In mathematics, a basis function is an element of a particular basis for a function space. Every function in the function space can be represented as...

In mathematics a radial basis function (RBF) is a real-valued function φ {\textstyle \varphi } whose value depends only on the distance between the input...

In machine learning, the radial basis function kernel, or RBF kernel, is a popular kernel function used in various kernelized learning algorithms. In particular...

modeling, a radial basis function network is an artificial neural network that uses radial basis functions as activation functions. The output of the...

Radial basis function (RBF) interpolation is an advanced method in approximation theory for constructing high-order accurate interpolants of unstructured...

square-integrable functions cannot be represented as finite linear combinations of these basis functions, which therefore do not comprise a Hamel basis. Every Hamel...

computational chemistry, a basis set is a set of functions (called basis functions) that is used to represent the electronic wave function in the Hartree–Fock...

"square-shaped" functions which together form a wavelet family or basis. Wavelet analysis is similar to Fourier analysis in that it allows a target function over...

Raviart–Thomas basis functions are vector basis functions used in finite element and boundary element methods. They are regularly used as basis functions when working...

the basis function of degree one is a triangle function. It rises from zero to one, then falls to zero again. While it rises, the basis function of the...

and a put option Basis function Basis (linear algebra) Dual basis Orthonormal basis Schauder basis Basis (universal algebra) Basis of a matroid Generating...

In machine learning, a Hyper basis function network, or HyperBF network, is a generalization of radial basis function (RBF) networks concept, where the...

automatic basis function construction, also known as basis discovery, is a technique that finds a set of general-purpose (task-independent) basis functions to...

a basis wave function. If spin is taken into account, there are two basis functions for each triple. The function space thus has a countable basis. The...

radial basis functions. Given a set of control points { c i , i = 1 , 2 , … , K } {\displaystyle \{c_{i},i=1,2,\ldots ,K\}} , a radial basis function defines...

chooses basis functions. We used piecewise linear basis functions in our discussion, but it is common to use piecewise polynomial basis functions. Separate...

combination of pre-defined basis functions; generally, the coefficients of these basis functions are the sought unknowns. Green's functions and Galerkin method...

the function space has an orthonormal basis given by the set of functions {u1(t), u2(t), …, un(t)}, where n may be infinite. For the orthonormal basis, ⟨...

processing and statistics, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside...

multivariate function whose variables are the coordinates on some basis of the vector on which the function is applied. When the basis is changed, the...

quantum chemistry to form basis sets. Gaussian functions arise by composing the exponential function with a concave quadratic function: f ( x ) = exp ⁡ ( α...

of functions related to Fourier analysis. Such transformations map a function to a set of coefficients of basis functions, where the basis functions are...

empirical orthogonal function (EOF) analysis is a decomposition of a signal or data set in terms of orthogonal basis functions which are determined from...

space of functions in which point evaluation is a continuous linear functional. Specifically, a Hilbert space H {\displaystyle H} of functions from a set...

line in the formula for ozone above is one basis function multiplied by its coefficient. Each basis function B i ( x ) {\displaystyle B_{i}(x)} takes one...

radial basis function (RBF, also called a kernel function) is applied to the distance to compute the weight (influence) for each neuron. The radial basis function...

functions are orthogonal over the sphere in the continuous case. Thus they can also be thought of as a generalized Fourier series in which the basis functions...

function ψ ∈ L 2 ( R ) {\displaystyle \psi \,\in \,L^{2}(\mathbb {R} )} is called an orthonormal wavelet if it can be used to define a Hilbert basis,...

base band. Hence, the signal space can be represented by the single basis function ϕ ( t ) = 2 T b cos ⁡ ( 2 π f t ) {\displaystyle \phi (t)={\sqrt {\frac...

proto-value functions (PVFs) are automatically learned basis functions that are useful in approximating task-specific value functions, providing a compact...