Papers^γ

The idea of coarse-graining the graph by merging "similar" nodes (using edge collapsing or star collapsing) before applying a graph embedding method is interesting. Bringing that idea to the next level by building a hierarchy of coarse-grained graphs is also relevant. The hierarchy of coarse-grained graphs allows finding a better initialization for embedding methods relying on deep learning. The two ways of collapsing (edge collapsing or star collapsing) are very simple and more sophisticated ways are not suggested: for instance based on modular decomposition or community detection. Maybe such more advanced ways lead to even better results. The experimental section shows that coarse-graining the input graph before applying a graph embedding methods leads to a "better" embedding. Indeed, using such an embedding improves the performance of the classification task compared to using the embedding obtained without coarse-graining. However, neither a theoretical justification of this fact is provided, nor an intuition. How about other machine learning tasks? For instance, does the suggested method also help for clustering and link prediction? The method does not make the embedding faster even though this might have been expected since the graphs are smaller. Figure 4: I do not understand in what the various level as relevant. To me, no level looks like the wished embedding. The graphs used in the experiments are extremely small (less than 30k nodes). It is not clear how the method would perform on large and sparse graphs, say 1G edges 100M nodes (for instance these: http://snap.stanford.edu/data/#communities).