Radial basis function

lastmod 2020-09-24created 2014-10-3120 edits

RBF stands for Radial Basis Function, and it can be called a radial basis function; neural network, and so on.

It is a surrogate model widely used in engineering since Hardy proposed it in 1971 for interpolating multivariate data. Compared with Kriging, RBF has the advantages of being easy to build and representing strongly nonlinear systems well. However, it has the disadvantage that the user must set the form and parameters of the basis function, and the prediction performance of RBF is sensitive to these values.

The RBF provided by PIAnO delivers robust prediction performance by automatically determining the form and parameters of the basis function best suited to the system. Also, although RBF is generally known as an interpolation model (Interpolation Model), the RBF provided by PIAnO can also be used as a regression model (Regression Model) through an option.

Radial basis function kernel

• Wikipedia (en) Description of RBF Kernel
• Kernels Part 1: What is an RBF Kernel? Really?

In machine learning, the (Gaussian) radial basis function kernel, or RBF kernel, is a popular kernel function used in support vector machine classification. ¹

The RBF kernel on two samples x and x', represented as feature vectors in some input space, is defined as²

Radial_basis_function_kernel_1.png may be recognized as the squared Euclidean distance between the two feature vectors. σ is a free parameter. An equivalent, but simpler, definition involves a parameter Radial_basis_function_kernel_2.png:

Since the value of the RBF kernel decreases with distance and ranges between zero (in the limit) and one (when x = x'), it has a ready interpretation as a similarity measure.³ The feature space of the kernel has an infinite number of dimensions; for σ= 1, its expansion is:

See also

• Support Vector Machine (SVM)
• Gamma function
• Euclidean distance
• Interpolation
• Exponential function
• Basis function

Favorite site

• Wikipedia (en) Description of RBF
• Gaussian kernel regression
• [Recommended] Image processing - Log 36 : On Radial Basis Function Interpolation Part 1 ⁴
• [Recommended] Image processing - Log 37 : On Radial Basis Function Interpolation Part 2 ⁵
• Radial basis function Networks, RBFN
• [Recommended] DOC: Mining algorithms of Intelligent Miner IV (prediction technique – Radial Basis Function) ⁶
• kernel function_matlab

References