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

TL;DR

This paper introduces a novel data augmentation method for simplicial complexes using linear, nonlinear, and convex clustering mixup techniques, improving classification performance on complex systems with multiway interactions.

Contribution

It presents the first mixup-based data augmentation framework for higher-order networks, specifically simplicial complexes, with theoretical and empirical validation.

Findings

Synthetic complexes interpolate existing data effectively.

Method improves classification accuracy on real-world datasets.

Convex clustering mixup captures relationships among multiple complexes.

Abstract

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.