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Workshop: Geometrical and Topological Representation Learning

A Piece-wise Polynomial Filtering Approach for Graph Neural Networks

Vijay Lingam · Chanakya Ekbote · Manan Sharma · Rahul Ragesh · Arun Iyer · SUNDARARAJAN SELLAMANICKAM

Keywords: [ graph neural networks ] [ graph representation learning ]


Graph Neural Networks (GNNs) exploit signals from node features and the input graph topology to improve node classification task performance. Recently proposed GNNs work across a variety of homophilic and heterophilic graphs. Among these, models relying on polynomial graph filters have shown promise. We observe that polynomial filter models, in several practical instances, need to learn a reasonably high degree polynomials without facing any over-smoothing effects. We find that existing methods, due to their designs, either have limited efficacy or can be enhanced further. We present a spectral method to learn a bank of filters using a piece-wise polynomial approach, where each filter acts on a different subsets of the eigen spectrum. The approach requires eigendecomposition for a few eigenvalues at extremes (i.e., low and high ends of the spectrum) and offers flexibility to learn sharper and complex shaped frequency responses with low-degree polynomials. We theoretically and empirically show that our proposed model learns a better filter, thereby improving classification accuracy. Our model achieves performance gains of up to ~6% over the state-of-the-art (SOTA) models.

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