A Novel Hypercomplex Graph Convolution Refining Mechanism

Hypercomplex graph convolutions with higher hypercomplex dimensions can extract more complex features in graphs and features with varying levels of complexity are suited for different situation. However, existing hypercomplex graph neural networks have a constraint that they can only carry out hypercomplex graph convolutions in a predetermined and unchangeable dimension. To address this limitation, this paper presents a solution to overcome this limitation by introducing the FFT-based Adaptive Fourier hypercomplex graph convolution filtering mechanism (FAF mechanism), which can adaptively select hypercomplex graph convolutions with the most appropriate dimensions for different situations by projecting the outputs from all candidate hypercomplex graph convolutions to the frequency domain and selecting the one with the highest energy via the FFT-based Adaptive Fourier Decomposition. Meanwhile, we apply the FAF mechanism to our proposed hypercomplex high-order interaction graph neural network (HHG-Net), which performs high-order interaction and strengthens interaction features through quantum graph hierarchical attention module and feature interaction gated graph convolution. During convolution filtering, the FAF mechanism projects the outputs from different candidate hypercomplex graph convolutions to the frequency domain, extracts their energy, and selects the convolution that outputs the largest energy. After that, the model with selected hypercomplex graph convolutions is trained again. Our method outperforms many benchmarks, including the model with hypercomplex graph convolutions selected by DARTS, in node classification, graph classification, and text classification. This showcases the versatility of our approach, which can be effectively applied to both graph and text data.