发表机构
University of Ngaoundéré; University of Garoua（恩加乌德雷大学; 加鲁阿大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出线性时间程序，在群组嵌入图信号处理的精确傅里叶分析的两种实现方式间选择，证实能量可预测信号保真度，在真实数据测试中展现相关特性。
AI 中文摘要
群组嵌入图信号处理要么通过将域放大到图等距嵌入阿贝尔凯莱图来获得精确傅里叶分析，要么通过将图扰动为阿贝尔凯莱图来实现。我们提出一种线性时间程序，用于在这两种方式之间做出选择，并研究有损分支的控制准则。我们证明，狄利克雷形式的扰动恰好是编辑边能量的带符号和，其模受这些能量的总和限制，而补全的组合代价并不包含在该总和中。实验证实，该能量能强烈预测信号保真度，尽管并非严格单调（在补全及代价固定的实例中，斯皮尔曼相关系数ρ=-0.79），而代价本身不包含相关信息。在代价相同的补全中，通过该能量选择，可在穷举范围内恢复61%的可用性能差距，该样本量过小，无法证明此效应在超过8个顶点时仍存在。在真实支付数据上，路由器在所有情况下都选择精确分支；在真实反洗钱数据上，补全不变量是最大度的重新编码，无法与其区分，且其可比拟的线性时间边界在近完全图上存在盲点。
英文摘要
Group-embedding graph signal processing buys exact Fourier analysis either by enlarging the domain until a graph embeds isometrically into an abelian Cayley graph, or by perturbing the graph until it is one. We give a linear-time procedure that chooses between the two, and study the criterion governing the lossy branch. We prove that the perturbation of the Dirichlet form is exactly the signed sum of the edited-edge energies, and is bounded in modulus by their total, into which the combinatorial cost of the completion does not enter. We confirm experimentally that this energy predicts signal fidelity strongly though not strictly monotonically (Spearman rho = -0.79 on an instance where the completion, and hence the cost, is held fixed), while the cost itself carries no information about it. Selecting among completions of identical cost by this energy recovers 61 percent of the available performance gap on the exhaustive range, on a sample too small to establish that the effect persists beyond eight vertices. On real payment data the router takes the exact branch everywhere; on real anti-money-laundering data the completion invariant is a re-encoding of maximum degree and is not distinguishable from it, and the linear-time bound it rivals is shown to have a blind spot on near-complete graphs.
