Comprehend DeepWalk as Matrix Factorization
This work provides a theoretical foundation for DeepWalk, clarifying its underlying mechanism for researchers in network analysis and graph representation learning.
The paper proves that the DeepWalk algorithm for learning node embeddings in graphs is equivalent to factorizing a matrix M, where each entry M_ij is the logarithm of the average probability that node i randomly walks to node j in a fixed number of steps.
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.