MOTIFNET: A MOTIF-BASED GRAPH CONVOLUTIONAL NETWORK FOR DIRECTED GRAPHS

By Federico Monti, Karl Otness, Michael M. Bronstein. 2018

153 citations recorded by the source corpus.

Deep learning on graphs and in particular, graph convolutional neural networks, have recently attracted significant attention in the machine learning community. Many of such techniques explore the analogy between the graph Laplacian eigenvectors and the classical Fourier basis, allowing to formulate the convolution as a multiplication in the spectral domain. One of the key drawback of spectral CNNs is their explicit assumption of an undirected graph, leading to a symmetric Laplacian matrix with orthogonal eigendecomposition. In this work we propose MotifNet, a graph CNN capable of dealing with directed graphs by exploiting local graph motifs. We present experimental evidence showing the advantage of our approach on real data.

Subfields: Artificial Intelligence, Cognitive Neuroscience, Statistical and Nonlinear Physics

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Citations in the corpus

Can graph neural networks count substructures? (2020, background): “While people have proposed variants of GNNs that take advantage of substructure information (Monti et al., 2018; Liu et al., 2018, 2019), often they rely on handcrafting rather than learning such information.”
PGM-Explainer: Probabilistic Graphical Model Explanations for Graph Neural Networks (2020, background): “Many GNN’s architectures with high predictive performance should be mentioned are ChebNets [4], Graph Convolutional Networks [5], GraphSage [6], Graph Attention Networks [7], among others [8, 9, 10, 11, 12, 13].”
Improving Graph Neural Network Expressivity via Subgraph Isomorphism Counting (2020, background): “Motif-based vertex embeddings [88], [89] and diffusion operators [90], [91],”
Fake News Detection on Social Media using Geometric Deep Learning (2019, background): “Such spectral ﬁlters typically scale linearly with the graph size and can be generalized to higher order structures [25], dual graphs (edge ﬁlters) [26], and product graphs [24].”
SIGN: Scalable Inception Graph Neural Networks (2020, background): “, 2020), or motifs (Monti et al., 2018) that can be tailored to the specific problem.”
Human Action Recognition From Various Data Modalities: A Review (2020, background): “Due to the expressive power of graph structures, analyzing graphs with learning models have received great attention recently [184], [185].”
Dual-Primal Graph Convolutional Networks (2018, methodology): “…of the Laplacian and expressed in terms of simple operations (scalar-and matrix multiplications, additions, and inversions), including polynomials [10, 26], rational functions [27], and multivariate polynomials [35, 36], thus avoiding explicit eigendecomposition of the Laplacian altogether.”
Graph convolutional networks for computational drug development and discovery (2019, background): “[120] investigated spectral graph convolution for motifs and validated on citation network data.”
Understanding over-squashing and bottlenecks on graphs via curvature (2021, methodology): “…subsampling or resampling to deal with scalability (Hamilton et al., 2017) or topological noise (Zhang et al., 2019), using larger motif-based (Monti et al., 2018) or multi-hop ﬁlters (Rossi et al., 2020), or changing the graph either as a preprocessing step (Klicpera et al., 2019; Alon &…”