# MM-GNN: Mix-Moment Graph Neural Network towards Modeling Neighborhood Feature Distribution

arXiv: https://arxiv.org/abs/2208.07012 · HTML: https://mlsanity.com/paper/2208.07012/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 64 references that are in the map.
- First posted on arXiv 15 Aug 2022.

## Builds on (most cited first, 30 of 40)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [GraphSAINT: Graph Sampling Based Inductive Learning Method](https://mlsanity.com/paper/1907.04931/) (2019)
- [Exploring Generalization in Deep Learning](https://mlsanity.com/paper/1706.08947/) (2017)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Principal Neighbourhood Aggregation for Graph Nets](https://mlsanity.com/paper/2004.05718/) (2020)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Graph Neural Networks with Learnable Structural and Positional Representations](https://mlsanity.com/paper/2110.07875/) (2021)
- [Do Transformers Really Perform Bad for Graph Representation?](https://mlsanity.com/paper/2106.05234/) (2021)
- [Towards Deeper Graph Neural Networks](https://mlsanity.com/paper/2007.09296/) (2020)
- [GraphSMOTE: Imbalanced Node Classification on Graphs with Graph Neural Networks](https://mlsanity.com/paper/2103.08826/) (2021)
- [How to learn a graph from smooth signals](https://mlsanity.com/paper/1601.02513/) (2016)
- [Graph Wavelet Neural Network](https://mlsanity.com/paper/1904.07785/) (2019)
- [Node Similarity Preserving Graph Convolutional Networks](https://mlsanity.com/paper/2011.09643/) (2020)
- [SimGNN: A Neural Network Approach to Fast Graph Similarity Computation](https://mlsanity.com/paper/1808.05689/) (2018)
- [GBK-GNN: Gated Bi-Kernel Graph Neural Networks for Modeling Both Homophily and Heterophily](https://mlsanity.com/paper/2110.15777/) (2021)
- [MotifNet: a motif-based Graph Convolutional Network for directed graphs](https://mlsanity.com/paper/1802.01572/) (2018)

## Built on by (most cited first, 11 of 11)

- [The Expressive Power of Graph Neural Networks: A Survey](https://mlsanity.com/paper/2308.08235/) (2023)
- [Make Heterophily Graphs Better Fit GNN: A Graph Rewiring Approach](https://mlsanity.com/paper/2209.08264/) (2022)
- [Homophily-oriented Heterogeneous Graph Rewiring](https://mlsanity.com/paper/2302.06299/) (2023)
- [GNNs Getting ComFy: Community and Feature Similarity Guided Rewiring](https://mlsanity.com/paper/2502.04891/) (2025)
- [Predicting the Silent Majority on Graphs: Knowledge Transferable Graph Neural Network](https://mlsanity.com/paper/2302.00873/) (2023)
- [Bridged-GNN: Knowledge Bridge Learning for Effective Knowledge Transfer](https://mlsanity.com/paper/2308.09499/) (2023)
- [On Manipulating Signals of User-Item Graph: A Jacobi Polynomial-based Graph Collaborative Filtering](https://mlsanity.com/paper/2306.03624/) (2023)
- [SAUC: Sparsity-Aware Uncertainty Calibration for Spatiotemporal Prediction with Graph Neural Networks](https://mlsanity.com/paper/2409.08766/) (2024)
- [ForecastGrapher: Redefining Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2405.18036/) (2024)
- [Professional Network Matters: Connections Empower Person-Job Fit](https://mlsanity.com/paper/2401.00010/) (2023)
- [Graph Structure Prompt Learning: A Novel Methodology to Improve Performance of Graph Neural Networks](https://mlsanity.com/paper/2407.11361/) (2024)

## Abstract (arXiv)

Graph Neural Networks (GNNs) have shown expressive performance on graph representation learning by aggregating information from neighbors. Recently, some studies have discussed the importance of modeling neighborhood distribution on the graph. However, most existing GNNs aggregate neighbors' features through single statistic (e.g., mean, max, sum), which loses the information related to neighbor's feature distribution and therefore degrades the model performance. In this paper, inspired by the method of moment in statistical theory, we propose to model neighbor's feature distribution with multi-order moments. We design a novel GNN model, namely Mix-Moment Graph Neural Network (MM-GNN), which includes a Multi-order Moment Embedding (MME) module and an Element-wise Attention-based Moment Adaptor module. MM-GNN first calculates the multi-order moments of the neighbors for each node as signatures, and then use an Element-wise Attention-based Moment Adaptor to assign larger weights to important moments for each node and update node representations. We conduct extensive experiments on 15 real-world graphs (including social networks, citation networks and web-page networks etc.) to evaluate our model, and the results demonstrate the superiority of MM-GNN over existing state-of-the-art models.