Diffusion-Convolutional Neural Networks

By James Atwood, D. Towsley. 2015

1,376 citations recorded by the source corpus.

We present diffusion-convolutional neural networks (DCNNs), a new model for graph-structured data. Through the introduction of a diffusion-convolution operation, we show how diffusion-based representations can be learned from graph-structured data and used as an effective basis for node classification. DCNNs have several attractive qualities, including a latent representation for graphical data that is invariant under isomorphism, as well as polynomial-time prediction and learning that can be represented as tensor operations and efficiently implemented on the GPU. Through several experiments with real structured datasets, we demonstrate that DCNNs are able to outperform probabilistic relational models and kernel-on-graph methods at relational node classification tasks.

Subfields: Artificial Intelligence, Building and Construction, Neurology, 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 Building and Construction

In Neurology

In Graph Learning

Citations in the corpus

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).”
Geometric Deep Learning on Graphs and Manifolds Using Mixture Model CNNs (2016, methodology): “Such a construction allows to formulate previously proposed Geodesic CNN (GCNN) [32] and Anisotropic CNN (ACNN) [7] on manifolds or GCN [26] and DCNN [2] on graphs as particular instances of our approach.”
On the Binding Problem in Artificial Neural Networks (2020, background): “, 2018), and bio-chemical modeling (Atwood and Towsley, 2016).”
How Powerful are Graph Neural Networks? (2018, neutral): “…the number of WL iterations ∈ { 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)…”
An End-to-End Deep Learning Architecture for Graph Classification (2018, methodology): “DiffusionCNN (DCNN) (Atwood and Towsley 2016) uses diffusion graph convolutions to extract multi-scale substructure features.”
Provably Powerful Graph Networks (2019, methodology): “(2015); Atwood and Towsley (2016); Niepert et al. (2016); Hamilton et al. (2017b); Veličković et al. (2017); Monti et al. (2018)). Many of these works were shown to be instances of the family of message passing neural networks (Gilmer et al., 2017): methods that apply parametric functions to a node ”
Geometric Deep Learning: Going beyond Euclidean data (2016, background): “In this setting, a generalization of convolution in the spatial domain using local charting [46], [47], [48] appears to be more appropriate.”
Simplifying Graph Convolutional Networks (2019, background): “Atwood & Towsley (2016), Abu-El-Haija et al. (2018), and Liao et al. (2019) exploit multi-scale information by raising S to higher order.”
A simple yet effective baseline for non-attribute graph classification (2018, background): “gnment kernel (WL-OA)[KGW16], and 5graphneuralnetworks: PATCHYSAN(PSCN)[NAK16],GRAPHSAGE[HYL17],DIFFPOOL[YYM+18], Graph Isomorphism Network GIN[XHLJ18], Diffusion-convolutional neural networks (DCNN) [AT16]. In particular, among above graph kernels, only FGSD and GK does not utilize label informatio”
Attention-based Graph Neural Network for Semi-supervised Learning (2018, background): “We give a typical example of a GNN in Section 3, but several diverse variations have been proposed in [10, 17, 29, 24, 39, 8, 15, 13, 3, 32, 38, 23, 37, 38].”
Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphs (2017, neutral): “The weights in ECC are tied by edge label, which is in contrast to tying them by hop distance from a vertex [2], according to a neighborhood linearization heuristic [27], by being the central vertex or not [20], indiscriminately [14], or not at all [6].”
A Comprehensive Survey on Graph Neural Networks (2019, methodology): “Spatial-based models are more ﬂexible to handle multi-source graph inputs such as edge inputs [15], [27], [86], [95], [96], directed graphs [25], [72], signed graphs [97], and heterogeneous graphs [98], [99], because these graph inputs can be incorporated into the aggregation function easily.”
Spherical CNNs on Unstructured Grids (2019, background): “, 2015; Badrinarayanan et al., 2015; Long et al., 2015; Jégou et al., 2017; Wang et al., 2018a). Song et al. (2017) study semantic segmentation of equirectangular omnidirectional images, but in the context of image inpainting, where only a partial view is given as input.”
Deconfounded Image Captioning: A Causal Retrospect (2020, methodology): “Inspired by this, researchers [44], [45], [46] proposed to learn a scene graph from the image and to apply Graph Neural Network [47], [48], [49] to transform this Fig.”
Skeleton-Based Action Recognition With Multi-Stream Adaptive Graph Convolutional Networks (2019, methodology): “Recently, graph convolutional networks (GCNs), which generalize convolution from image to graph, have been successfully adopted in many applications[23], [24], [25], [26], [27], [28], [29].”
GRAND: Graph Neural Diffusion (2021, methodology): “Additionally we compare to recent ODE-based GNN models, Continuous Graph Neural Networks (CGNN) (Xhonneux et al., 2020), Graph Neural Ordinary Differential Equations (GDE) (Poli et al., 2019), and Ordinary Differential Equations on Graphs (GODE) (Zhuang et al., 2020) and two versions of LanczosNet (”
Janossy Pooling: Learning Deep Permutation-Invariant Functions for Variable-Size Inputs (2018, background): “…each layer pools together embeddings of neighbors of a vertex to form a new embedding for that vertex, see for instance, (Kipf & Welling, 2016; Atwood & Towsley, 2016; Hamilton et al., 2017; Velick-ovic et al., 2017; Monti et al., 2017; Xu et al., 2018; Liu et al., 2018; Liben-Nowell &…”
Two-Stream Adaptive Graph Convolutional Networks for Skeleton-Based Action Recognition (2018, background): “There have been many works on graph convolution, and the principle of constructing GCNs mainly follows two streams: spatial perspective and spectral perspective [28, 2, 11, 25, 1, 16, 7, 5, 9, 24, 15].”
Message Passing Attention Networks for Document Understanding (2019, background): “6 Related work (Kipf and Welling 2016; Atwood and Towsley 2016; Veliˇckovi´c et al. 2017; Hamilton, Ying, and Leskovec 2017) conduct some node classiﬁcation experiments on citation networks, where nodes are scientiﬁc papers, i.e., textual data.”