Learning Label Initialization for Time-Dependent Harmonic Extension

TL;DR

This paper introduces a method to improve node classification on graphs by learning optimal initializations for the harmonic extension in a time-dependent Dirichlet problem, achieving competitive results with state-of-the-art techniques.

Contribution

It proposes a novel approach to learn initialization vectors for the time-dependent Dirichlet problem on graphs, enhancing harmonic extension solutions for node classification.

Findings

Improved classification accuracy over traditional harmonic extension methods.

The learned initialization is comparable to existing state-of-the-art node classification methods.

Discussion on the impact of parameter t and future research directions.

Abstract

Node classification on graphs can be formulated as the Dirichlet problem on graphs where the signal is given at the labeled nodes, and the harmonic extension is done on the unlabeled nodes. This paper considers a time-dependent version of the Dirichlet problem on graphs and shows how to improve its solution by learning the proper initialization vector on the unlabeled nodes. Further, we show that the improved solution is at par with state-of-the-art methods used for node classification. Finally, we conclude this paper by discussing the importance of parameter t, pros, and future directions.