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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
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
Radial_basis_function_kernel
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
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
Element of a basis for a function space
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
Basis_function
Real function on a Euclidean space whose value depends only on distance from the origin
In mathematics, a radial function is a real-valued function defined on a Euclidean space R n {\displaystyle \mathbb {R} ^{n}} whose value at each
Radial_function
Method of data interpolation and smoothing
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
Thin_plate_spline
Classification of Artificial Neural Networks (ANNs)
feedforward networks. Radial basis functions are functions that have a distance criterion with respect to a center. Radial basis functions have been applied
Types of artificial neural networks
Types_of_artificial_neural_networks
Machine learning technique
random 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}
Random_feature
In functional analysis, a Hilbert space
space of functions in which point evaluation is a continuous linear functional. Specifically, a Hilbert space H {\displaystyle H} of functions from a set
Reproducing kernel Hilbert space
Reproducing_kernel_Hilbert_space
Approximating an arbitrary function with a well-behaved one
theory Fitness approximation Kriging Least squares (function approximation) Radial basis function network Lakemeyer, Gerhard; Sklar, Elizabeth; Sorrenti
Function_approximation
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
Tool in multivariate statistical analysis
{\displaystyle \nu } is an integer, limiting values should be taken (see ). Radial basis function Genton, Marc G. (1 March 2002). "Classes of kernels for machine
Matérn_covariance_function
Topics referred to by the same term
basis Hilbert's basis theorem Generating set of a group Base (topology) Change of basis Greedoid Normal basis Polynomial basis Radial basis function Standard
Basis
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
Computational method for solving partial differential equations
first attempt to extend radial basis function (RBF), which was then quite popular in scattered data processing and function approximation, to the solution
Kansa_method
Mathematical function
patterns in the feature space. Bell-shaped function Cauchy distribution Normal distribution Radial basis function kernel Squires, G. L. (2001-08-30). Practical
Gaussian_function
Set of methods for supervised statistical learning
_{j})=(\mathbf {x} _{i}\cdot \mathbf {x} _{j}+r)^{d}} . Gaussian radial basis function: k ( x i , x j ) = exp ( − γ ‖ x i − x j ‖ 2 ) {\displaystyle
Support_vector_machine
Interpolation on functions of more than one variable
distance weighting Natural-neighbor interpolation Spline interpolation Radial basis function interpolation Barnes interpolation Bilinear interpolation Bicubic
Multivariate_interpolation
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
In machine learning, a Hyper basis function network, or HyperBF network, is a generalization of radial basis function (RBF) networks concept, where the
Hyper_basis_function_network
Engineering model
generalized Bayesian approaches; gradient-enhanced kriging (GEK); radial basis function; support vector machines; space mapping; artificial neural networks
Surrogate_model
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
Topics referred to by the same term
Rangierbahnhof, a railway marshalling yard in Germany Radial basis function in mathematics Radial basis function kernel or RBF kernel Random Block File, an OS-9
RBF
{\displaystyle 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
General regression neural network
General_regression_neural_network
Method for estimating new data within known data points
(statistics) Lagrange interpolation Missing data Newton–Cotes formulas Radial basis function interpolation Simple rational approximation Smoothing Sheppard,
Interpolation
Method of function approximation and data interpolation
A polyharmonic spline is a linear combination of polyharmonic radial basis functions (RBFs) denoted by φ {\displaystyle \varphi } plus a polynomial term:
Polyharmonic_spline
Property of artificial neural networks
Park, J.; Sandberg, I. W. (1991). "Universal Approximation Using Radial-Basis-Function Networks". Neural Computation. 3 (2): 246–257. doi:10.1162/neco
Universal approximation theorem
Universal_approximation_theorem
Overview of and topical guide to machine learning
unconstrained binary optimization Query-level feature Quickprop Radial basis function network Random forest Randomized weighted majority algorithm Reinforcement
Outline_of_machine_learning
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
Class of algorithms for pattern analysis
Fisher kernel Graph kernels Kernel smoother Polynomial kernel Radial basis function kernel (RBF) String kernels Neural tangent kernel Neural network
Kernel_method
Point of reference in Euclidean space
Pointed space, a topological space with a distinguished point Radial basis function, a function depending only on the distance from the origin Madsen, David
Origin_(mathematics)
Type of artificial neural network architecture
Nonlinear Function Approximation". arXiv:2405.07200 [cs.LG]. Ta, H. T. (2024). "BSRBF-KAN: a combination of B-splines and radial basis functions in Kolmogorov-Arnold
Kolmogorov–Arnold_Networks
British research scientist
