Algorithm for placement of reference points and choice of an appropriate variable shape parameter for the RBF approximation

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F20%3A43957171" target="_blank" >RIV/49777513:23520/20:43957171 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.3233/ICA-190610" target="_blank" >https://doi.org/10.3233/ICA-190610</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3233/ICA-190610" target="_blank" >10.3233/ICA-190610</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Algorithm for placement of reference points and choice of an appropriate variable shape parameter for the RBF approximation

Popis výsledku v původním jazyce

Many Radial Basis Functions (RBFs) contain a shape parameter which has an important role to ensure good quality of the RBF approximation. Determination of the optimal shape parameter is a difficult problem. In the majority of papers dealing with the RBF approximation, the shape parameter is set up experimentally or using some ad-hoc method. Moreover, the constant shape parameter is almost always used for the RBF approximation, but the variable shape parameter produces more accurate results. Several variable shape parameter methods, which are based on random strategy or on an evolutionary algorithm, have been developed. Another aspect which has an influence on the quality of the RBF approximation is the placement of reference points. A novel algorithm for finding an appropriate set of reference points and a variable shape parameter selection for the RBF approximation of functions y=f(x) (i.e. the case when a one-dimensional dataset is given and each point from this dataset is associated with a scalar value) is presented. Our approach has two steps and is based on exploiting features of the given dataset, such as extreme points or inflection points, and on comparison of the first curvature of a curve. The proposed algorithm can be used for the approximation of data describing a curve parameterized by one variable in multidimensional space, e.g. a robot path planning, etc.

Název v anglickém jazyce

Algorithm for placement of reference points and choice of an appropriate variable shape parameter for the RBF approximation

Popis výsledku anglicky

Many Radial Basis Functions (RBFs) contain a shape parameter which has an important role to ensure good quality of the RBF approximation. Determination of the optimal shape parameter is a difficult problem. In the majority of papers dealing with the RBF approximation, the shape parameter is set up experimentally or using some ad-hoc method. Moreover, the constant shape parameter is almost always used for the RBF approximation, but the variable shape parameter produces more accurate results. Several variable shape parameter methods, which are based on random strategy or on an evolutionary algorithm, have been developed. Another aspect which has an influence on the quality of the RBF approximation is the placement of reference points. A novel algorithm for finding an appropriate set of reference points and a variable shape parameter selection for the RBF approximation of functions y=f(x) (i.e. the case when a one-dimensional dataset is given and each point from this dataset is associated with a scalar value) is presented. Our approach has two steps and is based on exploiting features of the given dataset, such as extreme points or inflection points, and on comparison of the first curvature of a curve. The proposed algorithm can be used for the approximation of data describing a curve parameterized by one variable in multidimensional space, e.g. a robot path planning, etc.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/GA17-05534S" target="_blank" >GA17-05534S: Meshless metody pro vizualizaci velkých časově-prostorových vektorových dat</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Integrated Computer-Aided Engineering

ISSN

1069-2509

e-ISSN

—

Svazek periodika

27

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

15

Strana od-do

1-15

Kód UT WoS článku

000500958600001

EID výsledku v databázi Scopus

2-s2.0-85076343808