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The K-means algorithm utilises the Euclidean distance metric to quantify the similarity between data points and clusters, with the fundamental objective of assessing the rela-tionship between points. It is important to note that, during the process of clustering, the relationships between the remaining points in the cluster and the points to be measured are ignored. In consideration of the aforementioned issues, this paper pro-poses the utilisation of the extension distance for the purpose of evaluating the rela-tionship between the points to be measured and the cluster classes. Furthermore, it in-troduces a variant of the K-means algorithm based on the separator distance. Through a series of comparative experiments, the effectiveness of the proposed algorithm for clustering fan-shaped datasets is preliminarily verified.