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Using a polynomial kernel

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. gif). Figure gif shows the shape for a two dimensional polynomial kernel. The support vector tex2html_wrap_inline1624 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 tex2html_wrap_inline2474 .

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.

  equation1431

   figure1435
Figure: The Polynomial kernel



K.K. Chin
Thu Sep 10 11:05:30 BST 1998