tutorial on kernel method
Bernhard Schölkopf. Statistical learning and kernel methods. MSR-TR 2000-23, Microsoft Research, 2000.
Kernel methods retain te original representation of objects and use the object in algorithms only via computing a kernel function between a pair of objects. A kernel function is a similarity function satisfying certain properties. More precisely, a kernel function K over the object space X is binary function K:X*X ->[0, infinite] mapping a pair of objects x,y \in X to their similarity score K(x,y). A kernel function is required to be symmetric and positive-semidefinite.