This paper proposes a sketching strategy based on spherical designs, which is applied to the classical spherical basis function approach for massive spherical data fitting. We conduct theoretical analysis and numerical verifications to demonstrate the feasibility of the proposed { sketching} strategy. From the theoretical side, we prove that sketching based on spherical designs can reduce the computational burden of the spherical basis function approach without sacrificing its approximation capability. In particular, we provide upper and lower bounds for the proposed { sketching} strategy to fit noisy data on spheres. From the experimental side, we numerically illustrate the feasibility of the sketching strategy by showing its comparable fitting performance with the spherical basis function approach. These interesting findings show that the proposed sketching strategy is capable of fitting massive and noisy data on spheres.
翻译:本文提出了一个基于球体设计的草图战略,适用于用于大型球体数据安装的古典球体功能法。我们进行了理论分析和数字核查,以证明拟议的{草图}战略的可行性。从理论方面看,我们证明基于球体设计的草图可以减少球体功能法的计算负担,而不会牺牲其近似能力。特别是,我们为拟议的{草图}战略提供了上下界限,以适应球体上的繁杂数据。从实验方面看,我们用数字来说明草图战略的可行性,显示其与球体功能法的相似性能。这些有趣的研究结果表明,拟议的草图战略能够适应有关球体的大规模和噪音数据。</s>