Tensor Graph Convolutional Networks for Multi-Relational and Robust Learning

Vassilis N. Ioannidis, Antonio G. Marques, Georgios B. Giannakis

Research output: Contribution to journalArticlepeer-review


The era of 'data deluge' has sparked renewed interest in graph-based learning methods and their widespread applications ranging from sociology and biology to transportation and communications. In this context of graph-aware methods, the present paper introduces a tensor-graph convolutional network (TGCN) for scalable semi-supervised learning (SSL) from data associated with a collection of graphs, that are represented by a tensor. Key aspects of the novel TGCN architecture are the dynamic adaptation to different relations in the tensor graph via learnable weights, and the consideration of graph-based regularizers to promote smoothness and alleviate over-parameterization. The ultimate goal is to design a powerful learning architecture able to: discover complex and highly nonlinear data associations, combine (and select) multiple types of relations, scale gracefully with the graph size, and remain robust to perturbations on the graph edges. The proposed architecture is relevant not only in applications where the nodes are naturally involved in different relations (e.g., a multi-relational graph capturing family, friendship and work relations in a social network), but also in robust learning setups where the graph entails a certain level of uncertainty, and the different tensor slabs correspond to different versions (realizations) of the nominal graph. Numerical tests showcase that the proposed architecture achieves markedly improved performance relative to standard GCNs, copes with state-of-the-art adversarial attacks, and leads to remarkable SSL performance over protein-to-protein interaction networks.

Original languageEnglish (US)
Article number9216050
Pages (from-to)6535-6546
Number of pages12
JournalIEEE Transactions on Signal Processing
StatePublished - 2020

Bibliographical note

Funding Information:
Manuscript received March 15, 2020; revised August 8, 2020; accepted September 17, 2020. Date of publication October 7, 2020; date of current version December 1, 2020. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Vincent Gripon. This work was supported in part by the Doctoral Dissertation Fellowship of the University of Minnesota, the USA NSF under Grants 171141, 1500713, and 1442686, and in part by the Spanish Grants KLINILYCS (TEC2016-75361-R), SPGraph (PID2019-105032GB-I00) and Instituto de Salud Carlos III DTS17/00158. (Corresponding author: Georgios B. Giannakis.) Vassilis N. Ioannidis and Georgios B. Giannakis are with the Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455 USA (e-mail: ioann006@umn.edu; georgios@umn.edu).


  • adversarial attacks on graphs
  • Graph convolutional networks
  • multi-relational graphs
  • robust learning

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