Adaptive fractional order graph neural network

This paper proposes adaptive fractional order graph neural network (AFGNN), optimized by a time-varying fractional order gradient descent method to address the challenges of local optimum of classic and fractional GNNs which are specialised at aggregating information from the feature and adjacent matrices of connected nodes and their neighbours to solve learning tasks on non-Euclidean data such as graphs. To overcome the high computational complexity of fractional order derivations, the proposed model approximately calculates the fractional order gradients. We further prove such approximation is feasible and the AFGNN is unbiased. Extensive experiments on benchmark citation networks and object recognition challenges confirm the performance of AFGNN. The first group of experiments show that the results of AFGNN outperform the steepest gradient based method and conventional GNNs on the citation networks. The second group of experiments demonstrate that AFGNN excels at image recognition tasks where the images have a significant amount of missing pixels and expresses improved accuracy than GNNs.