Analysis of $p$-Laplacian Regularization in Semi-Supervised Learning

Understand

We investigate a family of regression problems in a semi-supervised setting.

• The task is to assign real-valued labels to a set of $n$ sample points, provided a small training subset of $N$ labeled points.
• A goal of semi-supervised learning is to take advantage of the (geometric) structure provided by the large number of unlabeled data when assigning labels.
• We consider random geometric graphs, with connection radius $\epsilon(n)$, to represent the geometry of the data set.