# SC-MAD: Mixtures of Higher-order Networks for Data Augmentation

arXiv: https://arxiv.org/abs/2309.07453 · HTML: https://mlsanity.com/paper/2309.07453/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 32 references that are in the map.
- First posted on arXiv 14 Sep 2023.

## Builds on (most cited first, 18 of 18)

- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [On Mixup Training: Improved Calibration and Predictive Uncertainty for Deep Neural Networks](https://mlsanity.com/paper/1905.11001/) (2019)
- [Graph Contrastive Learning Automated](https://mlsanity.com/paper/2106.07594/) (2021)
- [How Does Mixup Help With Robustness and Generalization?](https://mlsanity.com/paper/2010.04819/) (2020)
- [G-Mixup: Graph Data Augmentation for Graph Classification](https://mlsanity.com/paper/2202.07179/) (2022)
- [Simplicial Neural Networks](https://mlsanity.com/paper/2010.03633/) (2020)
- [Topological Signal Processing over Simplicial Complexes](https://mlsanity.com/paper/1907.11577/) (2019)
- [Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyond](https://mlsanity.com/paper/2101.05510/) (2021)
- [Principled Simplicial Neural Networks for Trajectory Prediction](https://mlsanity.com/paper/2102.10058/) (2021)
- [Data augmentation instead of explicit regularization](https://mlsanity.com/paper/1806.03852/) (2018)
- [Simplicial Attention Networks](https://mlsanity.com/paper/2204.09455/) (2022)
- [HodgeNet: Graph Neural Networks for Edge Data](https://mlsanity.com/paper/1912.02354/) (2019)
- [A Consistent Histogram Estimator for Exchangeable Graph Models](https://mlsanity.com/paper/1402.1888/) (2014)
- [Learning Graphons via Structured Gromov-Wasserstein Barycenters](https://mlsanity.com/paper/2012.05644/) (2020)
- [Augmentations in Hypergraph Contrastive Learning: Fabricated and Generative](https://mlsanity.com/paper/2210.03801/) (2022)
- [GraphMAD: Graph Mixup for Data Augmentation using Data-Driven Convex Clustering](https://mlsanity.com/paper/2210.15721/) (2022)
- [Hodgelets: Localized Spectral Representations of Flows on Simplicial Complexes](https://mlsanity.com/paper/2109.08728/) (2021)
- [Pooling Strategies for Simplicial Convolutional Networks](https://mlsanity.com/paper/2210.05490/) (2022)

## Abstract (arXiv)

The myriad complex systems with multiway interactions motivate the extension of graph-based pairwise connections to higher-order relations. In particular, the simplicial complex has inspired generalizations of graph neural networks (GNNs) to simplicial complex-based models. Learning on such systems requires large amounts of data, which can be expensive or impossible to obtain. We propose data augmentation of simplicial complexes through both linear and nonlinear mixup mechanisms that return mixtures of existing labeled samples. In addition to traditional pairwise mixup, we present a convex clustering mixup approach for a data-driven relationship among several simplicial complexes. We theoretically demonstrate that the resultant synthetic simplicial complexes interpolate among existing data with respect to homomorphism densities. Our method is demonstrated on both synthetic and real-world datasets for simplicial complex classification.