# Discovering the Graph Structure in the Clustering Results

## TL;DR

This paper introduces a pairwise overlapping k-means method to uncover the graph structure of relations between clusters, enhancing standard clustering with connectivity insights on both toy and real datasets.

## Contribution

The paper presents a novel pairwise overlapping k-means approach that reveals the graph structure of cluster relations, with a tunable parameter for sensitivity and overlap level.

## Key findings

- Works well on toy data
- Provides meaningful graph structures on real datasets
- Offers a formula for parameter tuning

## Abstract

In a standard cluster analysis, such as k-means, in addition to clusters locations and distances between them, it's important to know if they are connected or well separated from each other. The main focus of this paper is discovering the relations between the resulting clusters. We propose a new method which is based on pairwise overlapping k-means clustering, that in addition to means of clusters provides the graph structure of their relations. The proposed method has a set of parameters that can be tuned in order to control the sensitivity of the model and the desired relative size of the pairwise overlapping interval between means of two adjacent clusters, i.e., level of overlapping. We present the exact formula for calculating that parameter. The empirical study presented in the paper demonstrates that our approach works well not only on toy data but also compliments standard clustering results with a reasonable graph structure on real datasets, such as financial indices and restaurants.