Graph Kernels via Functional Embedding
This provides a more efficient and scalable method for graph classification tasks, though it appears incremental as it builds on existing kernel approaches.
The authors tackled the problem of graph classification by representing graphs as functional objects derived from adjacency matrix power iteration, which eliminates the need to handle exponentially many isomorphic forms. Their Bhattacharyya kernel outperformed state-of-the-art graph kernels on 3 out of 4 standard benchmark datasets and runs in linear time relative to edges, making it more efficient than cubic-time alternatives.
We propose a representation of graph as a functional object derived from the power iteration of the underlying adjacency matrix. The proposed functional representation is a graph invariant, i.e., the functional remains unchanged under any reordering of the vertices. This property eliminates the difficulty of handling exponentially many isomorphic forms. Bhattacharyya kernel constructed between these functionals significantly outperforms the state-of-the-art graph kernels on 3 out of the 4 standard benchmark graph classification datasets, demonstrating the superiority of our approach. The proposed methodology is simple and runs in time linear in the number of edges, which makes our kernel more efficient and scalable compared to many widely adopted graph kernels with running time cubic in the number of vertices.