Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphs

By Martin Simonovsky, Nikos Komodakis. 2017

1,361 citations recorded by the source corpus.

A number of problems can be formulated as prediction on graph-structured data. In this work, we generalize the convolution operator from regular grids to arbitrary graphs while avoiding the spectral domain, which allows us to handle graphs of varying size and connectivity. To move beyond a simple diffusion, filter weights are conditioned on the specific edge labels in the neighborhood of a vertex. Together with the proper choice of graph coarsening, we explore constructing deep neural networks for graph classification. In particular, we demonstrate the generality of our formulation in point cloud classification, where we set the new state of the art, and on a graph classification dataset, where we outperform other deep learning approaches.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Graph Learning

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Citations in the corpus

Dynamic Neural Networks: A Survey (2021, methodology): “Others Time series forecasting [248], [249], [250], Link prediction [251], Recommendation system [77], [252], [253], [254] Graph classification [121], Document classification [156], [255], [256], [257], Stereo confidence estimation [258]”
Fast Graph Representation Learning with PyTorch Geometric (2019, methodology): “We currently provide implementation examples for Graclus (Dhillon et al., 2007; Fagginger Auer & Bisseling, 2011) and voxel grid pooling (Simonovsky & Komodakis, 2017), the iterative farthest point sampling algorithm (Qi et al., 2017) followed by 𝑘 -NN or query ball graph generation (Qi et al.,…”
Unsupervised Inductive Whole-Graph Embedding by Preserving Graph Proximity (2019, background): “Here we highlight some existing works to demonstrate its popularity, including PATCHYSAN (Niepert et al., 2016), ECC (Simonovsky & Komodakis, 2017), SET2SET (Gilmer et al., 2017), GRAPHSAGE, DGCNN/SORTPOOL (Zhang et al., 2018), SAN (Zhao et al., 2018), DIFFPOOL (Ying et al., 2018), CAPSGNN (Zhang &…”
Pre-training Graph Neural Networks with Kernels (2018, positive): “Simonovsky and Komodakis [2017] propose an improvement of Duvenaud et al. [2015], weighting the sum over the neighbors of a node by weights conditioned by the edge labels.”
Hierarchical Graph Representation Learning with Differentiable Pooling (2018, methodology): “• Edge-conditioned filters in CNN for graphs (ECC) [35] incorporates edge information into the GCN model and performs pooling using a graph coarsening algorithm.”
An End-to-End Deep Learning Architecture for Graph Classification (2018, background): “Among these methods, PSCN and ECC can leverage additional edge features.”
Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data (2020, background): “…g θ has independent parameters for each of the inputs ( 1 , − 1) , ( 1 , 0) , . . . that − − In order to accommodate points are not on a regular grid, g θ can be parametrized as a small neural network, mapping input off-sets to ﬁlter matrices, explored with MLPs in Simonovsky and Komodakis (2017).”
Provably Powerful Graph Networks (2019, neutral): “4 ECC (Simonovsky and Komodakis, 2017) 76.”
Towards Sparse Hierarchical Graph Classifiers (2018, methodology): “The proposed strategies broadly fall into two categories: 1) aggregating node representations in a global pooling step after each [8] or after the final message passing step [19, 5, 11], and 2) aggregating node representations into clusters which coarsen the graph in a hierarchical manner [4, 22, 6,”
Dynamic Graph CNN for Learning on Point Clouds (2018, background): “…83.0 85.9 Subvolume [Qi et al. 2016] 86.0 89.2 VRN (single view) [Brock et al. 2016] 88.98 - VRN (multiple views) [Brock et al. 2016] 91.33 - ECC [Simonovsky and Komodakis 2017] 83.2 87.4 PointNet [Qi et al. 2017b] 86.0 89.2 PointNet++ [Qi et al. 2017c] - 90.7 Kd-net [Klokov and Lempitsky 2017]…”
Graph Convolutional Networks with EigenPooling (2019, background): “There are a few recent works [8, 13, 39, 48] investigating learning graph representations with a hierarchical pooling procedure.”
Deep Parametric Continuous Convolutional Neural Networks (2018, methodology): “Other Approaches: Edge-conditioned filter networks [27] use a weighting network to communicate between adjacent nodes on the graph [13] conditioned on edge labels, which is primarily formulated as relative point locations.”
Substructure Assembling Network for Graph Classification (2018, methodology): “(2) For the methods in graph space (Simonovsky and Komodakis 2017; Li et al. 2016; Duvenaud et al. 2015), they usually assume that feature se- lection behaves identically for neighbor nodes with the same node/edge attributes.”