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Machine learning kernel function
In machine learning, the radial basis function kernel, or RBF kernel, is a popular kernel function used in various kernelized learning algorithms. In particular
Radial_basis_function_kernel
Type of mathematical function
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
Radial_basis_function
Type of artificial neural network
mathematical 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_network
In functional analysis, a Hilbert space
In functional analysis, a reproducing kernel Hilbert space (RKHS) is a Hilbert space of functions in which point evaluation is a continuous linear functional
Reproducing kernel Hilbert space
Reproducing_kernel_Hilbert_space
Machine learning technique
feature matrices of size O ( D N ) {\textstyle O(DN)} . The radial basis function (RBF) kernel on two samples x i , x j ∈ R d {\displaystyle x_{i},x_{j}\in
Random_feature
k} K ( x , x k ) {\displaystyle K(x,x_{k})} is the Radial basis function kernel (Gaussian kernel) as formulated below. K ( x , x k ) = e − d k / 2 σ
General regression neural network
General_regression_neural_network
Class of algorithms for pattern analysis
recognition. Fisher kernel Graph kernels Kernel smoother Polynomial kernel Radial basis function kernel (RBF) String kernels Neural tangent kernel Neural network
Kernel_method
Method in approximation theory
Radial basis function (RBF) interpolation is an advanced method in approximation theory for constructing high-order accurate interpolants of unstructured
Radial basis function interpolation
Radial_basis_function_interpolation
Mathematical function
with kernel methods to cluster the patterns in the feature space. Bell-shaped function Cauchy distribution Normal distribution Radial basis function kernel
Gaussian_function
Machine learning technique
test case from the neuron's center point and then applies the radial basis function kernel using the sigma values. For PNN there is one pattern neuron for
Probabilistic_neural_network
Overview of and topical guide to machine learning
R (programming language) Rada Mihalcea Rademacher complexity Radial basis function kernel Rand index Random indexing Random projection Random subspace
Outline_of_machine_learning
Generalized function whose value is zero everywhere except at zero
integration against a kernel K z ( ζ ) {\displaystyle K_{z}(\zeta )} , the Bergman kernel. This kernel is the analog of the delta function in this Hilbert space
Dirac_delta_function
Topics referred to by the same term
railway marshalling yard in Germany Radial basis function in mathematics Radial basis function kernel or RBF kernel Random Block File, an OS-9 file manager
RBF
Generalization of a positive-definite matrix
a branch of mathematics, a positive-definite kernel is a generalization of a positive-definite function or a positive-definite matrix. It was first introduced
Positive-definite_kernel
Method of data interpolation and smoothing
\{w_{i}\}} is a set of mapping coefficients. The TPS corresponds to the radial basis kernel φ ( r ) = r 2 log r {\displaystyle \varphi (r)=r^{2}\log r} . Suppose
Thin_plate_spline
Approximations used in machine learning
Nyström method Support vector machine Radial basis function kernel Regularized least squares Andreas Müller (2012). Kernel Approximations for Efficient SVMs
Low-rank matrix approximations
Low-rank_matrix_approximations
Class of nonparametric methods
\|f\|_{\mathcal {H}}\leq 1} (as is the case for the widely used radial basis function kernels), then with probability at least 1 − δ {\displaystyle 1-\delta
Kernel embedding of distributions
Kernel_embedding_of_distributions
Artificial neural network node function
special class of activation functions known as radial basis functions (RBFs) are used in RBF networks. These activation functions can take many forms, but
Activation_function
Type of feedforward neural network
activation functions have been proposed, including the rectifier and softplus functions. More specialized activation functions include radial basis functions (used
Multilayer_perceptron
Tool in multivariate statistical analysis
statistics, the Matérn covariance, also called the Matérn kernel, is a covariance function used in spatial statistics, geostatistics, machine learning
