Therefore most often the representation should not fully follow homophily or structural equivalence. Remember we want to capture the network topology and the relationships within this network. However, most algorithms let this unfold more unsupervised, networks can be structured based on principles we do not know. There it’s Vincent that has a similar embedding to Joanna, since both connect the rectangle peer group with a triangle peer group. Please note that for example the embedding values are really similar for Joanna and Pierre if similarity is based on homophily but very different if it’s based on structural equivalence. HomophilyĮmbedding plot after dimensionality reduction /w e.g. □ So the vector representation of Joanna needs to be similar to the vector representation of Peter, since they are neighbors. That said, we want to group people together that spend time together. In many real world networks homophily was found to be an organising principle, especially in social networks. One concept that was found to be useful is called homophily. If we go back to the introductary network example where we have a social network and we want to assign the different people to groups (that was one possible question), we can try to form embeddings that help us to do so. Nodes that are similar in the network will have similar embeddings. We can decide to form embeddings based on the principle of similarity. Whatever this similarity might be, it’s upon us to decide. How are we going to grasp that in order that we have a clear procedure?Ī possible shortcut to this problem is to try to form embeddings such that node embeddings of two nodes are similar in some sense, if they happen to have some similarity in the real network. It depends on the questions we ask about the network.Įmbedding should capture the graph topology, relationships between nodes and further information. How the embeddings should capture this inherent information of the graph is not fixed. Graph representation, by author Node embeddingsīut what rules should node embeddings obey in order to allow inference?Įmbeddings should capture the graph topology, relationships between nodes and further relevant information.
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