Diffusion Wavelet Embedding: a Multi-resolution Approach for Graph Embedding in Vector Space

In this article, we propose a multiscale method of embedding a graph into a vector space using diffusion wavelets. At each scale, we extract a detail subspace and a corresponding lower-scale approximation subspace to represent the graph. Representative features are then extracted at each scale to provide a scale-space description of the graph. The lower-scale is constructed using a super-node merging strategy based on nearest neighbor or maximum participation and the new adjacency matrix is generated using vertex identification. This approach allows the comparison of graphs where the important structural differences may be present at varying scales. Additionally, this method can improve the differentiating power of the embedded vectors and this property reduces the possibility of cospectrality typical in spectral methods, substantially. The experimental results show that augmenting the features of abstract levels to the graph features increases the graph classification accuracies in different datasets.