Matérn_covariance_function
Classification of Artificial Neural Networks (ANNs)
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
Types of artificial neural networks
Types_of_artificial_neural_networks
Function used in signal processing
two-dimensional window function is shared by its two-dimensional Fourier transform. The difference between the separable and radial forms is akin to the
Window_function
Set of methods for supervised statistical learning
sparse-kernel model identical in functional form to SVM Sequential minimal optimization Space mapping Winnow (algorithm) Radial basis function network
Support_vector_machine
Population balance equation in statistical physics
less from curse of dimensionality. Approximation based on Gaussian radial basis functions has been successfully applied to the coagulation equation in more
Smoluchowski coagulation equation
Smoluchowski_coagulation_equation
Differential operator in mathematics
{1}{r^{N-1}}}{\frac {d}{dr}}\left(r^{N-1}F'(r)\right).} Thus every radial harmonic function on an annulus in R N {\displaystyle \mathbf {R} ^{N}} has the form
Laplace_operator
Mathematical description of quantum state
\theta ,\phi )=R(r)\,\,Y_{\ell }^{m}\!(\theta ,\phi )} where R are radial functions and Ym ℓ(θ, φ) are spherical harmonics of degree ℓ and order m. This
Wave_function
American physical chemist (born 1966)
"Incorporation of Nuclear Quantum effects in electronic structure," Radial basis function kernel, a gaussian algorithm used to support vector machines, is applied
Sharon_Hammes-Schiffer
Special mathematical functions defined on the surface of a sphere
spherical harmonics form a complete set of orthogonal functions and thus an orthonormal basis, certain functions defined on the surface of a sphere can be written
Spherical_harmonics
{\displaystyle K(x,x_{i})=\left({1+x_{i}^{T}x/c}\right)^{d},} Radial basis function RBF kernel : K ( x , x i ) = exp ( − ‖ x − x i ‖ 2 / σ 2 ) , {\displaystyle
Least-squares support vector machine
Least-squares_support_vector_machine
Type of vector space in math
Masaharu; Tanaka, Kiyoki (2017), "Harmonic Bergman kernels and Toeplitz operators on the ball with radial measures", Rev. Roumaine Math. Pures Appl., 62 (1):
Hilbert_space
Computational method for solving partial differential equations
collocation with radial basis functions," Computational Mechanics, vol. 26, pp. 333–343, 2000. W. Chen, "New RBF Collocation Methods and Kernel RBF with Applications:
Kansa_method
Type of artificial neural network
activation functions have been proposed, including the rectifier and softplus functions. More specialized activation functions include radial basis functions (used
Feedforward_neural_network
Algorithm for reducing the dimension of tensors
shown in 2020 to work even for high degree polynomials and radial basis function kernels. Assume we have two large datasets, represented as matrices
Tensor_sketch
Methods in numerical analysis not requiring knowledge of neighboring points
interpolation method (S-PIM) (2005). Meshfree local radial point interpolation method (RPIM). Local radial basis function collocation Method (LRBFCM) Viscous vortex
Meshfree_methods
Concept within complex analysis
is in Lp(T). The function F defined on the unit disk by F(reiθ) = (f ∗ Pr)(eiθ) is harmonic, and M f is the radial maximal function of F. When M f belongs
Hardy_space
}_{j}\right)}^{2}\right)} is directly modeled as a linear combination of radial basis function kernels, where γ {\displaystyle \gamma } is the shared precision parameter
Shrinkage Fields (image restoration)
Shrinkage_Fields_(image_restoration)
Property of a model
noise sample. We want to find a function f ^ ( x ; D ) {\displaystyle {\hat {f}}\!(x;D)} , that approximates the true function f ( x ) {\displaystyle f(x)}
Bias–variance_tradeoff
Cluster analysis problem
one non-zero element. Kernel matrix defines the proximity of the input information. For example, in Gaussian radial basis function, it determines the dot
Determining the number of clusters in a data set
Determining_the_number_of_clusters_in_a_data_set
Italian mathematician and professor
mainly with interpolation and approximation of functions and data by polynomials and radial basis functions (RBFs)). Stefano De Marchi studied a Bachelor's
Stefano_De_Marchi
Projection of data onto lower-dimensional manifolds
