Distribution of Node Embeddings as Multiresolution Features for Graphs Graph classification is an important problem in many fields, from bioinformatics and neuroscience to computer vision and social network analysis. That said, the task of comparing graphs for the purpose of graph classification faces several major challenges. In particular, an effective graph comparison method must (1) expressively and inductively compare graphs; (2) efficiently compare large graphs; and (3) enable the use of fast machine learning models for graph classification. To address such challenges, we propose Randomized Grid Mapping (RGM), a fasttocompute feature map that represents a graph via the distribution of its node embeddings in feature space. We justify RGM with close connections to kernel methods: RGM provably approximates the Laplacian kernel mean map and has the multiresolution properties of the pyramid match kernel. We also show that RGM can be extended to incorporate node labels using the WeisfeilerLehman framework. Extensive experiments show that graph classification accuracy with RGM feature maps is better than or competitive with many powerful graph kernels, unsupervised graph feature mappings, and deep neural networks. Moreover, comparing graphs based on their node embeddings with RGM is up to an order of magnitude faster than competitive baselines, while maintaining high classification accuracy.

Network2Vec: Learning Node Representation Based on Space Mapping in Networks Complex networks represented as node adjacency matrices constrains the application of machine learning and parallel algorithms. To address this limitation, network embedding (i.e., graph representation) has been intensively studied to learn a fixedlength vector for each node in an embedding space, where the node properties in the original graph are preserved. Existing methods mainly focus on learning embedding vectors to preserve nodes proximity, i.e., nodes next to each other in the graph space should also be closed in the embedding space, but do not enforce algebraic statistical properties to be shared between the embedding space and graph space. In this work, we propose a lightweight model, entitled Network2Vec, to learn network embedding on the base of semantic distance mapping between the graph space and embedding space. The model builds a bridge between the two spaces leveraging the property of group homomorphism. Experiments on different learning tasks, including node classification, link prediction, and community visualization, demonstrate the effectiveness and efficiency of the new embedding method, which improves the stateoftheart model by 19% in node classification and 7% in link prediction tasks at most. In addition, our method is significantly faster, consuming only a fraction of the time used by some famous methods.