(2010). "Prediction of Parkinson's disease tremor onset using radial basis function neural networks". Expert Systems with Applications. 37 (4): 2923
Mark_Gasson
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
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
Machine learning framework
(Perceptron) Hopfield Neural Network Jordan Recurrent Neural Network Radial Basis Function Network Recurrent Self Organizing Map (RSOM) Self Organizing Map
Encog
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)
Hidden Markov model algorithm
Hybrid Forward Algorithm (HFA) can be used for the construction of radial basis function (RBF) neural networks with tunable nodes. The RBF neural network
Forward_algorithm
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
Generalization of a positive-definite matrix
experiments", Ann. Stat. Gumerov, N. A. and Duraiswami, R. (2007). "Fast radial basis function interpolation via preconditioned Krylov iteration". SIAM J. Scient
Positive-definite_kernel
Branch of engineering and mathematics
design feedback control systems Positive systems Radial basis function – Type of mathematical function Root locus – Stability criterion in control theoryPages
Control_theory
image processing. Radial basis function network: an artificial neural network that uses radial basis functions as activation functions Self-organizing map:
List_of_algorithms
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
System of elements that are subordinated to each other
modeling Hierarchical modulation Hierarchical proportion Hierarchical radial basis function Hierarchical storage management Hierarchical task network Hierarchical
Hierarchy
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
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
State of thermodynamic systems where no net flow of matter or energy occurs
method Minor loop feedback Multi-loop feedback Positive systems Radial basis function Root locus Signal-flow graphs Stable polynomial State space representation
Thermodynamic_equilibrium
Method of interpolation
Gaussian process Multivariate interpolation Nonparametric regression Radial basis function interpolation Space mapping Spatial dependence Variogram Gradient-enhanced
Kriging
River in Sri Lanka
Model For Kalu River and Kelani River Basins in Sri Lanka using Radial Basis Function Neural Networks "Richmond Castle: A Tale Of Grandeur And Romance"
Kalu_Ganga
modeling Artificial neural networks including Multilayer perceptrons Radial basis function network Support vector machines Due to the limited number of training
Fitness_approximation
Linear function of explanatory variables used to predict a dependent variable
likely to be treated as K separate scalar-output basis functions). An example of this is radial basis functions (RBF's), which compute some transformed version
Linear_predictor_function
American scientist
scientist and applied mathematician known for her expertise on radial basis functions. She works as a research scientist in the Analytics and Integrative
Natasha_Flyer
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
Overview of and topical guide to deep learning
neural network Multilayer perceptron Convolutional neural network Radial basis function network Residual neural network U-Net Recurrent neural network Long
Outline_of_deep_learning
Hyperparameter optimization framework
(SVM): regularization parameter (C), kernel type (e.g., linear, radial basis function), and gamma (gamma). K-nearest neighbors (KNN): number of neighbors
Optuna
graphics, hierarchical RBF is an interpolation method based on radial basis functions (RBFs). Hierarchical RBF interpolation has applications in treatment
Hierarchical_RBF
Canadian electrical engineer (1931–2025)
Processing, IEEE Press, 2001 P. Yee and S. Haykin, Regularized Radial Basis Function Networks, Wiley, 2001 S. Haykin, Communication Systems, Fourth Edition
Simon_Haykin
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
Linear function approximation using basis functions is a common way of constructing a value function approximation, like radial basis functions, polynomial
Proto-value_function
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
Cluster analysis problem
the proximity of the input information. For example, in Gaussian radial basis function, it determines the dot product of the inputs in a higher-dimensional
Determining the number of clusters in a data set
Determining_the_number_of_clusters_in_a_data_set
Machine learning technique
the 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
Probabilistic_neural_network
Process of capturing the shape and appearance of real objects
some use a discrete function f, while other use a polyharmonic radial basis function is used to adjust the initial point set. Functions like Moving Least
3D_reconstruction
Geometric arrangement of a nodal group
(2015). "Brief Summary of Finite Difference Methods". A Primer on Radial Basis Functions with Applications to the Geosciences. Society for Industrial and
Stencil_(numerical_analysis)
Simple polynomial map exhibiting chaotic behavior
which the logistic map is a special case confined to the real line Radial basis function network, which illustrates the inverse problem for the logistic
Logistic_map
Applied mathematician (1936–2015)
conjugate direction method (also called Powell's method), and radial basis function.[citation needed] He had been working on derivative-free optimization
Michael_J._D._Powell
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
method, singular boundary method, and regularized meshless method. Radial basis function Boundary element method Boundary knot method Boundary particle method
