Big Geo Data Surface Approximation using Radial Basis Functions: A Comparative Study

TL;DR

This paper compares various Compactly Supported Radial Basis Functions (CS-RBFs) for big data surface approximation, introducing a new scalable approach that leverages matrix symmetry and sparse data structures to improve computational efficiency.

Contribution

It presents a novel scalable RBF approximation method for large datasets, utilizing matrix symmetry and sparse matrices, along with a comparative analysis of CS-RBFs.

Findings

The new approach improves computational efficiency for large datasets.

Different CS-RBFs vary in approximation accuracy.

Experiments confirm the method's effectiveness on synthetic and real data.

Abstract

Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for big scattered datasets in $n-$dimensional space. It is a non-separable approximation, as it is based on the distance between two points. This method leads to the solution of an overdetermined linear system of equations. In this paper the RBF approximation methods are briefly described, a new approach to the RBF approximation of big datasets is presented, and a comparison for different Compactly Supported RBFs (CS-RBFs) is made with respect to the accuracy of the computation. The proposed approach uses symmetry of a matrix, partitioning the matrix into blocks and data structures for storage of the sparse matrix. The experiments are performed for synthetic and real datasets.