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A method for optimizing Radial Basis Function using Hierarchical Matrices

IP.com Disclosure Number: IPCOM000234970D
Publication Date: 2014-Feb-20
Document File: 2 page(s) / 88K

Publishing Venue

The IP.com Prior Art Database

Abstract

The proposed algorithm allows extending the applicability of the radial basis function (RBF) techniques by coupling the method with hierarchical matrix storage (H-Matrix).

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A method for optimizing Radial Basis Function using Hierarchical Matrices

Introduction / Summary of the Invention

The proposed algorithm allows extending the applicability of the radial basis function (RBF) techniques by coupling the method with hierarchical matrix storage (H-Matrix).

Prior Art

Multipole method is commonly used to optimize RBF

Detailed Description of Invention Including Examples

            The radial basis functions are nowadays very common tool used in a broad range of domains. They have been shown to be most useful in surface reconstruction from point cloud data, mesh repairing, mesh morphing, image processing(*), function interpolation, artificial intelligence, statistics….In geology and geophysics software, RBF can be used to model Salt surface.

            The radial basis functions and multipole: with the aim of reducing the memory and performance costs of the rbf, the method has been mixed with multipole method: the idea consists on approximating the contribution of a bunch of sources (input entries) by an approximation called kernel faster to compute. The kernel depends on the nature of the problem and might be complex to calculate.

            The radial basis functions and hierarchical matrix: Compared to multipole expansion, Hierarchical matrices rely on local low-rank approximations. In order to approximate the entire problem, it is split into a family of subproblems. Large subproblems are stored in factorized representation, while small subproblems are stored in standard representation in order to improve the efficiency.

Advantages are that (i) it does not require calculating approximant of the kernel functions by hand, (ii) it is as faster as multipole method and (iii) the memory consumption is low.

            The aim of this invention is to couple the radial basis functions (RBF) techni...