Cohesive clustering algorithm based on high-dimensional generalized Fermat points

Abstract

Utilizing high-dimensional generalized Fermat points (Fd-points) as cluster centers, we propose a new method Fd-points Linkage (FL) for calculating intra-cluster and inter-cluster distances. First, we employ the Plant Growth Simulation Algorithm (PGSA) to solve for the Fd-points within clusters. The obtained Fd-points are then used to represent the corresponding clusters in the process of calculating the inter-cluster distance so as to guide the merging of clusters. To verify the effectiveness of the proposed method, we compared it with previous methods in terms of performance on multiple well-known datasets. Fd-points have not been utilized as cluster centers in clustering analysis, although they are theoretically optimal representations of datasets and are able to represent different clusters more accurately. We explore a new direction for refining clustering theory and improving the accuracy of clustering algorithms.