Nonlinear Higher-Order Label Spreading

TL;DR

This paper introduces a nonlinear higher-order label spreading algorithm that leverages graph triangles to improve semi-supervised learning, demonstrating better performance than classical methods on various datasets.

Contribution

It proposes a novel nonlinear extension of label spreading using higher-order graph structures, with proven convergence and improved empirical results.

Findings

Converges to the global solution of a semi-supervised loss.

Outperforms classical label spreading and hypergraph models.

Effective on point cloud and network datasets.

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.