Asymptotic Justification of Bandlimited Interpolation of Graph signals for Semi-Supervised Learning

TL;DR

This paper provides a theoretical foundation for bandlimited interpolation of graph signals in semi-supervised learning, showing its relation to low density separation as data size grows, supported by practical experiments.

Contribution

It offers a formal asymptotic justification for bandlimited graph signal interpolation in semi-supervised learning, linking it to low density separation principles.

Findings

Asymptotic analysis connects bandlimited interpolation to low density separation.

The method performs well with sufficient labeled data.

Experimental results support theoretical insights.

Abstract

Graph-based methods play an important role in unsupervised and semi-supervised learning tasks by taking into account the underlying geometry of the data set. In this paper, we consider a statistical setting for semi-supervised learning and provide a formal justification of the recently introduced framework of bandlimited interpolation of graph signals. Our analysis leads to the interpretation that, given enough labeled data, this method is very closely related to a constrained low density separation problem as the number of data points tends to infinity. We demonstrate the practical utility of our results through simple experiments.