# Learning with Multigraph Convolutional Filters

arXiv: https://arxiv.org/abs/2210.16272 · HTML: https://mlsanity.com/paper/2210.16272/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 27 references that are in the map.
- First posted on arXiv 28 Oct 2022.

## Builds on (most cited first, 15 of 15)

- [MAGNN: Metapath Aggregated Graph Neural Network for Heterogeneous Graph Embedding](https://mlsanity.com/paper/2002.01680/) (2020)
- [Convolutional Neural Network Architectures for Signals Supported on Graphs](https://mlsanity.com/paper/1805.00165/) (2018)
- [Representation Learning for Attributed Multiplex Heterogeneous Network](https://mlsanity.com/paper/1905.01669/) (2019)
- [Optimal Wireless Resource Allocation with Random Edge Graph Neural Networks](https://mlsanity.com/paper/1909.01865/) (2019)
- [An Attention-based Collaboration Framework for Multi-View Network Representation Learning](https://mlsanity.com/paper/1709.06636/) (2017)
- [Multiplex Heterogeneous Graph Convolutional Network](https://mlsanity.com/paper/2208.06129/) (2022)
- [Algebraic Neural Networks: Stability to Deformations](https://mlsanity.com/paper/2009.01433/) (2020)
- [Joint predictions of multi-modal ride-hailing demands: a deep multi-task multigraph learning-based approach](https://mlsanity.com/paper/2011.05602/) (2020)
- [Graphon Pooling in Graph Neural Networks](https://mlsanity.com/paper/2003.01795/) (2020)
- [Convolutional Learning on Multigraphs](https://mlsanity.com/paper/2209.11354/) (2022)
- [Discrete Signal Processing with Set Functions](https://mlsanity.com/paper/2001.10290/) (2020)
- [Discrete Signal Processing on Meet/Join Lattices](https://mlsanity.com/paper/2012.04358/) (2020)
- [Multiplex PageRank](https://mlsanity.com/paper/1306.3576/) (2013)
- [Quiver Signal Processing (QSP)](https://mlsanity.com/paper/2010.11525/) (2020)
- [Parallel Multi-Graph Convolution Network For Metro Passenger Volume Prediction](https://mlsanity.com/paper/2109.00924/) (2021)

## Built on by (most cited first, 5 of 5)

- [Graph neural networks and non-commuting operators](https://mlsanity.com/paper/2411.04265/) (2024)
- [Convolutional Filtering with RKHS Algebras](https://mlsanity.com/paper/2411.01341/) (2024)
- [RKHS Representation of Algebraic Convolutional Filters with Integral Operators](https://mlsanity.com/paper/2602.19094/) (2026)
- [Non Commutative Convolutional Signal Models in Neural Networks: Stability to Small Deformations](https://mlsanity.com/paper/2310.03879/) (2023)
- [Fundamental Limits of Transferability and Equivariance in Algebraic Signal Models I: Finite Dimensions](https://mlsanity.com/paper/2609.36106/) (2026)

## Abstract (arXiv)

In this paper, we introduce a convolutional architecture to perform learning when information is supported on multigraphs. Exploiting algebraic signal processing (ASP), we propose a convolutional signal processing model on multigraphs (MSP). Then, we introduce multigraph convolutional neural networks (MGNNs) as stacked and layered structures where information is processed according to an MSP model. We also develop a procedure for tractable computation of filter coefficients in the MGNN and a low cost method to reduce the dimensionality of the information transferred between layers. We conclude by comparing the performance of MGNNs against other learning architectures on an optimal resource allocation task for multi-channel communication systems.