A Grid-based Approach for Convexity Analysis of a Density-based Cluster

TL;DR

This paper introduces a grid-based geometrical method to analyze the convexity of density-based clusters, providing a reliable approximation of cluster boundaries and assessing convexity through experiments on synthetic data.

Contribution

The paper presents a novel grid-based approach for convexity analysis of density-based clusters, addressing the challenge of shape sharpness due to finite samples from infinite distributions.

Findings

Effective approximation of cluster boundaries.

Successful convexity assessment on synthetic datasets.

Reliable method for shape analysis in density-based clustering.

Abstract

This paper presents a novel geometrical approach to investigate the convexity of a density-based cluster. Our approach is grid-based and we are about to calibrate the value space of the cluster. However, the cluster objects are coming from an infinite distribution, their number is finite, and thus, the regarding shape will not be sharp. Therefore, we establish the precision of the grid properly in a way that, the reliable approximate boundaries of the cluster are founded. After that, regarding the simple notion of convex sets and midpoint convexity, we investigate whether or not the density-based cluster is convex. Moreover, our experiments on synthetic datasets demonstrate the desirable performance of our method.