draw attention to some of these easy to use options, that often perform better. This letter is a call to stop using the elbow method altogether, because it severely lacks theoretic support, and we want to encourage educators to discuss the problems of the method -- if introducing it in class at all -- and teach alternatives instead, while researchers and reviewers should reject conclusions drawn from the elbow method.