Multi-Prototypes Convex Merging Based K-Means Clustering Algorithm

doi:10.1109/TKDE.2023.3342209

Multi-Prototypes Convex Merging Based K-Means Clustering Algorithm

2024-11-01

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DOI：10.1109/TKDE.2023.3342209

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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. 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. Two theoretical proofs are given to guarantee that the cost of MCKM (MPS+CM) can achieve a constant factor approximation to the optimal cost of the K-Means problem. Experimental results performed on synthetic and real-world data sets have verified the effectiveness of the proposed algorithm.

Keywords:

Clustering algorithms

Prototypes

Merging

Partitioning algorithms

Approximation algorithms

Costs

Shape

Convex merging

K-means

multi-prototypes

multi-prototypes sampling

Multi-Prototypes Convex Merging Based K-Means Clustering Algorithm

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