3 research outputs found
Edge Dithering for Robust Adaptive Graph Convolutional Networks
Graph convolutional networks (GCNs) are vulnerable to perturbations of the
graph structure that are either random, or, adversarially designed. The
perturbed links modify the graph neighborhoods, which critically affects the
performance of GCNs in semi-supervised learning (SSL) tasks. Aiming at
robustifying GCNs conditioned on the perturbed graph, the present paper
generates multiple auxiliary graphs, each having its binary 0-1 edge weights
flip values with probabilities designed to enhance robustness. The resultant
edge-dithered auxiliary graphs are leveraged by an adaptive (A)GCN that
performs SSL. Robustness is enabled through learnable graph-combining weights
along with suitable regularizers. Relative to GCN, the novel AGCN achieves
markedly improved performance in tests with noisy inputs, graph perturbations,
and state-of-the-art adversarial attacks. Further experiments with protein
interaction networks showcase the competitive performance of AGCN for SSL over
multiple graphs
Tensor Graph Convolutional Networks for Multi-relational and Robust Learning
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.Comment: Graph Convolutinal Networks, Robustness, Adversarial Attacks,
Semi-supervised learning, Multi-relational/Heterogenous networks. arXiv admin
note: text overlap with arXiv:1910.09590, arXiv:1811.0206
Generalized Matrix Means for Semi-Supervised Learning with Multilayer Graphs
We study the task of semi-supervised learning on multilayer graphs by taking
into account both labeled and unlabeled observations together with the
information encoded by each individual graph layer. We propose a regularizer
based on the generalized matrix mean, which is a one-parameter family of matrix
means that includes the arithmetic, geometric and harmonic means as particular
cases. We analyze it in expectation under a Multilayer Stochastic Block Model
and verify numerically that it outperforms state of the art methods. Moreover,
we introduce a matrix-free numerical scheme based on contour integral
quadratures and Krylov subspace solvers that scales to large sparse multilayer
graphs.Comment: Accepted in NeurIPS 201