Mercel Kernel
Description
A Mercer Kernel is a Kernel that is positive semi-definite. When a kernel is positive semi-definite, one may exploit the kernel trick [1], the idea of mapping data to a high-dimensional feature space where some linear algorithm is applied that works exclusively with inner products. Assume we have some mapping 
from an input space 
to a feature space 
, then a kernel function (or kernel)
may be used to define the inner product in feature space . Figure 1 shows that the application of a linear algorithm in feature space could correspond to a nonlinear estimate in input space .
Figure 1: A mapping from input space to feature space .
Positive definiteness in the context of kernel functions also implies that a kernel matrix created using a particular kernel is positive semi-definite. A matrix is positive semi-definite if its associated eigenvalues 
are nonnegative.
Refinement of
Associated types
Notation
Definitions
Valid Expressions
Expression Semantics
Complexity Guarantees
Invariants
Models
Notes
See also
References
Mark Aizerman, Emmanuil Braverman, and Lev Rozonoèr. Theoretical foundations of the potential function method in pattern recognition learning. Automation and Remote Control, 25:821–837, 1964.