A forward k-means algorithm for regression clustering

We propose a novel forward k-means algorithm for regression clustering, where the “forward” strategy progressively partitions samples from a single cluster into multiple ones, using the current optimal clustering solutions as initialization for subsequent iterations, thereby ensuring a deterministic...

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Bibliographic Details
Published in:	Information sciences Vol. 711; p. 122105
Main Authors:	Lu, Jun, Luo, Tingjin, Li, Kai
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 01.09.2025
Subjects:	Forward k-means algorithm Partition optimization Regression clustering Forward k-means algorithm Regression clustering Partition optimization
ISSN:	0020-0255
Online Access:	Get full text
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Summary:	We propose a novel forward k-means algorithm for regression clustering, where the “forward” strategy progressively partitions samples from a single cluster into multiple ones, using the current optimal clustering solutions as initialization for subsequent iterations, thereby ensuring a deterministic result without any initialization requirements. We employ the mean squared error from the fitted clustering results as a criterion to guide partition optimization, which not only ensures rapid convergence of the algorithm to a stable solution but also yields desirable theoretical results. Meanwhile, we also suggest a difference-based threshold ridge ratio criterion to consistently determine the number of clusters. Comprehensive numerical studies are further conducted to demonstrate the algorithm's efficacy. •Forward k-means algorithm ensures deterministic clustering results.•MSE guides partition optimization for rapid convergence.•DTRR criterion consistently estimates the number of clusters.
ISSN:	0020-0255
DOI:	10.1016/j.ins.2025.122105