可精确调控图结构中特征异质性的生成模型。
A Generative Model for Controllable Feature Heterophily in Graphs
- 基于Lipschitz图函数与谱滤波器生成带可控异质性的图信号。
- 理论证明异质性度量在极限下收敛至确定性函数，且可稳定控制。
- 适用于需要精细调节节点特征相似性的图学习数据生成任务。
我们提出一种基于图函数的图信号生成框架，可显式控制特征异质性这一关键属性。模型结合了基于Lipschitz图函数的随机图生成器与通过重缩放拉普拉斯矩阵平滑谱函数过滤的高斯节点特征。理论方面，我们建立了两项新结果：(i) 经验异质性得分的浓度不等式；(ii) 特征异质性度量几乎必然收敛于图函数度分布的确定性函数，基于拉普拉斯特征值多项式平均的图函数极限定理。这些结果揭示了图函数与滤波器共同作用对极限异质性水平的影响，提供可调的数据建模机制。实验验证了在多种图族与谱滤波器下对同质性实现精确控制。
原文摘要 · Abstract (English)
We introduce a principled generative framework for graph signals that enables explicit control of feature heterophily, a key property underlying the effectiveness of graph learning methods. Our model combines a Lipschitz graphon-based random graph generator with Gaussian node features filtered through a smooth spectral function of the rescaled Laplacian. We establish new theoretical guarantees: (i) a concentration result for the empirical heterophily score; and (ii) almost-sure convergence of the feature heterophily measure to a deterministic functional of the graphon degree profile, based on a graphon-limit law for polynomial averages of Laplacian eigenvalues. These results elucidate how the interplay between the graphon and the filter governs the limiting level of feature heterophily, providing a tunable mechanism for data modeling and generation. We validate the theory through experiments demonstrating precise control of homophily across graph families and spectral filters.
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