Degree of isomorphism: a novel criterion for identifying and classifying orthogonal designs
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 alterna...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Weng, Lin-Chen [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2022 |
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| Anmerkung: |
© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022 |
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Enthalten in: Statistical papers - Springer Berlin Heidelberg, 1988, 64(2022), 1 vom: 24. Apr., Seite 93-116 |
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volume:64 ; year:2022 ; number:1 ; day:24 ; month:04 ; pages:93-116 |
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10.1007/s00362-022-01310-2 |
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| 520 | |a 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. | ||
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10.1007/s00362-022-01310-2 doi (DE-627)OLC2133490809 (DE-He213)s00362-022-01310-2-p DE-627 ger DE-627 rakwb eng 300 330 510 VZ Weng, Lin-Chen verfasserin aut Degree of isomorphism: a novel criterion for identifying and classifying orthogonal designs 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022 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. Combinatorial classification Design isomorphism Degree of isomorphism Saturated orthogonal design Non-saturated orthogonal design Fang, Kai-Tai aut Elsawah, A. M. (orcid)0000-0001-6116-4779 aut Enthalten in Statistical papers Springer Berlin Heidelberg, 1988 64(2022), 1 vom: 24. Apr., Seite 93-116 (DE-627)129572292 (DE-600)227641-0 (DE-576)015069486 0932-5026 nnns volume:64 year:2022 number:1 day:24 month:04 pages:93-116 https://doi.org/10.1007/s00362-022-01310-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_2018 GBV_ILN_4277 GBV_ILN_4326 AR 64 2022 1 24 04 93-116 |
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10.1007/s00362-022-01310-2 doi (DE-627)OLC2133490809 (DE-He213)s00362-022-01310-2-p DE-627 ger DE-627 rakwb eng 300 330 510 VZ Weng, Lin-Chen verfasserin aut Degree of isomorphism: a novel criterion for identifying and classifying orthogonal designs 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022 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. Combinatorial classification Design isomorphism Degree of isomorphism Saturated orthogonal design Non-saturated orthogonal design Fang, Kai-Tai aut Elsawah, A. M. (orcid)0000-0001-6116-4779 aut Enthalten in Statistical papers Springer Berlin Heidelberg, 1988 64(2022), 1 vom: 24. Apr., Seite 93-116 (DE-627)129572292 (DE-600)227641-0 (DE-576)015069486 0932-5026 nnns volume:64 year:2022 number:1 day:24 month:04 pages:93-116 https://doi.org/10.1007/s00362-022-01310-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_2018 GBV_ILN_4277 GBV_ILN_4326 AR 64 2022 1 24 04 93-116 |
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10.1007/s00362-022-01310-2 doi (DE-627)OLC2133490809 (DE-He213)s00362-022-01310-2-p DE-627 ger DE-627 rakwb eng 300 330 510 VZ Weng, Lin-Chen verfasserin aut Degree of isomorphism: a novel criterion for identifying and classifying orthogonal designs 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022 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. Combinatorial classification Design isomorphism Degree of isomorphism Saturated orthogonal design Non-saturated orthogonal design Fang, Kai-Tai aut Elsawah, A. M. (orcid)0000-0001-6116-4779 aut Enthalten in Statistical papers Springer Berlin Heidelberg, 1988 64(2022), 1 vom: 24. Apr., Seite 93-116 (DE-627)129572292 (DE-600)227641-0 (DE-576)015069486 0932-5026 nnns volume:64 year:2022 number:1 day:24 month:04 pages:93-116 https://doi.org/10.1007/s00362-022-01310-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_2018 GBV_ILN_4277 GBV_ILN_4326 AR 64 2022 1 24 04 93-116 |
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10.1007/s00362-022-01310-2 doi (DE-627)OLC2133490809 (DE-He213)s00362-022-01310-2-p DE-627 ger DE-627 rakwb eng 300 330 510 VZ Weng, Lin-Chen verfasserin aut Degree of isomorphism: a novel criterion for identifying and classifying orthogonal designs 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022 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. Combinatorial classification Design isomorphism Degree of isomorphism Saturated orthogonal design Non-saturated orthogonal design Fang, Kai-Tai aut Elsawah, A. M. (orcid)0000-0001-6116-4779 aut Enthalten in Statistical papers Springer Berlin Heidelberg, 1988 64(2022), 1 vom: 24. Apr., Seite 93-116 (DE-627)129572292 (DE-600)227641-0 (DE-576)015069486 0932-5026 nnns volume:64 year:2022 number:1 day:24 month:04 pages:93-116 https://doi.org/10.1007/s00362-022-01310-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_2018 GBV_ILN_4277 GBV_ILN_4326 AR 64 2022 1 24 04 93-116 |
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10.1007/s00362-022-01310-2 doi (DE-627)OLC2133490809 (DE-He213)s00362-022-01310-2-p DE-627 ger DE-627 rakwb eng 300 330 510 VZ Weng, Lin-Chen verfasserin aut Degree of isomorphism: a novel criterion for identifying and classifying orthogonal designs 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022 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. Combinatorial classification Design isomorphism Degree of isomorphism Saturated orthogonal design Non-saturated orthogonal design Fang, Kai-Tai aut Elsawah, A. M. (orcid)0000-0001-6116-4779 aut Enthalten in Statistical papers Springer Berlin Heidelberg, 1988 64(2022), 1 vom: 24. Apr., Seite 93-116 (DE-627)129572292 (DE-600)227641-0 (DE-576)015069486 0932-5026 nnns volume:64 year:2022 number:1 day:24 month:04 pages:93-116 https://doi.org/10.1007/s00362-022-01310-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_2018 GBV_ILN_4277 GBV_ILN_4326 AR 64 2022 1 24 04 93-116 |
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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. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022 |
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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. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022 |
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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. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022 |
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Degree of isomorphism: a novel criterion for identifying and classifying orthogonal designs |
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Fang, Kai-Tai Elsawah, A. M. |
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