Hypergraph p-Laplacian Equations for Data Interpolation and Semi-supervised Learning

Key Points

Improved classification accuracy in semi-supervised learning shows the effectiveness of the hypergraph p-Laplacian method.
Numerical experiments indicated that the simplified p-Laplacian equation efficiently reduces spiky solutions.
The proposed method showcases a low computational cost while maintaining robust accuracy in data interpolation tasks.
Hypergraph learning underpins complex relationships in datasets, thus enhancing analytical capability.

Abstract

Hypergraph learning with p-Laplacian regularization has attracted a lot of attention due to its flexibility in modeling higher-order relationships in data. This paper focuses on its fast numerical implementation, which is challenging due to the non-differentiability of the objective function and the non-uniqueness of the minimizer. We derive a hypergraph p-Laplacian equation from the subdifferential of the p-Laplacian regularization. A simplified equation that is mathematically well-posed and computationally efficient is proposed as an alternative. Numerical experiments verify that the simplified p-Laplacian equation suppresses spiky solutions in data interpolation and improves classification accuracy in semi-supervised learning. The remarkably low computational cost enables further applications.

Hypergraph p-Laplacian Equations for Data Interpolation and Semi-supervised Learning

Key Points

Abstract

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