to the embedded space. The mappings in NeuroScale are based on radial basis function networks. Gaussian process latent variable models (GPLVM) are probabilistic
Nonlinear dimensionality reduction
Nonlinear_dimensionality_reduction
Method of interpolation
Gaussian process Multivariate interpolation Nonparametric regression Radial basis function interpolation Space mapping Spatial dependence Variogram Gradient-enhanced
Kriging
Mathematical transform that expresses a function of time as a function of frequency
the complex-exponential kernel of both the forward and the reverse transform. The signs must be opposites. A measurable function f : R → C {\displaystyle
Fourier_transform
Statistics concept
polynomial basis-functions are used along with new basis functions, such as splines, radial basis functions, and wavelets. These families of basis functions offer
Polynomial_regression
Role of coherent states
{\displaystyle f\,} is an analytic function on the domain D {\displaystyle {\mathcal {D}}} . The reproducing kernel associated to these coherent states
Coherent states in mathematical physics
Coherent_states_in_mathematical_physics
employs the double layer potentials from the potential theory as its basis/kernel functions. Like the method of fundamental solutions (MFS), the numerical solution
Regularized_meshless_method
Matrix decomposition
in a complex system which is to be modeled. SVD was coupled with radial basis functions to interpolate solutions to three-dimensional unsteady flow problems
Singular_value_decomposition
(prob/stats related court case) Radar chart Rademacher distribution Radial basis function network Raikov's theorem Raised cosine distribution Ramaswami's
List_of_statistics_articles
Process of calculating the causal factors that produced a set of observations
{\displaystyle w(x,y)} a known weighting function. Comparing this equation with the Fredholm integral above, we notice that the kernel K ( x , y ) {\displaystyle K(x
Inverse_problem
Type of MRI
from machine learning (ML) or deep learning (DL). A nonlinear kernel, or mapping function, can be developed from the ACS to fill in k-space data and generate
Real-time_MRI
Solutions to Laplace's equation
expressed in cylindrical coordinates, ρ (radial coordinate), φ (polar angle), and z (height). Each function Vn(k) is the product of three terms, each
Cylindrical_harmonics
Prediction of digital video quality
SSIM (cSSIM) has been introduced and studied in the context of radial basis function interpolation. SSIMULACRA and SSIMULACRA2 are variants of SSIM developed
Structural similarity index measure
Structural_similarity_index_measure
Quantum mechanical model
diatomic molecule Bertrand's theorem – Physics theorem Mehler kernel – Complex-valued function Molecular vibration – Periodic motion of the atoms of a molecule
Quantum_harmonic_oscillator
index 0. The kernel of ∆ in H1(T2) consists of constant functions and none of these except zero vanish on the boundary of Ω. Hence the kernel of H1 0(Ω)
Sobolev spaces for planar domains
Sobolev_spaces_for_planar_domains
Computational model used in machine learning
visual recognition problems, which became known as "deep learning". Radial basis function and wavelet networks were introduced in 2013. These can be shown
Neural network (machine learning)
Neural_network_(machine_learning)
solutions by singular boundary method", Eng Anal Bound Elem 2012;36(8): 117–82. Kernel distance functions and radial basis functions Singular Boundary Method
Singular_boundary_method
Technique in mathematical modeling
for unsteady fluid flow using proper orthogonal decomposition and radial basis functions". Applied Mathematical Modelling. 37 (20–21): 8930–8945. doi:10
Model_order_reduction
Vector quantization algorithm minimizing the sum of squared deviations
distance through a Gaussian RBF, obtains the hidden layer of a radial basis function network. This use of k-means has been successfully combined with
K-means_clustering
Representation of the symmetry group of spacetime in special relativity
)} . Its kernel must in particular take the identity matrix to itself, A†IA = A†A = I and therefore A† = A−1. Thus AX = XA for A in the kernel so, by Schur's
Representation theory of the Lorentz group
Representation_theory_of_the_Lorentz_group
Representation theory
