QSAR Analysis with Support Vector Machines and Graph Kernels

Kernel methods, such as support vector machines, have been applied to solving various problems in bioinformatics. Recently, marginalized kernels between labeled graphs have been proposed [2, 3], which enable the application of kernel methods to the analysis and classification of chemical compounds such as QSAR (quantitative structure-activity relationship). These graph kernels are based on the detection of common paths between different graphs. These correspond to a dot product between the graphs mapped to an infinite-dimensional feature space, but can be computed in polynomial time with respect to the graph sizes. Encouraging experimental results suggest that this approach might be useful in analysis of chemical compounds. These graph kernels, however, are subject to several limitations. First, the choice of representing implicitly each graph by the set of path probabilities under a simple random walk model might be questioned. In chemoinformatics, subgraphs are believed to be more relevant features than paths. Moreover, the random walk model used is subject to “tottering”, in the sense that it can move to one direction and instantly come back to its original position, resulting in redundant paths which might decrease the characterization of a given graph once mapped to the feature space of these graph kernels. Second, the graph kernel has a computational complexity roughly proportional to the product of the sizes of the two graphs to be compared, which results in slow implementation for real-world problem.