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Positive-definite kernel

In operator theory, 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 by James Mercer in the early 20th century, in the context of solving integral operator equations. Since then, positive-definite functions and their various analogues and…

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Kernels and distances

Some applications

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Positive-definite kernel

Nodes56
Edges55
Triples32
Avg. degree1.96
Density0.035714
Components1

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Positive-definite kernel

Top relations

related to history · 10
Positive-definite kernel → Bochner, Fredholm, Hilbert, Hilbert’s, In, James Mercer, Mathias, Mercer’s, Positive-definite, Several
related to Numerical solution of partial differential equations · 9
Positive-definite kernel → MLPG, One, PDEs, Petrov Galerkin, Reproducing, RKPM, Some, SPH, These
related to Connection with reproducing kernel Hilbert spaces and feature maps · 7
Positive-definite kernel → For, Hilbert, In, Let, Positive-definite, RKHS, We
related to Kernels in machine learning · 4
Positive-definite kernel → Hilbert, Positive-definite, RKHS, This
is a · 1
Positive-definite kernel → generalization of a positive-definite function or a positive-definite matrix

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Important terminology

displaystyle kernel kernels mathbb function positive-definite hilbert mathcal reproducing times space functions theory integral equations every defined one positive quad

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Positive-definite kernelis ageneralization of a positive-definite function or a positive-definite matrix0.90text
nearest neighborsinstance ofKernels and distancesKernel methods are often compared to distance based methods0.80text
Positive-definite kernelrelated to Connection with reproducing kernel Hilbert spaces and feature mapsPositive-definite0.60section
Positive-definite kernelrelated to Connection with reproducing kernel Hilbert spaces and feature mapsHilbert0.60section
Positive-definite kernelrelated to Connection with reproducing kernel Hilbert spaces and feature mapsIn0.60section
Positive-definite kernelrelated to Connection with reproducing kernel Hilbert spaces and feature mapsLet0.60section
Positive-definite kernelrelated to Connection with reproducing kernel Hilbert spaces and feature mapsFor0.60section
Positive-definite kernelrelated to Connection with reproducing kernel Hilbert spaces and feature mapsWe0.60section
Positive-definite kernelrelated to Connection with reproducing kernel Hilbert spaces and feature mapsRKHS0.60section
Positive-definite kernelrelated to historyPositive-definite0.60section
Positive-definite kernelrelated to historyJames Mercer0.60section
Positive-definite kernelrelated to historySeveral0.60section

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