# CLAMS: A Cluster Ambiguity Measure for Estimating Perceptual Variability in Visual Clustering

arXiv: https://arxiv.org/abs/2308.00284 · HTML: https://mlsanity.com/paper/2308.00284/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 86 references that are in the map.
- First posted on arXiv 1 Aug 2023.

## Builds on (most cited first, 15 of 15)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [AutoML: A Survey of the State-of-the-Art](https://mlsanity.com/paper/1908.00709/) (2019)
- [Accelerated Hierarchical Density Clustering](https://mlsanity.com/paper/1705.07321/) (2017)
- [ActiVis: Visual Exploration of Industry-Scale Deep Neural Network Models](https://mlsanity.com/paper/1704.01942/) (2017)
- [Revisiting Dimensionality Reduction Techniques for Visual Cluster Analysis: An Empirical Study](https://mlsanity.com/paper/2110.02894/) (2021)
- [Measuring and Explaining the Inter-Cluster Reliability of Multidimensional Projections](https://mlsanity.com/paper/2107.07859/) (2021)
- [Uniform Manifold Approximation with Two-phase Optimization](https://mlsanity.com/paper/2205.00420/) (2022)
- [Feature Learning for Nonlinear Dimensionality Reduction toward Maximal Extraction of Hidden Patterns](https://mlsanity.com/paper/2206.13891/) (2022)
- [Modeling the Influence of Visual Density on Cluster Perception in Scatterplots Using Topology](https://mlsanity.com/paper/2007.13872/) (2020)
- [Survey on Individual Differences in Visualization](https://mlsanity.com/paper/2002.07950/) (2020)
- [Automatic Scatterplot Design Optimization for Clustering Identification](https://mlsanity.com/paper/2207.03355/) (2022)
- [Sanity Check for External Clustering Validation Benchmarks using Internal Validation Measures](https://mlsanity.com/paper/2209.10042/) (2022)
- [Distortion-Aware Brushing for Reliable Cluster Analysis in Multidimensional Projections](https://mlsanity.com/paper/2201.06379/) (2022)
- [The Risks of Ranking: Revisiting Graphical Perception to Model Individual Differences in Visualization Performance](https://mlsanity.com/paper/2212.10533/) (2022)
- [HPSCAN: Human Perception-Based Scattered Data Clustering](https://mlsanity.com/paper/2304.14185/) (2023)

## Built on by (most cited first, 8 of 8)

- [Stop Misusing t-SNE and UMAP for Visual Analytics](https://mlsanity.com/paper/2506.08725/) (2025)
- [Measuring the Validity of Clustering Validation Datasets](https://mlsanity.com/paper/2503.01097/) (2025)
- [A Large-Scale Sensitivity Analysis on Latent Embeddings and Dimensionality Reductions for Text Spatializations](https://mlsanity.com/paper/2407.17876/) (2024)
- [Assessing Graphical Perception of Image Embedding Models using Channel Effectiveness](https://mlsanity.com/paper/2407.20845/) (2024)
- [ChannelExplorer: Exploring Class Separability Through Activation Channel Visualization](https://mlsanity.com/paper/2505.04647/) (2025)
- [Dataset-Adaptive Dimensionality Reduction](https://mlsanity.com/paper/2507.11984/) (2025)
- [Understanding Bias in Perceiving Dimensionality Reduction Projections](https://mlsanity.com/paper/2507.20805/) (2025)
- [LEA: Label Enumeration Attack in Vertical Federated Learning](https://mlsanity.com/paper/2603.03777/) (2026)

## Abstract (arXiv)

Visual clustering is a common perceptual task in scatterplots that supports diverse analytics tasks (e.g., cluster identification). However, even with the same scatterplot, the ways of perceiving clusters (i.e., conducting visual clustering) can differ due to the differences among individuals and ambiguous cluster boundaries. Although such perceptual variability casts doubt on the reliability of data analysis based on visual clustering, we lack a systematic way to efficiently assess this variability. In this research, we study perceptual variability in conducting visual clustering, which we call Cluster Ambiguity. To this end, we introduce CLAMS, a data-driven visual quality measure for automatically predicting cluster ambiguity in monochrome scatterplots. We first conduct a qualitative study to identify key factors that affect the visual separation of clusters (e.g., proximity or size difference between clusters). Based on study findings, we deploy a regression module that estimates the human-judged separability of two clusters. Then, CLAMS predicts cluster ambiguity by analyzing the aggregated results of all pairwise separability between clusters that are generated by the module. CLAMS outperforms widely-used clustering techniques in predicting ground truth cluster ambiguity. Meanwhile, CLAMS exhibits performance on par with human annotators. We conclude our work by presenting two applications for optimizing and benchmarking data mining techniques using CLAMS. The interactive demo of CLAMS is available at clusterambiguity.dev.