Method of fundamental solutions
Method_of_fundamental_solutions
Basis used to express spherical tensors
using polar and azimuthal angles and radial distance, the spherical basis are constructed from the standard basis and use complex numbers. A vector A in
Spherical_basis
British engineer and robotics researcher
(2010). "Prediction of Parkinson's disease tremor onset using a radial basis function neural network based on particle swarm optimization". International
Kevin_Warwick
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
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)
Algorithm for reducing the dimension of tensors
was 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
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
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
Type of vector space in math
different basis functions for a space such as L2([0, 1]). In many circumstances, it is desirable not to decompose a function into trigonometric functions, but
Hilbert_space
Notion in statistics
mixtures, multinomial mixtures, Bayesian networks, neural networks, radial basis functions, hidden Markov models, stochastic context-free grammars, reduced
Fisher_information
Method of solving linear partial differential equations
technique approximates part of the integrand using radial basis functions (local interpolating functions) and converts the volume integral into boundary
Boundary_element_method
Mathematical description of quantum state
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
Wave_function
British award in mathematics
prizes: Martin Buhmann ("Multivariable cardinal interpolation with radial basis functions"), Bart De Moor ("The restrictricted singular value decomposition:
Leslie Fox Prize for Numerical Analysis
Leslie_Fox_Prize_for_Numerical_Analysis
Aspect of an artificial neural network
and is typically modified using such variations as Oja's rule, radial basis functions or the backpropagation algorithm. For biological networks, the effect
Synaptic_weight
American electrical engineer
de-noising technique for detecting MFL signals from seamless pipes, radial basis function neural networks and adaptive wavelets to predict defect depth profiles
Satish_Udpa
Physics concept
eφ for the radial coordinate system. The radial basis vectors er and eφ appear rotated anticlockwise with respect to the rectangular basis vectors ex
Covariant_transformation
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
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
etc. The suggested approach to the nonlinear mapping is to use a radial basis function network (RBF) to create a nonlinear mapping between the latent space
Generative_topographic_map
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
American environmental engineer
improved with the use of surrogate response surfaces (usually with radial basis function (RBF)). The surrogates are iteratively built during the search process
Christine_Shoemaker
Approximations used in machine learning
features based approach. Nyström method Support vector machine Radial basis function kernel Regularized least squares Andreas Müller (2012). Kernel Approximations
Low-rank matrix approximations
Low-rank_matrix_approximations
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
ALGOL 68, following on from ALGOL 68R developed by RRE), Coral 66, radial basis function networks, hierarchical self-organising networks (deep autoencoders)
Royal Signals and Radar Establishment
Royal_Signals_and_Radar_Establishment
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
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
Neural network development environment
Modular (programming) Jordan/Elman Principal component analysis (PCA) Radial basis function network (RBF) General regression neural network (GRNN) Probabilistic
NeuroSolutions
Algerian politician
Kamel, Aifa T., Djarfour N., Ferahtia J. (2009): Application of a radial basis function artificial neural network to seismic data inversion . Computer and
Kamel_Bidari
Transformation of a stem cell to a more specialized cell
C (October 2015). "Solution of the chemical master equation by radial basis functions approximation with interface tracking". BMC Systems Biology. 9 (1):
Cellular_differentiation
Signal analysis tool
applicable to two-dimensional signals. Therefore, Nunes et al. used radial basis functions and the Riesz transform to handle Genuine Two-Dimensional EMD. The
Hilbert–Huang_transform
Algorithm for approximating nonlinear relationships
tabulated data, as well as error control. Predictive analytics Radial basis function network Recurrent neural networks Support vector machine Tensor
In_situ_adaptive_tabulation
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
RADIAL BASIS-FUNCTION
RADIAL BASIS-FUNCTION
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
Tamil
Basil, Goddess Radha, Tulsi
Surname or Lastname
English
English : from Old French bas(se) ‘low’, ‘short’ (Latin bassus ‘thickset’; see Basso), either a descriptive nickname for a short person or a status name meaning ‘of humble origin’, not necessarily with derogatory connotations.English : in some instances, from Middle English bace ‘bass’ (the fish), hence a nickname for a person supposedly resembling this fish, or a metonymic occupational name for a fish seller or fisherman.Scottish : habitational name from a place in Aberdeenshire, of uncertain origin.Jewish (Ashkenazic) : metonymic occupational name for a maker or player of bass viols, from Polish, Ukrainian, and Yiddish bas ‘bass viol’.German : see Basse.