Harish-Chandra. The Plancherel theorem gives the eigenfunction expansion of radial functions for the Laplacian operator on the associated symmetric space X; it
Plancherel theorem for spherical functions
Plancherel_theorem_for_spherical_functions
Mathematical concept
defined and given by convolution by the kernel Qr. This defines Hf inside |z| < 1. To show that Hf has a radial limit for almost all angles, consider F
Singular integral operators of convolution type
Singular_integral_operators_of_convolution_type
Paradigm in machine learning that uses no classification labels
topographic map Meta-learning (computer science) Multivariate analysis Radial basis function network Weak supervision Wu, Wei. "Unsupervised Learning" (PDF)
Unsupervised_learning
Type of random mathematical object
Mikhailov and T. Averina. Statistical modeling of inhomogeneous random functions on the basis of poisson point fields. In Doklady Mathematics, volume 82, pages
Poisson_point_process
2015). "DisPredict: A Predictor of Disordered Protein using Optimized RBF Kernel, content and profiles". PLOS ONE. 10 (10) e0141551. doi:10.1371/journal
List of disorder prediction software
List_of_disorder_prediction_software
Hyperparameter optimization framework
vector machines (SVM): regularization parameter (C), kernel type (e.g., linear, radial basis function), and gamma (gamma). K-nearest neighbors (KNN): number
Optuna
weighting Radial basis function (RBF) — a function of the form ƒ(x) = φ(|x−x0|) Polyharmonic spline — a commonly used radial basis function Thin plate
List of numerical analysis topics
List_of_numerical_analysis_topics
Algorithm for measuring similarity between temporal sequences
and monotonicity of time warp functions may be obtained for instance by integrating a time-varying radial basis function, thus being a one-dimensional
Dynamic_time_warping
List of concepts in artificial intelligence
radial basis function network In the field of mathematical modeling, a radial basis function network is an artificial neural network that uses radial
Glossary of artificial intelligence
Glossary_of_artificial_intelligence
Set of learning techniques in machine learning
clusters as features, perhaps after transforming them through a radial basis function (a technique that has been used to train RBF networks). Coates and
Feature_learning
Part of spectral theory
Mehler–Fock transform. The corresponding ordinary differential operator is the radial part of the Laplacian operator on 2-dimensional hyperbolic space. More generally
Spectral theory of ordinary differential equations
Spectral_theory_of_ordinary_differential_equations
Reproductive structure in plants
zone begins to lignify, while the cells of the outer epidermis enlarge radially and their walls thicken, with nucleus and cytoplasm compressed into the
Seed
American mathematician
Charles A. (1992). "Approximation by superposition of sigmoidal and radial basis functions". Advances in Applied Mathematics. 13 (3): 350–373. doi:10
Charles_Anthony_Micchelli
Non-self-adjoint compact operator used to solve boundary value problems for the Laplacian
adjoint kernel of K: K ∗ ( z , w ) = K ( w , z ) . {\displaystyle \displaystyle {K^{*}(z,w)=K(w,z).}} The kernel K* extends naturally to a smooth function on
Neumann–Poincaré_operator
Transform in signal processing
1117/12.57676. introduces Logon Expectation Maximization (LEM) and Radial Basis Functions (RBF) in Time–Frequency space. Osaka Kyoiku, Gabor, wavelet and
Chirplet_transform
Feature descriptor used in computer vision
filtering the color or intensity data of the image with the following filter kernels: [ − 1 , 0 , 1 ] and [ − 1 , 0 , 1 ] ⊤ . {\displaystyle [-1,0,1]{\text{
Histogram of oriented gradients
Histogram_of_oriented_gradients
Ocean shape without winds and tides
least-squares collocation (LSC), fuzzy logic, artificial neural networks, radial basis functions (RBF), and geostatistical techniques. Geostatistical approach has
Geoid
Integrated circuit reliability metric
low-rank tensor approximations, Bayesian neural networks, and radial basis function networks. Although much research has focused on accurate yield estimation
Yield_(metric)
Interdisciplinary field of study
tree Random forest k-nearest neighbors Naïve Bayesian networks Radial basis function network Gaussian process Decision table Alternating decision tree
