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

• URL: http://arxiv.org/abs/2309.07453v1
• Date: Thu, 14 Sep 2023 06:25:39 GMT
• Title: SC-MAD: Mixtures of Higher-order Networks for Data Augmentation
• Authors: Madeline Navarro, Santiago Segarra
• Abstract summary: The simplicial complex has inspired generalizations of graph neural networks (GNNs) to simplicial complex-based models. We propose data augmentation of simplicial complexes through both linear and nonlinear mixup mechanisms. We theoretically demonstrate that the resultant synthetic simplicial complexes interpolate among existing data with respect to homomorphism densities.
• Score: 36.33265644447091
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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