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.
Figure: The Polynomial kernel