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arXiv · 2006.04762

Nonlinear Higher-Order Label Spreading

Francesco Tudisco·Austin R. Benson·Konstantin Prokopchik
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Abstract

Label spreading is a general technique for semi-supervised learning with point cloud or network data, which can be interpreted as a diffusion of labels on a graph. While there are many variants of label spreading, nearly all of them are linear models, where the incoming information to a node is a weighted sum of information from neighboring nodes. Here, we add nonlinearity to label spreading through nonlinear functions of higher-order structure in the graph, namely triangles in the graph. For a broad class of nonlinear functions, we prove convergence of our nonlinear higher-order label spreading algorithm to the global solution of a constrained semi-supervised loss function. We demonstrate the efficiency and efficacy of our approach on a variety of point cloud and network datasets, where the nonlinear higher-order model compares favorably to classical label spreading, as well as hypergraph models and graph neural networks.

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BibTeXRIS

Francesco Tudisco, Austin R. Benson, Konstantin Prokopchik. 2020-06-08. Nonlinear Higher-Order Label Spreading. https://arxiv.org/abs/2006.04762

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