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MichaelMaggs (talk | contribs) Adding local short description: "Type of mathematical function", overriding Wikidata description "real-valued function whose value depends only on the distance between the input and some fixed point, which forms a basis for some function space" |
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{{Short description|Type of mathematical function}}
A '''radial basis function''' ('''RBF''') is a [[real-valued function]] <math display="inline">\varphi</math> whose value depends only on the distance between the input and some fixed point, either the [[Origin (mathematics)|origin]], so that <math display="inline">\varphi(\mathbf{x}) = \hat\varphi(\left\|\mathbf{x}\right\|)</math>, or some other fixed point <math display="inline">\mathbf{c}</math>, called a ''center'', so that <math display="inline">\varphi(\mathbf{x}) = \hat\varphi(\left\|\mathbf{x}-\mathbf{c}\right\|)</math>. Any function <math display="inline">\varphi</math> that satisfies the property <math display="inline">\varphi(\mathbf{x}) = \hat\varphi(\left\|\mathbf{x}\right\|)</math> is a [[radial function]]. The distance is usually [[Euclidean distance]], although other [[distance function|metric]]s are sometimes used. They are often used as a collection <math>\{ \varphi_k \}_k</math> which forms a [[Basis (linear algebra)|basis]] for some [[function space]] of interest, hence the name.
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