Kernel Methods
Overview
The concept of a kernel is used in various ways within mathematics and machine learning. As such,
there are varying definitions (not always compatible) for what a kernel is. Within mathematics, the word
kernel is overloaded to mean different things depending on the context.
Kernel Definition
A simple intuitive definition of a kernel is a function
{% k(x,y) : E \times E \rightarrow \mathbb{R} %}
which represents in some what a similarity between the two inputted elements. That is, a higher value represents a higher
similarity. (This is in some sense, the opposite of a
metric)
For a list of kernel functions, see
example kernels.
A more rigorous definition used within the theory of
Reproducing Kernel Hilber Spaces is given.
Given a set {% X %}, a function {% k %} is called a kernel if there exists a Hilbert space {% H %} and a map
{% \phi:X \rightarrow H %}
such that
{% k(x,x') = < \phi(x),\phi(x') > %}
Topics
Kernel Based Algorithms
