# Geometric Matrix Completion with Recurrent Multi-Graph Neural Networks

arXiv: https://arxiv.org/abs/1704.06803 · HTML: https://mlsanity.com/paper/1704.06803/

## Key facts

- Cited by 88 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Apr 2017.

## Built on by (most cited first, 30 of 88)

- [Dirichlet Energy Constrained Learning for Deep Graph Neural Networks](https://mlsanity.com/paper/2107.02392/) (2021)
- [Decoupling the Depth and Scope of Graph Neural Networks](https://mlsanity.com/paper/2201.07858/) (2022)
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- [On the Unreasonable Effectiveness of Feature propagation in Learning on Graphs with Missing Node Features](https://mlsanity.com/paper/2111.12128/) (2021)
- [Graph Learning based Recommender Systems: A Review](https://mlsanity.com/paper/2105.06339/) (2021)
- [GKAN: Graph Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.06470/) (2024)
- [PaSca: a Graph Neural Architecture Search System under the Scalable Paradigm](https://mlsanity.com/paper/2203.00638/) (2022)
- [Bag of Tricks for Training Deeper Graph Neural Networks: A Comprehensive Benchmark Study](https://mlsanity.com/paper/2108.10521/) (2021)
- [Harnessing Multimodal Large Language Models for Multimodal Sequential Recommendation](https://mlsanity.com/paper/2408.09698/) (2024)
- [Network of Tensor Time Series](https://mlsanity.com/paper/2102.07736/) (2021)
- [Spiking Graph Convolutional Networks](https://mlsanity.com/paper/2205.02767/) (2022)
- [Evaluating Deep Graph Neural Networks](https://mlsanity.com/paper/2108.00955/) (2021)
- [Graph Neural Networks: Methods, Applications, and Opportunities](https://mlsanity.com/paper/2108.10733/) (2021)
- [Deconvolutional Networks on Graph Data](https://mlsanity.com/paper/2110.15528/) (2021)
- [Wide and Deep Graph Neural Network with Distributed Online Learning](https://mlsanity.com/paper/2107.09203/) (2021)
- [Confidence-Based Feature Imputation for Graphs with Partially Known Features](https://mlsanity.com/paper/2305.16618/) (2023)
- [Mitigating Performance Saturation in Neural Marked Point Processes: Architectures and Loss Functions](https://mlsanity.com/paper/2107.03354/) (2021)
- [Handling Missing Data via Max-Entropy Regularized Graph Autoencoder](https://mlsanity.com/paper/2211.16771/) (2022)
- [GLocal-K: Global and Local Kernels for Recommender Systems](https://mlsanity.com/paper/2108.12184/) (2021)
- [Graph Tensor Networks: An Intuitive Framework for Designing Large-Scale Neural Learning Systems on Multiple Domains](https://mlsanity.com/paper/2303.13565/) (2023)
- [Inductive Matrix Completion Using Graph Autoencoder](https://mlsanity.com/paper/2108.11124/) (2021)
- [Graph-based Neural Acceleration for Nonnegative Matrix Factorization](https://mlsanity.com/paper/2202.00264/) (2022)
- [Temporal Graph Signal Decomposition](https://mlsanity.com/paper/2106.13517/) (2021)
- [Efficient Dynamic Graph Representation Learning at Scale](https://mlsanity.com/paper/2112.07768/) (2021)
- [Continuous Product Graph Neural Networks](https://mlsanity.com/paper/2405.18877/) (2024)
- [Are deep learning models superior for missing data imputation in large surveys? Evidence from an empirical comparison](https://mlsanity.com/paper/2103.09316/) (2021)
- [Node-Variant Graph Filters in Graph Neural Networks](https://mlsanity.com/paper/2106.00089/) (2021)
- [Search For Deep Graph Neural Networks](https://mlsanity.com/paper/2109.10047/) (2021)
- [Siamese Attribute-missing Graph Auto-encoder](https://mlsanity.com/paper/2112.04842/) (2021)

## Abstract (arXiv)

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.