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Hypergraph $p$-Laplacian equations for data interpolation and semi-supervised learning

Year: 2024

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2411.12601

Authors: Shi, Kehan, Burger, Martin

Institutions: China Jiliang University, Universität Hamburg, Deutsches Elektronen-Synchrotron DESY

Language: English

Topic: Machine Learning and Algorithms

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: China Scholarship Council, Deutsches Elektronen-Synchrotron

OpenAlex ID: W4404574085

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