Geometric Matrix Completion with Recurrent Multi-Graph Neural Networks

By Federico Monti, Michael M. Bronstein, Xavier Bresson. 2017

554 citations recorded by the source corpus.

Matrix completion models are among the most common formulations of recommender systems. Recent works have showed a boost of performance of these techniques when introducing the pairwise relationships between users/items in the form of graphs, and imposing smoothness priors on these graphs. However, such techniques do not fully exploit the local stationarity structures of user/item graphs, and the number of parameters to learn is linear w.r.t. the number of users and items. We propose a novel approach to overcome these limitations by using geometric deep learning on graphs. Our matrix completion architecture combines graph convolutional neural networks and recurrent neural networks to learn meaningful statistical graph-structured patterns and the non-linear diffusion process that generates the known ratings. This neural network system requires a constant number of parameters independent of the matrix size. We apply our method on both synthetic and real datasets, showing that it outperforms state-of-the-art techniques.

Subfields: Model Architectures, Graph Learning

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Citations in the corpus

Graph Convolutional Neural Networks for Web-Scale Recommender Systems (2018, methodology): “Most prominent among these recent advancements is the success of deep learning architectures known as Graph Convolutional Networks (GCNs) [19, 21, 24, 29].”
Geometric Deep Learning: Going beyond Euclidean data (2016, methodology): “The interest in deep learning on graphs or manifolds has exploded in the past year, resulting in numerous attempts to apply these methods in a broad spectrum of problems ranging from biochemistry [55] to recommender systems [56].”
Dynamic Graph CNN for Learning on Point Clouds (2018, methodology): “ Laplacian eigenvectors [Shuman et al. 2013]. Computational drawbacks of this foundational approach were alleviated in follow-up works using polynomial [Defferrard et al. 2016; Kipf and Welling 2017; Monti et al. 2017b, 2018], or rational [Levie et al. 2017] spectral filters that avoid Laplacian eig”
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.”
MOTIFNET: A MOTIF-BASED GRAPH CONVOLUTIONAL NETWORK FOR DIRECTED GRAPHS (2018, methodology): “Spectral approaches [5, 6, 7, 8, 9, 10] use the analogy between the eigenfunctions of the graph Laplacian and the classical Fourier transform, and define a convolution-like operation in the spectral domain.”
Graph Neural Networks for Social Recommendation (2019, methodology): “he task of recommender systems, the user-item interaction contains the ratings on items by users, which is a typical graph data. Therefore, GNNs have been proposed to solve the recommendation problem [1, 22, 39]. sRMGCNN [22] adopted GNNs to extract graph embeddings for users and items, and then com”
Benchmarking Graph Neural Networks (2023, methodology): “In the last few years, graph neural networks (GNNs) have seen a great surge of interest with promising methods being developed for myriad of domains including chemistry [25, 31], physics [20, 73], social sciences [44, 65], knowledge graphs [76, 16], recommendation [64, 91], and neuroscience [32].”
Deep Learning with Graph Convolutional Networks: An Overview and Latest Applications in Computational Intelligence (2023, methodology): “[74] combined a multi-graph convolutional neural network with a recurrent neural network, in which the multigraph convolutional neural network was used to extract locally stationary features, and the recurrent neural network could difuse the fractional values and reconstruct the matrix.”
Propagation Model Search for Graph Neural Networks (2020, methodology): “Paired Graphs We evaluate POSE on the task of geometric matrix completion using two recommender sys-tem datasets, MovieLens and Flixster (Monti, Bronstein, and Bresson 2017), along with a spatial-temporal dataset CCDS (Lozano et al. 2009).”
A federated graph neural network framework for privacy-preserving personalization (2021, methodology): “, 2015), a collaborative filtering approach with graph information; (4) sRGCNN (Monti et al., 2017), a matrix completion method with recurrent multi-graph neural networks; (5) GC-MC (Berg et al.”
Link Prediction Based on Graph Neural Networks (2018, methodology): “We omit path ranking methods [28] as well as other recent methods which are specifically designed for knowledge graphs or recommender systems [23, 35].”
Revisiting Graph based Collaborative Filtering: A Linear Residual Graph Convolutional Network Approach (2020, methodology): “With the huge success of GCNs, researchers attempted to formulate recommendation as a user-item bipartite graph, and adapted GCNs for recommendation (Wang et al. 2019; Monti, Bronstein, and Bresson 2017; Ying et al. 2018).”
Knowledge-driven Encode, Retrieve, Paraphrase for Medical Image Report Generation (2019, background): “have gained increasing research interests (Defferrard, Bres-son, and Vandergheynst 2016; Kipf and Welling 2017; Monti, Bronstein, and Bresson 2017).”
Graph Transformer Networks (2019, background): “The representation learnt by GNNs has been proven to be effective in achieving state-ofthe-art performance in a variety of graph datasets such as social networks [7, 14, 35], citation networks [19, 33], functional structure of brains [20], recommender systems [1, 27, 39].”