The spherical k-means problem (SKMP) is an important variant of the k-means clustering problem (KMP). In this paper, we consider the SKMP, which aims to divide the n points in a given data point set \({\mathcal {S}}\) into k clusters so as to minimize the total sum of the cosine dissimilarity measure from each data point to their respective closest cluster center. Our main contribution is to design an expected constant approximation algorithm for the SKMP by integrating the seeding algorithm for the KMP and the local search technique. By utilizing the structure of the clusters, we further obtain an improved LocalSearch++ algorithm involving \(\varepsilon k\) local search steps.

球形k均值问题（SKMP）是k均值聚类问题（KMP）的重要变体。在本文中，我们考虑了SKMP，其目的是将给定数据点集\（{\ mathcal {S}} \\}中的n个点划分为k个聚类，以最大程度地减少每个余弦相似度度量的总和数据指向它们各自最近的聚类中心。我们的主要贡献是通过整合KMP的播种算法和本地搜索技术，为SKMP设计期望的常数近似算法。通过利用聚类的结构，我们进一步获得了一种改进的LocalSearch ++算法，其中涉及\（\ varepsilon k \）本地搜索步骤。