Asymptotic Justification of Bandlimited Interpolation of Graph signals for Semi-Supervised Learning
This provides theoretical justification for a graph-based semi-supervised learning method, which is incremental as it formalizes an existing framework.
The paper tackles the problem of justifying bandlimited interpolation for semi-supervised learning on graphs by showing that, with sufficient labeled data, it relates to a constrained low density separation problem as data points increase to infinity, and demonstrates this through experiments.
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.