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Degree of isomorphism: a novel criterion for identifying and classifying orthogonal designs

Author

Listed:
  • Lin-Chen Weng

    (Beijing Normal University-Hong Kong Baptist University United International College)

  • Kai-Tai Fang

    (Beijing Normal University-Hong Kong Baptist University United International College
    The Chinese Academy of Sciences)

  • A. M. Elsawah

    (Beijing Normal University-Hong Kong Baptist University United International College
    Zagazig University)

Abstract

The fundamental problem in the orthogonal design theory is the design isomorphism, which involves two classes of methods in the statistical literature. One is to identify the isomorphic designs by costly computation, another is only to detect the non-isomorphic designs as a feasible alternative. In this paper we explore the design structure to propose the degree of isomorphism, as a novel criterion showing the similarity between orthogonal designs. A column-wise framework is proposed to accommodate different issues of the design isomorphism, including the detection of non-isomorphism, identification of isomorphism and determination of subclasses for symmetric orthogonal designs. Our framework shows surprisingly high efficiency, where the average time of identifying the isomorphism between two designs in selected classes is all down to about one second. By applying the hierarchical clustering on the average linkage, a novel classification is also presented for non-isomorphic orthogonal designs in a combinatorial view.

Suggested Citation

  • Lin-Chen Weng & Kai-Tai Fang & A. M. Elsawah, 2023. "Degree of isomorphism: a novel criterion for identifying and classifying orthogonal designs," Statistical Papers, Springer, vol. 64(1), pages 93-116, February.
    • Handle: RePEc:spr:stpapr:v:64:y:2023:i:1:d:10.1007_s00362-022-01310-2
    DOI: 10.1007/s00362-022-01310-2
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    References listed on IDEAS

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    1. H. Evangelaras & C. Koukouvinos & E. Lappas, 2007. "18-run nonisomorphic three level orthogonal arrays," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 66(1), pages 31-37, July.
    2. A. M. Elsawah & Kai-Tai Fang & Xiao Ke, 2021. "New recommended designs for screening either qualitative or quantitative factors," Statistical Papers, Springer, vol. 62(1), pages 267-307, February.
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