# Clustering performance analysis using a new correlation-based cluster validity index

arXiv: https://arxiv.org/abs/2109.11172 · HTML: https://mlsanity.com/paper/2109.11172/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 58 references that are in the map.
- First posted on arXiv 23 Sep 2021.

## Builds on (most cited first, 2 of 2)

- [Towards K-means-friendly Spaces: Simultaneous Deep Learning and Clustering](https://mlsanity.com/paper/1610.04794/) (2016)
- [Linking Points With Labels in 3D: A Review of Point Cloud Semantic Segmentation](https://mlsanity.com/paper/1908.08854/) (2019)

## Built on by (most cited first, 9 of 9)

- [A Bayesian cluster validity index](https://mlsanity.com/paper/2402.02162/) (2024)
- [On the Use of Relative Validity Indices for Comparing Clustering Approaches](https://mlsanity.com/paper/2404.10351/) (2024)
- [A correlation-based fuzzy cluster validity index with secondary options detector](https://mlsanity.com/paper/2308.14785/) (2023)
- [Ranked differences Pearson correlation dissimilarity with an application to electricity users time series clustering](https://mlsanity.com/paper/2505.02173/) (2025)
- [Wasserstein-based Kernel Principal Component Analysis for Clustering Applications](https://mlsanity.com/paper/2503.14357/) (2025)
- [4TaStiC: Time and trend traveling time series clustering for classifying long-term type 2 diabetes patients](https://mlsanity.com/paper/2505.07702/) (2025)
- [An upper bound on the silhouette evaluation metric for clustering](https://mlsanity.com/paper/2509.08625/) (2025)
- [Absolute indices for determining compactness, separability and number of clusters](https://mlsanity.com/paper/2510.13065/) (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)

## Abstract (arXiv)

There are various cluster validity indices used for evaluating clustering results. One of the main objectives of using these indices is to seek the optimal unknown number of clusters. Some indices work well for clusters with different densities, sizes, and shapes. Yet, one shared weakness of those validity indices is that they often provide only one optimal number of clusters. That number is unknown in real-world problems, and there might be more than one possible option. We develop a new cluster validity index based on a correlation between an actual distance between a pair of data points and a centroid distance of clusters that the two points occupy. Our proposed index constantly yields several local peaks and overcomes the previously stated weakness. Several experiments in different scenarios, including UCI real-world data sets, have been conducted to compare the proposed validity index with several well-known ones. An R package related to this new index called NCvalid is available at https://github.com/nwiroonsri/NCvalid.