In this work, we propose novel methods to overcome these challenges.

Graph-structured data arise in wide applications, such as computer vision, bioinformatics, and social networks. Quantifying similarities among graphs is a fundamental problem. In this paper, we develop a framework for computing graph kernels, based on return probabilities of random walks. The advantages of our proposed kernels are that they can effectively exploit various node attributes, while being scalable to large datasets. We conduct extensive graph classification experiments to evaluate our graph kernels. The experimental results show that our graph kernels significantly outperform other state-of-the-art approaches in both accuracy and computational efficiency.

The paper proposes a kernel for graphs able to deal with discrete and continuous labels. In particular, the topology information of a graph is encoded at node level by a return random walk probability vector (each dimension being associated to a different walk length). This probability vector is obtained by classical equations used by random walk kernels for graphs (T. Thanks to that the computational complexity can be reduced since only the entries on the diagonal of the powers of the transition probability matrix need to be computed. This can be done via eigen-decomposition of a rescaled version of the adjacency matrix.

Graph-structured data arise in wide applications, such as computer vision, bioinformatics, and social networks. Quantifying similarities among graphs is a fundamental problem. In this paper, we develop a framework for computing graph kernels, based on return probabilities of random walks. The advantages of our proposed kernels are that they can effectively exploit various node attributes, while being scalable to large datasets. We conduct extensive graph classification experiments to evaluate our graph kernels.