Linear Kernel

A Linear Kernel is a kernel function that ...

• Example(s):
  • a Vector Kernel.
  • a Matrix Kernel.
  • …
• Counter-Example(s):
  • a Non-Linear Kernel.
  • a Logistic Function.
  • a Graph Kernel.
• See: Linear SVM, Set-Builder Notation, Linear Algebra, Functional Analysis, Linear Map, Vector Space, Zero Vector.

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References

2017

• (Wikipedia, 2017) ⇒ https://en.wikipedia.org/wiki/Kernel_(linear_algebra) Retrieved:2017-6-27.
  • In mathematics, and more specifically in linear algebra and functional analysis, the kernel (also known as null space or nullspace) of a linear map between two vector spaces V and W, is the set of all elements v of V for which , where 0 denotes the zero vector in W. That is, in set-builder notation, : [math]\displaystyle{ \ker(L) = \left\{ \mathbf{v}\in V | L(\mathbf{v})=\mathbf{0} \right\}\text{.} }[/math]

2015

• http://scikit-learn.org/stable/modules/svm.html#svm-kernels
  • The kernel function can be any of the following:
    • linear [math]\displaystyle{ \langle x, x'\rangle }[/math].
    • polynomial [math]\displaystyle{ (\gamma \langle x, x'\rangle + r)^d }[/math]. d is specified by keyword degree, r by coef0.
    • rbf [math]\displaystyle{ \exp(-\gamma |x-x'|^2). \gamma }[/math] is specified by keyword gamma, must be greater than 0.
    • sigmoid [math]\displaystyle{ (\tanh(\gamma \langle x,x'\rangle + r)) }[/math], where r is specified by coef0.

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