Radial Basis Functions for High-Dimensional Visualization

Abstract

High-dimensional visualization is usually connected with large data processing. Because of dimensionality, it is nearly impossible to make a tessellation, like the Delaunay tessellation in Ed, followed by data interpolation. One possibility of data interpolation is the use of the Radial Basis Functions (RBF) interpolation. The RBF interpolation supports the interpolation of scattered data in d-dimensional space. The computational cost of the RBF interpolation is higher but does not increase significantly with the data dimensionality. It increases with the number of values to be processed non-linearly. In this paper, the RBF interpolation properties will be discussed as well as how to process data incrementally. Incremental computation decreases computational complexity and decreases RBF computational cost for the given data set significantly, especially for the visualization purposes, when the interpolated/approximated data are used many times. As the proposed approach is based on a solution of a system of linear equations, the RBF interpolation is convenient especially for data sets processing using matrix-vector or GPU architectures.