kernel

A Kernel is a function that quantifies the similarity between two observations. It takes the data from a low dimensional feature space and maps it to a high dimensional space. This method is  known as kernel trick.

For example, it takes the data points into higher dimensional space through the mapping and separates the points by a simple plane as shown in the figure.
 

Kernels are of mainly four types:
 

1. Linear kernel                              K (x_i ,x_j) =  x_i.x_j

2. Polynomial kernel:                    K (x_i ,x_j) = (1 + x_i.x_j)d  

3. Sigmoid kernel:                         K (x_i, x_j ) = tanh ((x_i. x_j) + 1)

4. Radial basis function:                K (x_i,x_j) = exp (-γ ||xi - xj||²)

      where, xi ,xj are input vectors