# Absolute indices for determining compactness, separability and number of clusters

arXiv: https://arxiv.org/abs/2510.13065 · HTML: https://mlsanity.com/paper/2510.13065/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 45 references that are in the map.
- First posted on arXiv 15 Oct 2025.

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

- [Are Cluster Validity Measures (In)valid?](https://mlsanity.com/paper/2208.01261/) (2022)
- [Clustering performance analysis using a new correlation-based cluster validity index](https://mlsanity.com/paper/2109.11172/) (2021)
- [CNAK : Cluster Number Assisted K-means](https://mlsanity.com/paper/1911.08871/) (2019)
- [A Distance-based Separability Measure for Internal Cluster Validation](https://mlsanity.com/paper/2106.09794/) (2021)

## Abstract (arXiv)

Finding "true" clusters in a data set is a challenging problem. Clustering solutions obtained using different models and algorithms do not necessarily provide compact and well-separated clusters or the optimal number of clusters. Cluster validity indices are commonly applied to identify such clusters. Nevertheless, these indices are typically relative, and they are used to compare clustering algorithms or choose the parameters of a clustering algorithm. Moreover, the success of these indices depends on the underlying data structure. This paper introduces novel absolute cluster indices to determine both the compactness and separability of clusters. We define a compactness function for each cluster and a set of neighboring points for cluster pairs. This function is utilized to determine the compactness of each cluster and the whole cluster distribution. The set of neighboring points is used to define the margin between clusters and the overall distribution margin. The proposed compactness and separability indices are applied to identify the true number of clusters. Using a number of synthetic and real-world data sets, we demonstrate the performance of these new indices and compare them with other widely-used cluster validity indices.