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Node Embeddings
How do we do node embeddings? ([source](http://snap.stanford.edu/proj/embeddings-www/index.html#materials)) Intuition: Find embedding of nodes so that “similar” nodes in the graph have embeddings that are close together. 1. Define an encoder (i.e., a mapping from nodes to embeddings) - Shallow embedding (simplest encoding approach): encoder is just an embedding-lookup. Ex: [node2vec](/tag/node2vec), DeepWalk, LINE 2. Define a node similarity function, eg. nodes are similar if: - they are connected? - they share neighbours? - have structural similar roles? - ... 3. Optimize the parameters of the encoder so that similarity in the embedding space (e.g., dot product) approximates similarity in the original network Defining similarity: - Adjacency-based Similarity - "Multihop" similarity (measure overlap between node neighborhoods) these two methods are expensive. -> **Random-walk Embeddings** (Estimate probability of visiting node v on a random walk starting from node u using some random walk strategy, optimize embeddings to encode random walk statistics). Expressivity (incorporates both local and higher-order neighbourhood information) and efficiency (do not need to consider all pairs when training) Which random walk strategy? - fixed-length random walks starting from each node: **DeepWalk** (Perozzi et al., 2013) - "biased random walks" that can trade off between local and global views of the network: **Node2Vec** (Micro-view / marco-view of neighbourhood) No method wins in all the cases
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