CODEWITHSUNDEEP
machine-learningregression
shan
shan

Reputation: 583

Explanation of Isotropic Kernel

What is Isotropic Kernel . What are its features . How can we use it in context of non parametric regression like Kernel Regression ? An intuitive explanation followed with metrics will be helpful.

Upvotes: 1

Views: 6823

Answers (1)

davidhigh
davidhigh

Reputation: 15518

An isotropic Kernel is a kernel which depends only on the distance of the kernel arguments,

K(x,y) = f(||x-y||)

||.|| is any suitable norm, usually the L2-norm.

Intuitively this means that the direction of the deviation is of no importance. For instance, in two dimensions a change in variable x1 is equally important to a change in variable x2 -- which is of course often a too strong assumption. Therefore the predictor variables are often scaled appropriately.

How you can use it in regression? Like any other kernel, but it's often simpler as the number of parameters is often quite small. The isotropic Gaussian for example has only one parameter.

Upvotes: 1

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