A new support vector machine with an optimal additive kernel

Although the kernel support vector machine (SVM) outperforms linear SVM, its application to real world problems is limited because the evaluation of its decision function is computationally very expensive due to kernel expansion. On the other hand, additive kernel (AK) SVM enables fast evaluation of a decision function using look-up tables (LUTs). The AKs, however, assume a specific functional form for kernels such as the intersection kernel (IK) or χ² kernel, and are problematic in that their performance is seriously degraded when a given problem is highly nonlinear. To address this issue, an optimal additive kernel (OAK) is proposed in this paper. The OAK does not assume any specific kernel form, but the kernel is represented by a quantized Gram table. The training of the OAK SVM is formulated as semi-definite programming (SDP), and it is solved by convex optimization. In the experiment, the proposed method is tested with 2D synthetic datasets, UCI repository datasets and LIBSVM datasets. The experimental results show that the proposed OAK SVM has better performance than the previous AKs and RBF kernel while maintaining fast computation using look-up tables.