In order to cluster the textual data with high dimension in modern data analysis, the spherical k-means clustering is presented. It aims to partition the given points with unit length into k sets so as to minimize the within-cluster sum of cosine dissimilarity. In this paper, we mainly study seeding algorithms for spherical k-means clustering, for its special case (with separable sets), as well as for its generalized problem (\(\alpha \)-spherical k-means clustering). About the spherical k-means clustering with separable sets, an approximate algorithm with a constant factor is presented. Moreover, it can be generalized to the \(\alpha \)-spherical separable k-means clustering. By slickly constructing a useful function, we also show that the famous seeding algorithms such as k-means++ and k-means|| for k-means problem can be applied directly to solve the \(\alpha \)-spherical k-means clustering. Except for theoretical analysis, the numerical experiment is also included.

为了在现代数据分析中对高维文本数据进行聚类，提出了球形k均值聚类。它的目的是将单位长度的给定点划分为k个集合，以最大程度地减少集群内的余弦不相似度之和。在本文中，我们主要研究球形k均值聚类的种子算法，特殊情况（具有可分离集）以及其广义问题（\（\ alpha \）球形k均值聚类）。关于具有可分离集的球面k均值聚类，提出了一种具有恒定因子的近似算法。而且，它可以推广为\（\ alpha \）-球形可分离的k-均值聚类。通过巧妙地构造一个有用的函数，我们还展示了著名的种子算法，例如k -means ++和k -means ||。对于k-均值问题，可以直接应用来解决\（\ alpha \）-球形k-均值聚类。除理论分析外，还包括数值实验。