The polynomial kernel function is directional, i.e. the output depends
on the direction of the two vectors in low-dimensional
space. This is due to the dot product in the kernel
(Eqn. 
). Figure shows the shape for a
two dimensional polynomial kernel. The support vector 
is [7.5,
7.5]. All vectors with the same direction will have a high output from
the kernel. The magnitude of the output is also dependent on the
magnitude of the vector 
.
From these observations, polynomial kernels are suited for problems where all the training data in normalised. Experiments with the TIMIT and Peterson_Barney database show that the polynomial kernel is not suitable for the 1-to-rest type of classifier. When used in these classifiers, the training will fail to converge. This may be due to the directional and magnitude dependency of the polynomial kernel.
