Hyperkernel Construction for Support Vector Machines

Construction of kernel functions is crucial for research and application of support vector machines (SVM). In this paper, we propose a combinatorial construction of hyperkernel functions for SVM. We first analyze the under and over-learning phenomena of common kernel functions. Then, we construct hyperkernel function with a polynomial combination of common kernels, and prove the Mercer condition of the hyperkernel. Finally, we experiment both on simulation and benchmark data to demonstrate the performance of hyperkernel for SVM. The theoretical proofs and experimental results illuminate the validity and feasibility of hyperkernel.