arXiv:1501.00358cs.LG
Comprehend DeepWalk as Matrix Factorization
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Abstract
Word2vec, as an efficient tool for learning vector representation of words has shown its effectiveness in many natural language processing tasks. Mikolov et al. issued Skip-Gram and Negative Sampling model for developing this toolbox. Perozzi et al. introduced the Skip-Gram model into the study of social network for the first time, and designed an algorithm named DeepWalk for learning node embedding on a graph. We prove that the DeepWalk algorithm is actually factoring a matrix M where each entry M_{ij} is logarithm of the average probability that node i randomly walks to node j in fix steps.
The connection between the random walk and embeddings has been characterized in [1] (disclosure: I am an author). It turns out embedding in this setting is exactly smarter page rank as you suggested, since PageRank recovers the underlying density structure of an embedding. I'm…
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