ABSTRACT Traditional clustering algorithms often assume that the distribution of cluster centers is unconstrained. This assumption may not be appropriate in practical problems that involve specific requirements for the cluster centers. An improved Fuzzy C‐means Clustering with Cluster Center Constraints (ICFCM‐CDO) is proposed in this paper. The new algorithm develops a dynamic adjustment mechanism by penalty functions, enabling the incorporation of specific distribution requirements of cluster centers during the clustering process. The key idea of our approach is to impose center constraints in the traditional clustering by introducing a penalty function that encourages the cluster centers to converge in expected regions. Through this improvement, the algorithm is capable of generating clustering results that are more accurate, particularly in applications where the distribution of cluster centers must satisfy specific constraints. Various experiments are conducted to evaluate the efficacy of the proposed algorithm in applications. The results reveal that the ICFCM‐CDO algorithm provides more precise clustering results than traditional methods, especially when handling complex cluster center distribution problems. It achieves a Constraint Satisfaction Degree of 0.97735, a Uniformity Index of 0.65141, and a Region Coverage Rate of 0.53056, significantly outperforming conventional clustering algorithms and showing strong adaptability and generalization in constrained clustering tasks. The performance of the new algorithm is excellent when the constraints on the cluster centers are required.
Mingxuan et al. (Sun,) studied this question.
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