branch of mathematics, a positive-definite kernel is a generalization of a positive-definite function or a positive-definite matrix. It was first introduced...

in the reproducing kernel Hilbert space theory where it characterizes a symmetric positive-definite kernel as a reproducing kernel. To explain Mercer's...

Positive-definite kernel Positive-definite matrix Positive-definite operator Positive-definite quadratic form Fasshauer, Gregory E. (2011), "Positive...

with real entries is positive-definite if the real number x ⊤ M x {\displaystyle \mathbf {x} ^{\top }M\mathbf {x} } is positive for every nonzero real...

in neural network settings.[citation needed] Positive definite kernel Mercer's theorem Kernel trick Kernel embedding of distributions Representer theorem...

coefficients ( c 1 , … , c n ) {\displaystyle (c_{1},\dots ,c_{n})} (cf. positive definite kernel), then the function k {\displaystyle k} satisfies Mercer's condition...

and algebraic groups. It can be viewed as a particular type of positive-definite kernel where the underlying set has the additional group structure. Let...

In mathematics, a positive-definite function is, depending on the context, either of two types of function. Let R {\displaystyle \mathbb {R} } be the...

Kernel density estimation Kernel smoother Stochastic kernel Positive-definite kernel Density estimation Multivariate kernel density estimation Kernel...

mathematical finance Positive-definite kernel, a generalization of a positive-definite matrix Kernel trick, in statistics Reproducing kernel Hilbert space Seed...

{\displaystyle {\mathcal {H}}(R)} be a reproducing kernel Hilbert space with positive definite kernel R {\displaystyle R} . Driscoll's zero-one law is a...

\Omega } and distribution P {\displaystyle P} . Given a symmetric, positive-definite kernel k : Ω × Ω → R {\displaystyle k:\Omega \times \Omega \rightarrow...

states that positive-definite kernels can be expressed as a dot product in a high-dimensional space. This theorem is the basis of the kernel trick (applied...

In machine learning, tree kernels are the application of the more general concept of positive-definite kernel to tree structures. They find applications...

(f)+\lambda R(f),\lambda >0} A RKHS can be defined by a symmetric positive-definite kernel function K ( x , z ) {\displaystyle K(x,z)} with the reproducing...

allows ANNs to be studied using theoretical tools from kernel methods. In general, a kernel is a positive-semidefinite symmetric function of two inputs which...

speaking, the inner product is required only to be positive semi-definite rather than positive definite, so that it gives rise to a seminorm rather than...

due to Schölkopf, Herbrich, and Smola: Theorem: Consider a positive-definite real-valued kernel k : X × X → R {\displaystyle k:{\mathcal {X}}\times {\mathcal...

belong to the Reproducing Kernel Hilbert Space associated with any arbitrary (possibly non-linear), symmetric positive-definite kernel. The linear regression...

generalization is kernel PCA, which corresponds to PCA performed in a reproducing kernel Hilbert space associated with a positive definite kernel. In multilinear...

matrix Covariance operator – Operator in probability theory Kriging Positive-definite kernel Random field Stochastic process Variogram Wackernagel, Hans (2003)...

bandwidth (or smoothing) d×d matrix which is symmetric and positive definite; K is the kernel function which is a symmetric multivariate density; K H (...

in functional analysis, a seminorm is like a norm but need not be positive definite. Seminorms are intimately connected with convex sets: every seminorm...

b b c ] {\displaystyle {\begin{bmatrix}a&b\\b&c\end{bmatrix}}} is positive-definite. Using this formulation, the figure on the right can be created using...

(pronounced /ʃəˈlɛski/ shə-LES-kee) is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate...

Nyström method from integral equation theory. : 357  Consider a positive-definite kernel function k : X × X → R {\displaystyle k:X\times X\to \mathbb {R}...

Tatlow (In Our Time, May 25, 2006) Measuring note similarity with positive definite kernels, Measuring note similarity with positive definite kernels...

That is, suppose K {\displaystyle K} is a continuous symmetric positive-definite kernel on L 2 ( [ a , b ] ) {\displaystyle L^{2}([a,b])} , defined as...

matrices with the positive elements being the positive-definite matrices. The trace function defined on this C*-algebra is a positive functional, as the...

{\displaystyle h(g)=0} for all but finitely many g {\displaystyle g} . The positive-definite kernel K ( g 1 , g 2 ) = f ( g 1 − g 2 ) {\displaystyle K(g_{1},g_{2})=f(g_{1}-g_{2})}...