Scattered Data Interpolation: Tests of Some Method

Franke, Richard

doi:10.2307/2007474

Cited by 412 publications

(102 citation statements)

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“…As reported in the comparative studies of Franke (1982) and Jin et al (2001), different problems may require different types of metamodels. To reflect this, four different sets of 2000 Gaussian random fields have been generated for a study on the effect of metamodeling methods on the efficiency of the optimization procedure.…”

Section: Metamodeling Methodsmentioning

confidence: 99%

“…The Gaussian basis function is most frequently used, but the multiquadric basis function (Hardy 1971) has proven to have good predictive capability in several comparative studies (Franke 1982;Jin et al 2001):…”

Section: Radial Basis Functionsmentioning

confidence: 99%

“…An interpolating metamodeling method which may be adapted to account for clustering of DOE points is RBF interpolation. Good fitting capabilities for nonlinear functions have been reported for RBF interpolation in several studies (Franke 1982;Jin et al 2001). However, the uncertainty measures which have been developed for RBF are not suitable for sequential optimization.…”

Section: Introductionmentioning

confidence: 99%

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Sequential improvement for robust optimization using an uncertainty measure for radial basis functions

Havinga

Boogaard

Klaseboer

2016

Struct Multidisc Optim

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The performance of the sequential metamodel based optimization procedure depends strongly on the chosen building blocks for the algorithm, such as the used metamodeling method and sequential improvement criterion. In this study, the effect of these choices on the efficiency of the robust optimization procedure is investigated. A novel sequential improvement criterion for robust optimization is proposed, as well as an improved implementation of radial basis function interpolation suitable for sequential optimization. The leave-one-out cross-validation measure is used to estimate the uncertainty of the radial basis function metamodel. The metamodeling methods and sequential improvement criteria are compared, based on a test with Gaussian random fields as well as on the optimization of a strip bending process with five design variables and two noise variables. For this process, better results are obtained in the runs with the novel sequential improvement criterion as well as with the novel radial basis function implementation, compared to the runs with conventional sequential improvement criteria and kriging interpolation.

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Section: Metamodeling Methodsmentioning

confidence: 99%

Section: Radial Basis Functionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Sequential improvement for robust optimization using an uncertainty measure for radial basis functions

Havinga

Boogaard

Klaseboer

2016

Struct Multidisc Optim

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“…040077-3 where D is the diameter of the smallest circle containing all the collocation points [9], are taken as the values of the shape parameter of the scaled linear functions. …”

Section: Analyzing the Effectiveness Of The Application Of The Dual Rmentioning

confidence: 99%

Solving a two-dimensional nonlinear heat conduction equation with degeneration by the boundary element method with the application of the dual reciprocity method

Спевак¹,

Нефедова²

2016

AIP Conference Proceedings

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Abstract. The paper discusses the development of an algorithm for solving two-dimensional boundary value problems for a nonlinear partial parabolic differential equation with degeneration. The nonlinearity of the equation is dictated by a power law between the heat conductivity coefficient and temperature. The solution algorithm is based on the boundary element method with the application of the dual reciprocity method. The solution accuracy is analyzed for the discussed type of problems, with the application of different systems of radial basis functions. The most suitable system of functions and their parameters are determined.

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“…In addition, Micchelli showed that the problem was solvable for any conditionally positive (or negative) definite kernels among which is the mutiquadric function [20]. Some studies have shown that multiquadric interpolations tend to be more robust than interpolations based on others RBF kernels, especially than the widely used Gaussian kernel [8]. More generally the advantage of using RBF kernels is that they allow to approximate any functions or boundaries [24].…”

Section: Related Workmentioning

confidence: 99%

Reconstructing faces from their signatures using RBF regression

Mignon¹,

Jurie²

2013

Procedings of the British Machine Vision Conference 2013

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The increasing popularity of social networks raises critical issues regarding privacy and protection of personal information. One typical example -which is the motivation of the paper -is face images and face recognition, face recognition being ubiquitous on the web now. Assuming someone with bad intentions steals a database containing face signatures, would it be possible to reconstruct the corresponding face images, revealing who was in the database? Would these reconstructed images be good enough to allow them to gain access via a face recognition system? This paper brings a contribution to this topic by proposing a face reconstruction algorithm, based on RBF-regression in eigenspace, which is able to reconstruct face images from their signatures (i.e. neither knowing the identity of the persons nor their true facial appearance). We show that in addition to being visually realistic, the images generated by the proposed method can fool a state-of-the-art face recognition algorithm.

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Scattered Data Interpolation: Tests of Some Method

Cited by 412 publications

References 0 publications

Sequential improvement for robust optimization using an uncertainty measure for radial basis functions

Sequential improvement for robust optimization using an uncertainty measure for radial basis functions

Solving a two-dimensional nonlinear heat conduction equation with degeneration by the boundary element method with the application of the dual reciprocity method

Reconstructing faces from their signatures using RBF regression

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