On the Supermodularity of Active Graph-based Semi-supervised Learning with Stieltjes Matrix Regularization
This work addresses active learning for graph-based semi-supervised learning, providing a theoretical guarantee for greedy sampling, which is incremental as it builds on existing formulations.
The paper tackled the problem of selecting labeled examples in active graph-based semi-supervised learning by proving the supermodularity of the objective function under Stieltjes matrix regularization, resulting in a greedy algorithm that achieved superior classification accuracy compared to state-of-the-art methods on community detection datasets.
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.