Diffusion wavelet embedding: A multi-resolution approach for graph embedding in vector space. (February 2018) - Bahonar, Hoda; Mirzaei, Abdolreza; Wilson, Richard C.
Highlights: The abstract graphs of different levels are extracted through the proposed diffusion-wavelet-based graph summarization. The abstract graphs are mapped into the approximation/detail subspaces using diffusion wavelet and form the s/d subgraphs . The adjacency matrices of the reference graph and s/d subgraphs form the abstract subgraphs set . The graph feature vector is formed by applying a selected base embedding method on the members of the abstract subgraphs set. Two strategies are used for combining embedded vectors of the abstract subgraphs: the selected combination long vector and ensemble learning. Using multiple embedded vectors for different subgraphs in a raw, suggests the proposed method as a good candidate for cospectrality reduction. Utilizing diffusion wavelet, makes the extracted subgraphs of different graphs comparable and this effect increases the classification accuracy. Abstract: 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.