  Active graph-based semi-supervised learning (AG-SSL) aims to select a small
set of labeled examples and utilize their graph-based relation to other
unlabeled examples to aid in machine learning tasks. It is also closely related
to the sampling theory in graph signal processing. In this paper, we revisit
the original formulation of graph-based SSL and prove the supermodularity of an
AG-SSL objective function under a broad class of regularization functions
parameterized by Stieltjes matrices. Under this setting, supermodularity yields
a novel greedy label sampling algorithm with guaranteed performance relative to
the optimal sampling set. Compared to three state-of-the-art graph signal
sampling and recovery methods on two real-life community detection datasets,
the proposed AG-SSL method attains superior classification accuracy given
limited sample budgets.
