What kernel size separates my data?

In This work we prove a new theorem applicable to polynomial kernels for SVM classification tasks. This theorem relates the properties of the input space to the kernel function space. Thus, we find basic requirements for polynomial kernels if it is to linearly separate the data in feature space. Assuming the data in input space is separable by a polynomial function of some order u, the theorem establishes that the order of a polynomial kernel to reach linear separability must meet m ≥ u. Several experiments illustrate the applicability of the theorem in classification tasks.