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

Lin-Chen Weng, Kai-Tai Fang and A. M. Elsawah ()
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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
A. M. Elsawah: Beijing Normal University-Hong Kong Baptist University United International College

Statistical Papers, 2023, vol. 64, issue 1, No 5, 93-116

Abstract: 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.

Keywords: Combinatorial classification; Design isomorphism; Degree of isomorphism; Saturated orthogonal design; Non-saturated orthogonal design; 05B15; 03D15 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00362-022-01310-2

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