Experimental evaluation of graph classification with Hadamard code graph kernels

Abstract

When mining information from a database comprising graphs, kernel methods are used to efficiently classify graphs that have similar structures into the same classes. Instances represented by graphs usually have similar properties if their graph representations have high structural similarity. The neighborhood hash kernel (NHK) and Weisfeiler-Lehman subtree kernel (WLSK) have previously been proposed as kernels that compute more quickly than the random-walk kernel; however, they each have drawbacks. NHK can produce hash collision and WLSK must sort vertex labels. We propose a novel graph kernel equivalent to NHK in terms of time and space complexities, and comparable to WLSK in terms of expressiveness. The proposed kernel is based on the Hadamard code. Labels assigned by our graph kernel follow a binomial distribution with zero mean. The expected value of a label is zero; thus, such labels do not require large memory. This allows the compression of vertex labels in graphs, as well as fast computation. This paper presents the Hadamard code kernel (HCK) and shortened HCK (SHCK), a version of HCK that compresses vertex labels in graphs. The performance and practicality of the proposed method are demonstrated in experiments that compare the computation time, scalability and classification accuracy of HCK and SHCK with those of NHK and WLSK for both artificial and real-world datasets. The effect of assigning initial labels is also investigated.