Nonlinear Higher-Order Label Spreading
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.
Cite
@article{arxiv.2006.04762,
title = {Nonlinear Higher-Order Label Spreading},
author = {Francesco Tudisco and Austin R. Benson and Konstantin Prokopchik},
journal= {arXiv preprint arXiv:2006.04762},
year = {2020}
}