mlsanityData to 14 Oct 2026

Convergence Guarantees for the DeepWalk Embedding on Block Models

arXiv 2410.20248 ↗First posted 26 Oct 2024cs.LG stat.MLcited by 0

Not on the map. Why?

Abstract (arXiv)

Graph embeddings have emerged as a powerful tool for understanding the structure of graphs. Unlike classical spectral methods, recent methods such as DeepWalk, Node2Vec, etc. are based on solving nonlinear optimization problems on the graph, using local information obtained by performing random walks. These techniques have empirically been shown to produce ''better'' embeddings than their classical counterparts. However, due to their reliance on solving a nonconvex optimization problem, obtaining theoretical guarantees on the properties of the solution has remained a challenge, even for simple classes of graphs. In this work, we show convergence properties for the DeepWalk algorithm on graphs obtained from the Stochastic Block Model (SBM). Despite being simplistic, the SBM has proved to be a classic model for analyzing the behavior of algorithms on large graphs. Our results mirror the existing ones for spectral embeddings on SBMs, showing that even in the case of one-dimensional embeddings, the output of the DeepWalk algorithm provably recovers the cluster structure with high probability.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 16 of its 38 references that are in the map. First posted on arXiv 26 Oct 2024.

Builds on

16 of 38 references.

References · 16

  1. 2017Inductive Representation Learning on Large Graphscited by 6,320
  2. 2013Efficient Estimation of Word Representations in Vector Spacecited by 4,375
  3. 2013Distributed Representations of Words and Phrases and their Compositionalitycited by 3,474
  4. 2016node2vec: Scalable Feature Learning for Networkscited by 1,918
  5. 2014DeepWalk: Online Learning of Social Representationscited by 1,547
  6. 2015LINE: Large-scale Information Network Embeddingcited by 582
  7. 2017Community Detection and Stochastic Block Modelscited by 319
  8. 2017Network Embedding as Matrix Factorization: Unifying DeepWalk, LINE, PTE, and node2veccited by 198
  9. 2021Small random initialization is akin to spectral learning: Optimization and generalization guarantees for overparameterized low-rank matrix reconstructioncited by 78
  10. 2021Theoretical Foundations of t-SNE for Visualizing High-Dimensional Clustered Datacited by 55
  11. 2017Clustering with t-SNE, provablycited by 51
  12. 2018An Analysis of the t-SNE Algorithm for Data Visualizationcited by 49
4 more
  1. 2020InfiniteWalk: Deep Network Embeddings as Laplacian Embeddings with a Nonlinearitycited by 19
  2. 2021The Dynamics of Gradient Descent for Overparametrized Neural Networkscited by 11
  3. 2021Community detection using low-dimensional network embedding algorithmscited by 4
  4. 2021Delving Into Deep Walkers: A Convergence Analysis of Random-Walk-Based Vertex Embeddingscited by 1

Built on by

Not cited yet.