2023/03/08 by Shao-Bo Lin, Di Wang, Lin, Shao-Bo +3
Computer Science · Engineering · Mathematics · #Advanced Multi-Objective Optimization Algorithms #Advanced Numerical Analysis Techniques #FOS: Computer and information sciences #Machine Learning (cs.LG) #Mathematical Approximation and Integration
paper · pdf · doi:10.48550/arxiv.2303.04550
openalex publication_date 2023/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.