Boy/Male
Muslim
King, Basil the herb (1)
Girl/Female
Hindu
Basil, Radha, Holy
Male
English
Variant spelling of English Gaddiel, GADIEL means "God is my fortune."Â
Female
Hebrew
 Variant spelling of Hebrew Basya, BASIA means "daughter of God."
Girl/Female
Assamese, Christian, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Mythological, Oriya, Sanskrit, Sindhi, Telugu, Traditional
Basil; Tulsi; Goddess Radha
Girl/Female
Hindu
Basil, Radha, Holy
Boy/Male
Hindu, Indian
God's Kindness
Girl/Female
Tamil
Basil, Radha, Holy
Girl/Female
Gujarati, Hindu, Indian, Jain, Marathi, Mythological, Oriya, Sanskrit, Sindhi, Traditional
Basil; Goddess Radha; Tulsi
Female
Serbian
(Радмила) Feminine form of Serbian Radmilo, RADMILA means "happy favor."
Boy/Male
Greek
Royal. Kingly. St Basil the Great was Bishop of Caesarea in the latter half of the 4th century....
Male
English
 English form of French Basile, BASIL means "king." Also sometimes given as an herb name.
Boy/Male
Hindu
King, Basil the herb
Boy/Male
Hindu
Basil, Goddess Radha, Tulsi
Male
English
Medieval form of English Randolf, RANDAL means "shield-wolf."
Girl/Female
Tamil
Brindha | பà¯à®°à¯€à®¨à¯à®¤à®¾Â
Tulsi (Basil) or Goddess Radha
Brindha | பà¯à®°à¯€à®¨à¯à®¤à®¾Â
Girl/Female
Tamil
Basil, Radha, Holy
RADIAL BASIS-FUNCTION
RADIAL BASIS-FUNCTION
Boy/Male
Hindu, Indian, Kannada, Marathi, Telugu
Lord Siva
Boy/Male
Hindu
Girl/Female
Indian, Tamil
Name of a Beautiful Flower
Girl/Female
Arabic, Muslim
Olive
Girl/Female
Tamil
Rajathilaka | ராஜதிலக
Name of a Raga
Boy/Male
Afghan, Arabic, Australian, Danish, French, German, Hebrew, Indian, Japanese, Muslim, Portuguese, Spanish, Swedish
Close; Near; God is My Judge
Female
English
Variant spelling of English Bonnie, BONNY means both "good" and "pretty."Â
Girl/Female
American, German
True
Girl/Female
Indian, Telugu
Beautiful Girl
Female
Babylonian
, ("the lady"), par excellence.
RADIAL BASIS-FUNCTION
RADIAL BASIS-FUNCTION
RADIAL BASIS-FUNCTION
RADIAL BASIS-FUNCTION
RADIAL BASIS-FUNCTION
pl.
of Bass
a.
Of or pertaining to a radix or root; as, a radical quantity; a radical sign. See below.
pl.
of Radiale
n.
The two American fresh-water species of black bass (genus Micropterus). See Black bass.
a.
Hence: Of or pertaining to the root or origin; reaching to the center, to the foundation, to the ultimate sources, to the principles, or the like; original; fundamental; thorough-going; unsparing; extreme; as, radical evils; radical reform; a radical party.
n.
A radiate.
a.
A radical vessel. See under Radical, a.
a.
Situated around the radii, or radial tubes, of a radiate.
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.
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.
a.
See Predial.
n.
A radical quantity. See under Radical, a.
a.
A bass, or deep, sound or tone.
pl.
of Basis
n.
The quantity contained in a basin.
a.
One who sings, or the instrument which plays, bass.
n.
Radial plates in the calyx of a crinoid.
adv.
In a radial manner.