Optimal clustering by merge-based branch-and-bound

Pasi Fränti; Olli Virmajoki; Pasi Fränti; Olli Virmajoki

doi:10.3934/aci.2022004

Applied Computing and Intelligence

2022, Volume 2, Issue 1: 63-82. doi: 10.3934/aci.2022004

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Research article

Optimal clustering by merge-based branch-and-bound

Pasi Fränti ^,,
Olli Virmajoki

School of Computing, University of Eastern Finland, Joensuu, Finland

Academic Editor: Chih-Cheng Hung

Received: 18 March 2022 Accepted: 22 March 2022 Published: 31 March 2022

We present a method to construct optimal clustering via a sequence of merge steps. We formulate the merge-based clustering as a minimum redundancy search tree, and then search the optimal clustering by a branch-and-bound technique. Optimal clustering is found regardless of the objective function used. We also consider two suboptimal polynomial time variants based on the proposed branch-and-bound technique. However, all variants are slow and has merely theoretical interest. We discuss the reasons for the results.

Keywords:

Citation: Pasi Fränti, Olli Virmajoki. Optimal clustering by merge-based branch-and-bound[J]. Applied Computing and Intelligence, 2022, 2(1): 63-82. doi: 10.3934/aci.2022004

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Abstract

The journal retracts the paper entitled "Decay estimates for the wave equation with partial boundary memory damping" ^[1].

After the article was published, the authors decided to withdraw the article.

This retraction was approved by the Editor in Chief of the journal Networks and Heterogeneous Media.

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