Graph Neural Networks (GNNs) exploit signals from node features and the input graph topology to improve node classification task performance. However, these models tend to perform poorly on heterophilic graphs, where connected nodes have different labels. Recently proposed GNNs work across graphs having varying levels of homophily. Among these, models relying on polynomial graph filters have shown promise. We observe that solutions to these polynomial graph filter models are also solutions to an overdetermined system of equations. It suggests that in some instances, the model needs to learn a reasonably high order polynomial. On investigation, we find the proposed models ineffective at learning such polynomials due to their designs. To mitigate this issue, we perform an eigendecomposition of the graph and propose to learn multiple adaptive polynomial filters acting on different subsets of the spectrum. We theoretically and empirically show that our proposed model learns a better filter, thereby improving classification accuracy. We study various aspects of our proposed model including, dependency on the number of eigencomponents utilized, latent polynomial filters learned, and performance of the individual polynomials on the node classification task. We further show that our model is scalable by evaluating over large graphs. Our model achieves performance gains of up to 5% over the state-of-the-art models and outperforms existing polynomial filter-based approaches in general.

翻译：神经网络(GNNs) 利用节点特性和输入图示表层的信号来改进节点分类任务性能。 然而, 这些模型在相连接节点有不同标签的异统图形上表现不佳。 最近提出的GNNs在具有不同水平同质的图形上工作。 其中,依靠多面图过滤器的模型显示了希望。 我们观察到, 这些多面图过滤模型的解决方案也是超定方程系统的解决办法。 它表明, 在某些情况下, 模型需要学习一个相当高的顺序多面体。 在调查中, 我们发现建议的模式在学习由于设计而形成的多面体图时无效。 为了缓解这一问题, 我们对图形进行电子化的配置, 我们提议的模式在理论上和实验上显示, 我们提议的模型学习了一个更好的过滤器, 从而提高了分类的准确性。 我们研究了我们拟议模型的各方面, 包括, 依赖使用过的双向型模型的数量, 隐含的多面体模型过滤器, 并且通过我们所学的大型任务分类, 我们所学的成绩是超越了我们现有五面图式的成绩。 通过我们所学的大型的成绩, 我们所学的模型, 通过进一步的成绩是超越了我们所学的。