用几何流方法优化图上数据的标签分配，提升一致性与不确定性评估能力。
Riemannian Patch Assignment Gradient Flows
- 基于竞争标签块的动态交互机制，通过几何数值积分求解
- 在多个数据集上实现标签分配的一致性提升，支持不确定性量化
- 适合需要高置信度标签分配的图数据分析任务
本文提出用于图上度量数据标记的块分配流方法。标签由初始局部标签经图中标签与标签分配间的动态交互正则化决定，完全由一组竞争性带标签块构成的字典编码，并通过块分配变量调节。通过黎曼上升流的几何数值积分实现块分配的最大一致性，该流是拉格朗日作用泛函的临界点。实验展示了该方法的性质，包括标签分配的不确定性量化。
原文摘要 · Abstract (English)
This paper introduces patch assignment flows for metric data labeling on graphs. Labelings are determined by regularizing initial local labelings through the dynamic interaction of both labels and label assignments across the graph, entirely encoded by a dictionary of competing labeled patches and mediated by patch assignment variables. Maximal consistency of patch assignments is achieved by geometric numerical integration of a Riemannian ascent flow, as critical point of a Lagrangian action functional. Experiments illustrate properties of the approach, including uncertainty quantification of label assignments.
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