Constructing Kernels

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 Properties of Kernel Functions

To perform this transformation we need to chose proper kernel functions. Functions that satisfy the following properties make good kernel functions.

1. Symmetry

K(x,y) = K(y,x)

That is, the similarity measure between x and y is the same as the similarity measure between y and x. The kernel matrix will be a symmetric matrix.

2. Positive Semidefinitiveness

The kernel matrix formed must be positive semidefinite.


Eigenvalues and Eigenvectors



Mercer's Theorem

It states that a continuous, symmetric and positive semidefinite function is a valid kernel. It also states that the kernel function corresponds to the dot product(inner product in Euclidean space) in higher dimensional space.

Constructing Common Kernel functions


The following pdf shows how to construct kernels and check for valid kernels.



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