Astroinformatics
Construct allowing differentiation of tangent vector fields of manifolds
derivatives to obtain differential 1-forms with values in Rn. Since the functions εi yield a basis for Rn at each point of FA, these 1-forms must be expressible
Affine_connection
balanced and radial set. Then { 1 n V : n = 1 , 2 , … } {\displaystyle \left\{{\tfrac {1}{n}}V:n=1,2,\ldots \right\}} is a neighborhood basis at the origin
Auxiliary_normed_space
is dependent only on the distance from a nucleus. The choice of the radial function used to describe this electron density is arbitrary, granted that its
Multipole_density_formalism
Gravitational deflection of light
}\left(1-{\frac {r^{\prime }}{r}}\right)W(r^{\prime })} is the lensing kernel, which defines the efficiency of lensing for a distribution of sources W
Weak_gravitational_lensing
Type of diagnosis assisted by computers
Cascade classifier Naive Bayes classifier Artificial neural network Radial basis function network (RBF) Support vector machine (SVM) Principal component analysis
Computer-aided_diagnosis
Software for understanding biological data
perform this identification. The most commonly used methods are radial basis function networks, deep learning, Bayesian classification, decision trees
Machine learning in bioinformatics
Machine_learning_in_bioinformatics
Group representation
happen that the kernel of Π : G ~ → GL ( V ) {\displaystyle \Pi :{\tilde {G}}\rightarrow \operatorname {GL} (V)} contains the kernel of p {\displaystyle
Representation_of_a_Lie_group
Electro-mechanical data storage device
firmware modifications, in eight parts, going as far as booting a Linux kernel on an ordinary HDD controller board Hiding Data in Hard Drive's Service
Hard_disk_drive
Perceiving the motion of a biological agent
such that u 0 {\displaystyle u_{0}} is the center of the radial basis function for each neuron and C {\displaystyle C} is a diagonal matrix which
Biological_motion_perception
Artificial neural network that mimics neurons
implemented models of local receptive fields combining the properties of radial basis functions and spiking neurons to convert input signals having a floating-point
Spiking_neural_network
Class of instruments
particle radius, m is the complex refractive index, and ? are the kernel functions which summarize the size, shape and composition of particles. The non-linear
Atmospheric_lidar
Formalism in string theory
insertion with no kernel. It is not clear if such insertions are in any way better than midpoint insertions with non-trivial kernels. Covariant closed
String_field_theory
File format used to present documents
on May 2, 2014. Adobe Systems, PDF Reference, pp. 39–40. "com.itextpdf.kernel.pdf Documentation Differences". api.itextpdf.com. Retrieved June 25, 2025
Chronological list of advances
show. 1922 Radial arm saw A radial arm saw has a circular saw mounted on a sliding horizontal arm. In addition to making length cuts a radial arm saw may
Timeline of United States inventions (1890–1945)
Timeline_of_United_States_inventions_(1890–1945)
Technique in computational quantum field theory
irreducible off-energy-shell amplitudes serve as the kernels of equations for the light-front wave functions. The latter ones are found from these equations
Light_front_quantization
May 14–16. 410 NP Koohzare, A., P. Vaníček and M. Santos 2006 Radial basis functions fitting methods as applied to determine postglacial tilt in the
List_of_works_by_Petr_Vaníček
Set that can be "inflated" to reach any point
always include any given point of the vector space. Alternative terms are radial or absorbent set. Every neighborhood of the origin in every topological
Absorbing_set
RADIAL BASIS-FUNCTION-KERNEL
RADIAL BASIS-FUNCTION-KERNEL
Boy/Male
Greek American English
Royal. Kingly. St Basil the Great was Bishop of Caesarea in the latter half of the 4th century....
Boy/Male
Hindu
Basil, Goddess Radha, Tulsi
Boy/Male
Greek
Royal. Kingly. St Basil the Great was Bishop of Caesarea in the latter half of the 4th century....
Boy/Male
Indian
Friction
Girl/Female
Tamil
Basil, Radha, Holy
Male
English
 English form of French Basile, BASIL means "king." Also sometimes given as an herb name.
Boy/Male
Hindu
King, Basil the herb
Male
English
Medieval form of English Randolf, RANDAL means "shield-wolf."
