AI 中文总结
该研究提出带理论保证的ROSA算子，用于放大噪声图的谱距离，可提升逆变异系数稳定性得分，在合成图及多种真实图数据上验证了其有效性。
AI 中文摘要
在许多应用中，需反复观测图，任务是在噪声下观测并跟踪微弱的局域结构扰动，如固定顶点集上的顶点坐标位移或边权重/属性变化。单次图距离可能遗漏这些局域扰动，或波动过强无法支持可靠监测，尤其在大图中，信号会随规模稀释。我们提出鲁棒有序感知谱放大（ROSA），这是一种距离放大算子，它结合了沿有序感知边移除滤波的度量评估。我们证明，ROSA不会减小所包含的基础距离，且当滤波步骤暴露额外信号时会有条件地增大它；此外，我们证明，在可经验检验的显式充分条件下，它能严格提升逆变异系数稳定性得分（IS²），IS²定义为带噪图距离的均值除以其标准差。在合成图上的实验中，这些合成图在三种噪声模型下带有局域编辑，且图密度和算法选择的编辑位点均有变化，结果显示ROSA常能将基础谱距离的IS²近似加倍。我们在真实世界用例（包括线粒体网络、fMRI相关矩阵、组织网络、蛋白质构象图和视网膜血管多路复用图）上展示了ROSA的适用与不适用场景。跨图、算子和噪声设置的经验结果与理论放大条件及边界构造一致。用经验估计的操作量评估时，该界在方向和近似尺度上与观测到的增益相符。
英文摘要
In many applications, graphs are observed repeatedly, where the task is to observe and track weak localized structural perturbations under noise, such as vertex-coordinate displacements or edge-weight/attribute changes on a fixed vertex set. One-shot graph distances can miss these localized perturbations or fluctuate too strongly to support reliable monitoring, especially in large graphs where signal dilutes with scale. We propose Robust Order-aware Spectral Amplification (ROSA), a distance-amplification operator that integrates metric evaluations along an order-aware edge-removal filtration. We prove that ROSA cannot reduce the included base distance and conditionally increases it whenever a filtered step exposes additional signal; separately, we prove that it can strictly improve an inverse coefficient of variation stability score (IS$^2$), defined as the mean of a noisy graph distance divided by its standard deviation, under an explicit sufficient condition that can be checked empirically. Experiments on synthetic graphs with localized edits under three noise models, varying graph densities, and three algorithmically selected edit sites show that ROSA can often approximately double the IS$^2$ of the base spectral distance. We show where ROSA works and stops working on real-world use cases including mitochondrial networks, fMRI correlation matrices, tissue networks, protein conformer graphs, and retinal vasculature multiplex graphs. The empirical results across graph, operator, and noise settings are consistent with the theoretical amplification conditions and boundary constructions. Evaluated with empirically estimated operative quantities, the bound agrees with the observed gain in direction and approximate scale.
Comments35 pages, 15 figures
