HeatGSNs: integrating eigenfilters and low-pass graph heat kernels into graph spectral convolutional networks for brain tumor segmentation and classification

Recent studies on graph representation learning in brain tumor learning tasks have garnered significant interest by encoding and learning inherent relationships among the geometric features of tumors. There are serious class imbalance problems that occur on brain tumor MRI datasets. Impressive deep learning models like CNN- and Transformer-based can easily address this problem through their complex model architectures with large parameters.
However, graph-based networks are not suitable for this approach because of chronic over-smoothing and oscillation convergence problems. To address these challenges at once, we propose novel graph spectral convolutional networks called HeatGSNs, which incorporate eigenfilters and learnable low-pass graph heat kernels to capture geometric similarities within tumor classes. They operate to a continuous feature propagation mechanism derived by the forward finite difference of graph heat kernels, which is approximated by the cosine form for the shift-scaled Chebyshev polynomial and modified Bessel functions, leading to fast and accurate performance achievement. Our experimental results show a best average Dice score of 90%, an average Hausdorff Distance (95%) of 5.45mm, and an average accuracy of 80.11% in the BRATS2021 dataset. Moreover, HeatGSNs require significantly fewer parameters, averaging 1.79M, compared to other existing methods, demonstrating efficiency and effectiveness.