A Grid-based Approach for Convexity Analysis of a Density-based Cluster
This work addresses a specific problem in cluster analysis for researchers in data mining, but it appears incremental as it builds on existing concepts of convex sets and density-based clustering.
The paper tackles the problem of analyzing the convexity of density-based clusters by introducing a grid-based geometrical approach that calibrates the value space and establishes grid precision to approximate cluster boundaries, with experiments on synthetic datasets demonstrating desirable performance.
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.