Learning Convolutional Neural Networks for Graphs

By Mathias Niepert, Mohamed Ahmed, Konstantin Kutzkov. 2016

2,290 citations recorded by the source corpus.

Numerous important problems can be framed as learning from graph data. We propose a framework for learning convolutional neural networks for arbitrary graphs. These graphs may be undirected, directed, and with both discrete and continuous node and edge attributes. Analogous to image-based convolutional networks that operate on locally connected regions of the input, we present a general approach to extracting locally connected regions from graphs. Using established benchmark data sets, we demonstrate that the learned feature representations are competitive with state of the art graph kernels and that their computation is highly efficient.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Graph Learning

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Computer Vision and Pattern Recognition

In Graph Learning

Citations in the corpus

Semi-Supervised Classification with Graph Convolutional Networks (2016, methodology): “We leave memory-efﬁcient extensions with mini-batch stochastic gradient descent for future work.”
Graph Attention Networks (2017, methodology): “…degree (Duvenaud et al., 2015), using the powers of a transition matrix to deﬁne the neighborhood while learning weights for each input channel and neighborhood degree (Atwood & Towsley, 2016), or extracting and normalizing neighborhoods containing a ﬁxed number of nodes (Niepert et al., 2016).”
Inductive Representation Learning on Large Graphs (2017, neutral): “The majority of these methods do not scale to large graphs or are designed for whole-graph classification (or both) [4, 9, 8, 24].”
Learning Non-maximum Suppression (2017, background): “[18] operates on graphs, but requires a pre-processing that defines a node ordering, which is ill-defined in our case.”
A simple neural network module for relational reasoning (2017, background): “approaches [11, 32] and has been explicitly pursued using neural networks as well [4]. There is recent work applying neural networks to graphs, which are a natural structure for formalising relations [12, 19, 33, 37, 26, 2]. Perhaps a crucial dierence between this work and our work here is that RNs ”
Knowledge Graph Convolutional Networks for Recommender Systems (2019, background): “To handle the neighborhoods with varying size and maintain the weight sharing property of CNN, researchers propose learning a weight matrix for each node degree [6], extracting locally connected regions from graphs [13], or sampling a fixed-size set of neighbors as the support size [7].”
Neural Message Passing for Quantum Chemistry (2017, background): “Examples in this family include Niepert et al. (2016) and Rupp et al.”
Relational inductive biases, deep learning, and graph networks (2018, background): “passing neural network (MPNN), which unied various graph neural network and graph convolutional network approaches (Monti et al., 2017; Bruna et al., 2014; Hena et al., 2015; Deerrard et al., 2016; Niepert et al., 2016; Kipf and Welling, 2017; Bronstein et al., 2017) by analogy to message-passing in”
Physics-Informed Neural Networks for Cardiac Activation Mapping (2020, methodology): “We can address this limitation by using more complex architectures, such as convolutional neural networks on graphs [43], which we plan to explore in the future.”
Relational Deep Reinforcement Learning (2018, neutral): “more generally, message passing computations [26, 27, 28, 12].”
The More You Know: Using Knowledge Graphs for Image Classification (2016, background): “There has been a lot of work in end-to-end learning on graphs or neural network trained on graphs [31, 2, 6, 11, 25, 22, 9, 21].”
Unsupervised Inductive Whole-Graph Embedding by Preserving Graph Proximity (2019, methodology): “, 2016), Convolutional Neural Networks (Niepert et al., 2016), etc.”
How Powerful are Graph Neural Networks? (2018, background): “…∈ { 1 , 2 , . . . , 6 } ; (2) state-of-the-art deep learning architectures Diffusion-convolutional neural networks (DCNN) (Atwood & Towsley, 2016), PATCHY-SAN (Niepert et al., 2016) and Deep Graph CNN (DGCNN) (Zhang et al., 2018); (3) Anonymous Walk Embeddings (AWL) (Ivanov & Burnaev, 2018).”
Hierarchical Graph Representation Learning with Differentiable Pooling (2018, methodology): “network (GNN) models have been proposed in recent years, including methods inspired by convolutional neural networks [5, 8, 11, 16, 21, 24, 29, 36], recurrent neural networks [25], recursive neural networks [1, 30] and loopy belief propagation [7].”
An End-to-End Deep Learning Architecture for Graph Classification (2018, methodology): “Among these methods, PSCN and ECC can leverage additional edge features.”
Representation Learning on Graphs: Methods and Applications (2017, background): “The most prominent application domain is for classifying the properties of graphs corresponding to different molecules [16, 21, 43, 33].”
Learning Graph-Level Representation for Drug Discovery (2017, background): “…and other general graph neural networks designed for all types of graph(Li et al. 2015; Bruna et al. 2013; Defferrard, Bresson, and Vandergheynst 2016; Kipf and Welling 2016; Niepert, Ahmed, and Kutzkov 2016), all focus on learning node-level representation rather than graphlevel representation.”
subgraph2vec: Learning Distributed Representations of Rooted Sub-graphs from Large Graphs (2016, background): “Once skipgram training converges, semantically similar words are mapped to closer positions in the embedding space Algorithm 1: subgraph2vec (G, D, δ, e) input : G = {G1, G2, ..., Gn}: set of graphs such that each graph Gi = (Vi, Ei, λi) from which embeddings are learnt D: Maximum degree of…”