Multi-Prototypes Convex Merging Based K-Means Clustering Algorithm

• URL: http://arxiv.org/abs/2302.07045v1
• Date: Tue, 14 Feb 2023 13:57:33 GMT
• Title: Multi-Prototypes Convex Merging Based K-Means Clustering Algorithm
• Authors: Dong Li, Shuisheng Zhou, Tieyong Zeng, and Raymond H. Chan
• Abstract summary: Multi-prototypes convex merging based K-Means clustering algorithm (MCKM) is presented. MCKM is an efficient and explainable clustering algorithm for escaping the undesirable local minima of K-Means problem without given k first.
• Score: 20.341309224377866
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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