arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2302.07045cs.LG
收藏

基于多原型凸合并的K-Means聚类算法

Multi-Prototypes Convex Merging Based K-Means Clustering Algorithm

Xidian University(西安电子科技大学);The Chinese University of Hong Kong(香港中文大学);City University of Hong Kong(香港城市大学);Hong Kong Centre for Cerebro-Cardiovascular Health Engineering(香港心脑血管健康工程中心)

Dong Li, Shuisheng Zhou, Tieyong Zeng, Raymond H. Chan

摘要:

K-Means算法是一种流行的聚类方法。然而,它有两个局限性:1)它很容易陷入虚假的局部最小值,2)聚类数k必须事先给定。针对这两个问题,提出了一种基于多原型凸合并的K-Means聚类算法(MCKM)。首先,基于K-Means问题的伪局部极小点的结构,设计了多原型采样(MPS),以选择适当数量的多原型数据与任意形状。从理论上证明了MPS选择的多个原型能够以常数因子逼近K-Means问题的最优成本。然后,一个合并技术,称为凸合并(CM),合并的多个原型,以获得一个更好的局部最小值,而无需k是给定的先验。具体地,CM可以获得最优合并并估计正确的k。通过将这两种技术与K-Means算法相结合,所提出的MCKM是一种有效的和可解释的聚类算法,用于在不首先给定k的情况下避免K-Means问题的不期望的局部极小值。在合成数据集和真实数据集上的实验结果验证了该算法的有效性。

英文摘要:

K-Means algorithm is a popular clustering method. However, it has two limitations: 1) it gets stuck easily in spurious local minima, and 2) the number of clusters k has to be given a priori. To solve these two issues, a multi-prototypes convex merging based K-Means clustering algorithm (MCKM) is presented. First, based on the structure of the spurious local minima of the K-Means problem, a multi-prototypes sampling (MPS) is designed to select the appropriate number of multi-prototypes for data with arbitrary shapes. A theoretical proof is given to guarantee that the multi-prototypes selected by MPS can achieve a constant factor approximation to the optimal cost of the K-Means problem. Then, a merging technique, called convex merging (CM), merges the multi-prototypes to get a better local minima without k being given a priori. Specifically, CM can obtain the optimal merging and estimate the correct k. By integrating these two techniques with K-Means algorithm, the proposed MCKM is an efficient and explainable clustering algorithm for escaping the undesirable local minima of K-Means problem without given k first. Experimental results performed on synthetic and real-world data sets have verified the effectiveness of the proposed algorithm.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