# Comprehend DeepWalk as Matrix Factorization

arXiv: https://arxiv.org/abs/1501.00358 · HTML: https://mlsanity.com/paper/1501.00358/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jan 2015.

## Built on by (most cited first, 3 of 3)

- [Adversarial Attack Framework on Graph Embedding Models with Limited Knowledge](https://mlsanity.com/paper/2105.12419/) (2021)
- [Recommender systems based on graph embedding techniques: A comprehensive review](https://mlsanity.com/paper/2109.09587/) (2021)
- [Zoo Guide to Network Embedding](https://mlsanity.com/paper/2305.03474/) (2023)

## Abstract (arXiv)

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.