Spectral Filtering Using Periodic Autoregressive Moving Average Graph Neural Networks for Heterophilic Graphs
Kalmyrzayev B. Ali H. Tahir Akhtar M.
2026Institute of Electrical and Electronics Engineers Inc.
IEEE Access
2026#149696 - 9716 pp.
The importance of Graph Neural Networks (GNNs) has increased over the years due to their ability to handle non-Euclidean data. Most of the existing research mainly focuses on spatial relationships using neighboring nodes to aggregate information, which usually corresponds to lowpass filtering from the perspective of graph signal processing theory. However, many real-world applications involve heterophilic graphs, where nodes with dissimilar labels or features frequently connect, necessitating highpass filtering capabilities. Existing highpass GNNs are typically parameter-intensive, limiting their efficiency and practical development. This problem can be addressed by utilizing Autoregressive Moving Average graph (ARMA) filters. Thus, a novel periodic ARMA GNN (pARMA-GNN) model that efficiently approximates rational spectral filters using periodic recursive filtering is proposed. The proposed pARMA-GNN model consists of periodic ARMA convolutional (pARMAConv) layers that significantly reduce computational complexity and parameter count compared to the current state-of-the-art models specializing in capturing both high-frequency and low-frequency information. The theoretical analysis of the frequency response of the proposed model has shown its ability to capture high-frequency and low-frequency components. Additionally, several variants of the proposed model have been developed to solve specific issues related to homophilic and heterophilic datasets. The results of experiments conducted on synthetic data have shown the practical capabilities of the model to filter different frequencies compared to other baseline models. Moreover, results on real-world datasets indicate that pARMA-GNN provides competitive performance on homophilic graphs, while outperforming prior models by about 1-10% on heterophilic graph datasets. The analysis of computational complexity of ARMA-based GNNs indicates that the proposed model has a great advantage in certain scenarios. Finally, ablation study on the effect of number of period has been conducted to show the impact of periodic weights on both homophilic and heterophilic datasets.
Autoregressive moving average filter , graph neural networks , graph signal processing , highpass filtering , spectral graph neural networks
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School of Engineering and Digital Sciences, Nazarbayev University, Astana, 010000, Kazakhstan
School of Engineering and Digital Sciences
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