Shortest-Path Kernels on Graphs

Abstract

Data mining algorithms are facing the challenge to deal with an increasing number of complex objects. For graph data, a whole toolbox of data mining algorithms becomes available by defining a kernel function on instances of graphs. Graph kernels based on walks, subtrees and cycles in graphs have been proposed so far. As a general problem, these kernels are either computationally expensive or limited in their expressiveness. We try to overcome this problem by defining expressive graph kernels which are based on paths. As the computation of all paths and longest paths in a graph is NP-hard, we propose graph kernels based on shortest paths. These kernels are computable in polynomial time, retain expressivity and are still positive definite. In experiments on classification of graph models of proteins, our shortest-path kernels show significantly higher classification accuracy than walk-based kernels.

Transitive State Alignment for the Quantum Jensen-Shannon Kernel

“…More specifically, we compare our kernel with the unaligned QJSD kernel [1], the Weisfeiler-Lehman kernel [16], the graphlet kernel [17], the shortest-path kernel [3], and the random walk kernel [8]. Note that for the Weisfeiler-Lehman we set the number of iterations h = 3 and we attribute each node with its degree.…”

“…Classification accuracy (± standard error) on unattributed graph datasets. SA QJSD and QJSD denote the proposed kernel and its original unaligned version, respectively, WL is the Weisfeiler-Lehman kernel [16], GR denotes the graphlet kernel computed using all graphlets of size 3 [17], SP is the shortest-path kernel [3], and RW is the random walk kernel [8]. For each kernel and dataset, the best performing kernel is highlighted in bold.…”

“…Most R-convolution kernels simply count the number of isomorphic substructures in the two graphs. For example, Kashima et al [8] compute the kernel by decomposing the graph into random walks, while Borgwardt et al [3] have proposed a kernel based on shortest paths. Here, the similarity is determined by counting the numbers of pairs of shortest paths of the same length in a pair of graphs.…”

Using graph-based program characterization for predictive modeling

“…Among all recent developments, graph kernels based on shortest paths [7] are a remarkable class of kernel functions. They retain expressivity while comparing graphs at acceptable polynomial time.…”

“…Shortest Path Graph Kernel Roughly speaking, the basic idea of a shortest path graph kernel [7] is to quantify the number of common shortest paths in two input graphs. To this end, prior to the kernel computation, the original graphs must be transformed into shortest path graphs.…”