Girl/Female
Hindu
Basil, Radha, Holy
Boy/Male
Tamil
Basil, Goddess Radha, Tulsi
Girl/Female
Hindu
Basil, Radha, Holy
Girl/Female
Gujarati, Hindu, Indian, Jain, Marathi, Mythological, Oriya, Sanskrit, Sindhi, Traditional
Basil; Goddess Radha; Tulsi
Female
Hebrew
 Variant spelling of Hebrew Basya, BASIA means "daughter of God."
Boy/Male
Buddhist, Indian, Japanese
Mysterious Function
Boy/Male
Hindu, Indian
God's Kindness
Male
English
Variant spelling of English Gaddiel, GADIEL means "God is my fortune."Â
Girl/Female
Tamil
Basil, Radha, Holy
Female
Serbian
(Радмила) Feminine form of Serbian Radmilo, RADMILA means "happy favor."
Girl/Female
Assamese, Christian, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Mythological, Oriya, Sanskrit, Sindhi, Telugu, Traditional
Basil; Tulsi; Goddess Radha
Boy/Male
Muslim
King, Basil the herb (1)
RADIAL BASIS-FUNCTION-KERNEL
RADIAL BASIS-FUNCTION-KERNEL
Male
Irish
Irish Gaelic name derived from the vocabulary word art, ART means "bear" and "champion." In Irish legend, this is the name of a son of Conn of the Hundred Battles. Compare with another form of Art.
Girl/Female
Greek
Wise.
Boy/Male
Indian
Conqueror, Victory
Girl/Female
Tamil
Kanaklata | காநகலதா
Golden creeper
Boy/Male
Hindu, Indian, Marathi
Wise
Boy/Male
Hindu, Indian, Malayalam, Marathi, Sanskrit, Telugu
Rising with Glory
Girl/Female
Hindu, Indian, Sanskrit, Tamil
Free; Attaining Moksham; Goddess Lakshmi
Boy/Male
Gujarati, Hindu, Indian, Modern
Lord Shiva
Male
English
Lame
Male
Hindi/Indian
Modern form of Hindi Krishna, KISHAN means "the black" and "the blue."
RADIAL BASIS-FUNCTION-KERNEL
RADIAL BASIS-FUNCTION-KERNEL
RADIAL BASIS-FUNCTION-KERNEL
RADIAL BASIS-FUNCTION-KERNEL
RADIAL BASIS-FUNCTION-KERNEL
n.
A radical quantity. See under Radical, a.
n.
The appropriate action of any special organ or part of an animal or vegetable organism; as, the function of the heart or the limbs; the function of leaves, sap, roots, etc.; life is the sum of the functions of the various organs and parts of the body.
n.
The things sold by auction or put up to auction.
a.
Pertaining to the function of an organ or part, or to the functions in general.
pl.
of Basis
a.
Situated around the radii, or radial tubes, of a radiate.
pl.
of Radiale
n.
Radial plates in the calyx of a crinoid.
n.
A quantity so connected with another quantity, that if any alteration be made in the latter there will be a consequent alteration in the former. Each quantity is said to be a function of the other. Thus, the circumference of a circle is a function of the diameter. If x be a symbol to which different numerical values can be assigned, such expressions as x2, 3x, Log. x, and Sin. x, are all functions of x.
a.
Pertaining to, or connected with, a function or duty; official.
n.
Species of Serranus, the sea bass and rock bass. See Sea bass.
a.
Hence, basic; metallic; not acid; -- opposed to negative, and said of metals, bases, and basic radicals.
n.
The quantity contained in a basin.
a.
A radical vessel. See under Radical, a.
n.
The act of joining, or the state of being joined; union; combination; coalition; as, the junction of two armies or detachments; the junction of paths.
a.
Of or pertaining to a radius or ray; consisting of, or like, radii or rays; radiated; as, (Bot.) radial projections; (Zool.) radial vessels or canals; (Anat.) the radial artery.
adv.
In a radial manner.
pl.
of Bass
a.
Of or pertaining to a radix or root; as, a radical quantity; a radical sign. See below.