改进格林函数法，让大图半监督学习更稳定高效。
Fast Semi-supervised Learning on Large Graphs: An Improved Green-function Method
- 从优化视角重构格林函数法，解释其在稀疏图中失效原因。
- 新方法在大图上准确率提升15%以上，且计算更稳定。
- 适合处理大规模稀疏图的半监督学习任务，尤其看重效率与鲁棒性。
基于图的半监督学习中，格林函数法通过计算图空间中的格林函数来工作。然而，在大型图尤其是稀疏图上，该方法表现不稳定且效果不佳。本文对此进行详细分析，提出一种新的优化视角方法：在完全连通图上，该方法等价于原格林函数法，具有物理意义的另一种解释；而在非完全连通图中，能解释原方法为何在大稀疏图上导致混乱。为解决此问题，我们提出可实际应用的改进方法，并引入高斯消元与锚点图两种加速技术，显著提升在大图上的效率。大量实验验证了理论结论，证明所提方法在准确性、稳定性和效率方面均优于原方法。
原文摘要 · Abstract (English)
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.
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