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Uniform Design on Manifold

In: Contemporary Experimental Design, Multivariate Analysis and Data Mining

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  • Yu Tang

    (Soochow University, School of Mathematical Science)

Abstract

Uniform design aims to scatter points as evenly as possible on certain domain. Although in real applications, the experimental domain is often quite arbitrary, the discrepancies frequently used to measure the uniformity of experimental designs are often defined on the unit cube. In this paper, we will introduce a unified framework to measure the uniformity of an experimental design on manifold. We will give some examples to illustrate the construction of uniform designs on some specific manifolds and provide a stochastic algorithm to construct uniform designs on the unit semi-spherical surface and on the unit spherical surface. Numerical results show that the algorithm performs well.

Suggested Citation

  • Yu Tang, 2020. "Uniform Design on Manifold," Springer Books, in: Jianqing Fan & Jianxin Pan (ed.), Contemporary Experimental Design, Multivariate Analysis and Data Mining, chapter 0, pages 177-186, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-46161-4_11
    DOI: 10.1007/978-3-030-46161-4_11
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