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Comparing Local Search Initialization for K-Means and K-Medoids Clustering in a Planar Pareto Front, a Computational Study

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Optimization and Learning (OLA 2021)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1443))

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Abstract

Having N points in a planar Pareto Front (2D PF), k-means and k-medoids are solvable in \(O(N^3)\) time by dynamic programming algorithms. Standard local search approaches, PAM and Lloyd’s heuristics, are investigated in the 2D PF case to solve faster large instances. Specific initialization strategies related to 2D PF cases are implemented with the generic ones (Forgy’s, Hartigans, k-means++). Applying PAM and Lloyd’s local search iterations, the quality of local minimums are compared with optimal values. Numerical results are computed using generated instances, which were made public. This study highlights that local minimums of a poor quality exist for 2D PF cases. A parallel or multi-start heuristic using four initialization strategies improves the accuracy to avoid poor local optimums. Perspectives are still open to improve local search heuristics for the specific 2D PF cases.

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Authors and Affiliations

  1. Université Paris-Saclay, LISN, 91405, Orsay, France

    Jiangnan Huang, Zixi Chen & Nicolas Dupin

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  1. Jiangnan Huang
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  2. Zixi Chen
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  3. Nicolas Dupin
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Correspondence to Nicolas Dupin .

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Editors and Affiliations

  1. University of Cádiz, Cádiz, Spain

    Bernabé Dorronsoro

  2. University of Technology of Troyes, Troyes, France

    Lionel Amodeo

  3. University of Catania, Catania, Italy

    Mario Pavone

  4. University of Cádiz, Cádiz, Spain

    Patricia Ruiz

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Huang, J., Chen, Z., Dupin, N. (2021). Comparing Local Search Initialization for K-Means and K-Medoids Clustering in a Planar Pareto Front, a Computational Study. In: Dorronsoro, B., Amodeo, L., Pavone, M., Ruiz, P. (eds) Optimization and Learning. OLA 2021. Communications in Computer and Information Science, vol 1443. Springer, Cham. https://doi.org/10.1007/978-3-030-85672-4_2

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  • DOI: https://doi.org/10.1007/978-3-030-85672-4_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-85671-7

  • Online ISBN: 978-3-030-85672-4

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