Adaptive diffusions for scalable learning over graphs

Dimitris Berberidis, Athanasios N. Nikolakopoulos, Georgios B. Giannakis

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


Diffusion-based classifiers such as those relying on the Personalized PageRank and the heat kernel enjoy remarkable classification accuracy at modest computational requirements. Their performance however is affected by the extent to which the chosen diffusion captures a typically unknown label propagation mechanism, which can be specific to the underlying graph, and potentially different for each class. This paper introduces a disciplined, data-efficient approach to learning class-specific diffusion functions adapted to the underlying network topology. The novel learning approach leverages the notion of "landing probabilities" of class-specific random walks, which can be computed efficiently, thereby ensuring scalability to large graphs. This is supported by rigorous analysis of the properties of the model as well as the proposed algorithms. Furthermore, a robust version of the classifier facilitates learning even in noisy environments. Classification tests on real networks demonstrate that adapting the diffusion function to the given graph and observed labels significantly improves the performance over fixed diffusions, reaching-and many times surpassing-the classification accuracy of computationally heavier state-of-the-art competing methods, which rely on node embeddings and deep neural networks.

Original languageEnglish (US)
Article number8590776
Pages (from-to)1307-1321
Number of pages15
JournalIEEE Transactions on Signal Processing
Issue number5
StatePublished - Mar 1 2019

Bibliographical note

Funding Information:
Manuscript received April 5, 2018; revised September 10, 2018 and December 6, 2018; accepted December 12, 2018. Date of publication December 27, 2018; date of current version January 15, 2019. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Alexander Bertrand. This work was supported by the National Science Foundation under Grants 171141, 1514056, 1500713, and 1442686. (Corresponding author: Georgios B. Giannakis.) D. Berberidis is with the Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455 USA (e-mail:,

Publisher Copyright:
© 2018 IEEE.


  • Diffusions
  • Random walks
  • Semi-supervised classification


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