Distance based Kernels for First-Order Logic Data

Support Vector Machines (SVM) and kernel techniques have been proven effective on various application domains using attributevalue representation. A number of works have been done to apply SVM on First-Order Logic (FOL) data as well as using SVM with Inductive Logic Programming (ILP). In this paper, we propose kernel functions for FOL data developed from the four-layer distance metric. Since our proposed kernels are not positive definite, we apply the shift spectrum transformation to ensure that the kernel matrices are positive semidefinite before use them in the SVM optimization algorithm. The proposed kernels yields higher accuracies than the baseline ILP system on Mutagenesis and Alzheimer dataset. They significantly outperform the existing kernel functions on the Alzheimer dataset. On the Mutagenesis dataset, our kernel functions performs not significantly different from the best accuracy.