Accelerated Two-Stage Particle Swarm Optimization for Clustering Not-Well-Separated Data

Xiangping Xu, Jun Li, Meng Chu Zhou, Jun Xu, Jinde Cao

Research output: Contribution to journalArticlepeer-review

62 Scopus citations


Cluster analysis is a data mining technique that has been widely used to exploit useful information in a great amount of data. Because of their evaluation mechanism based on an intracluster distance (ICD) function, traditional single-objective clustering algorithms are not appropriate for not-well-separated data. Specifically, they may easily result in the drop of the optimal solution accuracy on their late stages of search when dealing with the latter. To overcome the problem, in this paper a novel index reflecting the similarity of data within a cluster is presented and called intracluster cohesion (ICC). However, if a multiobjective method is used to cluster with ICD and ICC as the specified objectives, its clustering accuracy may depend on one's experience. Motivated by these, we propose an accelerated two-stage particle swarm optimization (ATPSO) in which K -means is utilized to accelerate particles' convergence during the population initialization. Its clustering process consists of two stages. First, the main objective of minimizing ICD is to execute preliminary clustering; second, ICC is optimized to promote the clustering accuracy. Extensive experiments with the help of 17 open-source clustering sets in various geometric distributions are conducted. The results show that ATPSO outperforms PSO, K -means PSO (KPSO), chaotic PSO (CPSO), and accelerated CPSO in terms of accuracy, and its efficiency is approximate to that of KPSO. Its convergence trend indicates that the adoption of the proposed ICC contributes to the clustering accuracy. Remarkably, compared with the Pareto-based multiobjective PSO, ATPSO can detect clusters more accurately and quickly through the proposed two-stage search.

Original languageEnglish (US)
Article number8400589
Pages (from-to)4212-4223
Number of pages12
JournalIEEE Transactions on Systems, Man, and Cybernetics: Systems
Issue number11
StatePublished - Nov 2020

All Science Journal Classification (ASJC) codes

  • Software
  • Control and Systems Engineering
  • Human-Computer Interaction
  • Computer Science Applications
  • Electrical and Electronic Engineering


  • Clustering
  • intracluster cohesion (ICC)
  • particle swarm optimization (PSO)
  • two-stage strategy


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