Three-way k-means: integrating k-means and three-way decision

  • Pingxin WangEmail author
  • Hong Shi
  • Xibei Yang
  • Jusheng Mi
Original Article


The traditional k-means, which unambiguously assigns an object precisely to a single cluster with crisp boundary, does not adequately show the fact that a cluster may not have a well-defined cluster boundary. This paper presents a three-way k-means clustering algorithm based on three-way strategy. In the proposed method, an overlap clustering is used to obtain the supports (unions of the core regions and the fringe regions) of the clusters and perturbation analysis is applied to separate the core regions from the supports. The difference between the support and the core region is regarded as the fringe region of the specific cluster. Therefore, a three-way explanation of the cluster is naturally formed. Davies–Bouldin index (DB), Average Silhouette index (AS) and Accuracy (ACC) are computed by using core region to evaluate the structure of three-way k-means result. The experimental results on UCI data sets and USPS data sets show that such strategy is effective in improving the structure of clustering results.


Three-way clustering Three-way decision K-means Cluster validity index 



The authors would like to thank the editor and the anonymous reviewers for their constructive and valuable comments. This work was supported in part by National Natural Science Foundation of China (nos. 61503160, 61773012 and 61572242), Natural Science Foundation of the Jiangsu Higher Education Institutions of China (no. 15KJB110004).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of ScienceJiangsu University of Science and TechnologyZhenjiangPeople’s Republic of China
  2. 2.College of Mathematics and Information ScienceHebei Normal UniversityShijiazhuangPeople’s Republic of China
  3. 3.School of Computer ScienceJiangsu University of Science and TechnologyZhenjiangPeople’s Republic of China

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