PC-Fermat：用 Fermat 距离改进覆盖式主动学习

技术实现上，作者构建加权欧氏邻域图，并用截断最短路径算法计算 Fermat 覆盖图，从而降低计算开销。论文还给出了该构造能精确保留完整图上 Fermat 覆盖结果的充分条件，为方法的理论可靠性提供支撑。

实验在 8 个分类数据集、不同标注预算下进行，重点测试极低预算场景。结果显示 PC-Fermat 在多数数据集上优于多种现有主动学习方法，对标注预算紧张的开发者和研究团队有参考价值。

Fermat ProbCover: Coverage-Based Active Learning on Fermat Distance Graphs

Active learning aims to reduce annotation cost by selecting the most informative examples for labeling. In the low-budget regime, where uncertainty-based methods often fail, coverage-based active learning methods such as ProbCover have been shown to be effective. However, these methods typically rely on Euclidean distance, which may not adequately capture the underlying geometry of data. In this article, we propose PC-Fermat, a coverage-based active learning method that replaces Euclidean coverage neighborhoods with neighborhoods defined by a Fermat distance, i.e., a data-adaptive distance that reflects the underlying distribution of the data points. To facilitate computation, we construct a weighted Euclidean neighborhood graph and use a truncated shortest-path algorithm to compute the Fermat coverage graph. We also establish sufficient conditions under which this construction exactly preserves the Fermat coverage computed on the complete graph. Finally, we evaluate PC-Fermat on eight classification datasets across varying labeling budgets, with particular emphasis on the very low-budget regime. Our experimental results demonstrate that PC-Fermat outperforms several existing active learning methods on the majority of the datasets.

This report is categorized under AITOP's "Papers" desk. Within our cross-regional analytical framework, it directly maps to AI developer toolchains, coding agents, and engineering workflows. Key entities and technical topics under continuous tracking include 主动学习, ProbCover, Fermat距离, 论文解读.

Source attribution: curated from arXiv cs.LG (@Gokul Bhusal, Delanna Do, Kevin Miller, Ekaterina Merkurjev, Stephan Wojtowytsch).