发现信号子图：图上的迭代筛选方法
Discovering the Signal Subgraph: An Iterative Screening Approach on Graphs
AI总结：
针对图数据高维与结构依赖问题，提出迭代顶点筛选方法识别信号子图以降维，理论证明其能高概率估计真实子图并实现渐近最优分类，实验验证了其卓越性能。
摘要：
由于数据的高维性和固有的结构依赖性（其中每条边依赖于一对顶点），图上的监督学习是一项具有挑战性的任务。现有的传统方法专为标准欧几里得数据设计，未考虑图固有的结构信息。本文提出一种迭代顶点筛选方法，以在具有匹配顶点集及相关图属性的多个图数据集上实现降维。该方法旨在识别信号子图，以提供对完整图更简洁的表示，从而潜在地有益于后续顶点分类任务。该方法同时筛选邻接矩阵的行和列，并在结果距离相关性最大化时停止。我们通过证明该方法以高概率估计真实信号子图来建立其理论基础。此外，我们在Erdos-Renyi随机图模型下建立了分类误差的收敛速度，并证明后续分类可渐近最优，在高维条件下优于使用整个图。我们在多种模拟数据集和源自功能及结构磁共振图像的真实人类和小鼠图上评估了该方法。结果表明其在估计真实信号子图和实现卓越分类精度方面的优异性能。
英文摘要：
Supervised learning on graphs is a challenging task due to the high dimensionality and inherent structural dependencies in the data, where each edge depends on a pair of vertices. Existing conventional methods are designed for standard Euclidean data and do not account for the structural information inherent in graphs. In this paper, we propose an iterative vertex screening method to achieve dimension reduction across multiple graph datasets with matched vertex sets and associated graph attributes. Our method aims to identify a signal subgraph to provide a more concise representation of the full graphs, potentially benefiting subsequent vertex classification tasks. The method screens the rows and columns of the adjacency matrix concurrently and stops when the resulting distance correlation is maximized. We establish the theoretical foundation of our method by proving that it estimates the true signal subgraph with high probability. Additionally, we establish the convergence rate of classification error under the Erdos-Renyi random graph model and prove that the subsequent classification can be asymptotically optimal, outperforming the entire graph under high-dimensional conditions. Our method is evaluated on various simulated datasets and real-world human and murine graphs derived from functional and structural magnetic resonance images. The results demonstrate its excellent performance in estimating the ground-truth signal subgraph and achieving superior classification accuracy.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
