In the graph-based semi-supervised learning, the Green-function method is a classical method that works by computing the Green's function in the graph space. However, when applied to large graphs, especially those sparse ones, this method performs unstably and unsatisfactorily. We make a detailed analysis on it and propose a novel method from the perspective of optimization. On fully connected graphs, the method is equivalent to the Green-function method and can be seen as another interpretation with physical meanings, while on non-fully connected graphs, it helps to explain why the Green-function method causes a mess on large sparse graphs. To solve this dilemma, we propose a workable approach to improve our proposed method. Unlike the original method, our improved method can also apply two accelerating techniques, Gaussian Elimination, and Anchored Graphs to become more efficient on large graphs. Finally, the extensive experiments prove our conclusions and the efficiency, accuracy, and stability of our improved Green's function method.

本研究针对传统格林函数方法在大规模稀疏图上的不稳定性和不满意性能进行了深入分析，提出了一种从优化角度出发的新方法。该方法不仅与完全连接图的格林函数方法等效，还为理解其在稀疏图上的表现提供了物理意义，同时引入两项加速技术以提高效率，最终通过大量实验验证了改进方法的有效性和稳定性。

大规模图的快速半监督学习：改进的格林函数方法