Algebraic Multigrid Acceleration for Efficient Label Spreading

用于高效标签传播的代数多重网格加速

Abstract: Modern machine learning models rely on large amounts of labeled data. However, manual annotation of large-scale datasets is expensive and time-consuming. Label spreading is a semi-supervised learning technique that addresses this challenge by propagating information from a few labeled examples to a larger pool of unlabeled data.

摘要： 现代机器学习模型依赖于大量的标注数据。然而，大规模数据集的人工标注既昂贵又耗时。标签传播（Label spreading）是一种半监督学习技术，它通过将信息从少量标注样本传播到更大规模的未标注数据池中，从而应对这一挑战。

Despite its effectiveness, its application to large-scale, high-dimensional datasets is limited by computational costs and memory constraints. To address these limitations, we propose Algebraic Multigrid Acceleration for Efficient Label Spreading (AMELS), an efficient label spreading framework that improves scalability by fast construction of neighborhood graphs and the incorporation of algebraic multigrid solvers.

尽管该技术非常有效，但其在大规模、高维数据集上的应用受到计算成本和内存限制的制约。为了解决这些局限性，我们提出了“用于高效标签传播的代数多重网格加速”（AMELS）。这是一个高效的标签传播框架，通过快速构建邻域图并结合代数多重网格求解器，显著提升了可扩展性。

The latter is an iterative solver that replaces the ordinary random walk iteration typically performed in label spreading. Due to the multilevel nature of algebraic multigrid solvers, AMELS spreads given label information across a graph of any size in a single multigrid cycle.

后者是一种迭代求解器，用于替代标签传播中通常使用的普通随机游走迭代。得益于代数多重网格求解器的多层特性，AMELS 能够在单个多重网格周期内，将给定的标签信息传播到任意规模的图结构中。

We demonstrate that AMELS achieves significant runtime reductions compared to existing implementations while also being more robust to hyperparameter choices in terms of both runtime and classification accuracy. Our framework therefore enables efficient label spreading on large-scale image datasets and produces accurate labels even when only a few labeled samples are available.

我们证明，与现有实现相比，AMELS 在显著缩短运行时间的同时，在运行时间和分类准确率方面对超参数的选择也更加稳健。因此，我们的框架能够在大型图像数据集上实现高效的标签传播，即使在仅有少量标注样本的情况下，也能产生准确的标签。