Spatially Aware GCNs for efficient, high-accuracy cancer grading: Mitigating oversmoothing via frequency analysis

We present a Spatially Aware Graph Convolutional Network (SA-GCN) for classifying colorectal and non-small cell lung cancer grades, with a focus on preserving high-resolution spatial features and leveraging frequency information in histopathological data. Cancer grading relies on complex, cell-level spatial relationships-an ideal setting for Graph Convolutional Networks (GCNs). However, deeper GCNs typically suffer from oversmoothing, which severely limits their ability to capture intricate structures. To overcome this, we develop SA-GCN, incorporating both a dilated layer and a quantile-based aggregation function to balance low- and high-frequency information in graph-structured data. Our experiments on colorectal and non-small cell lung cancer datasets show a 0.87% and 0.81% improvement respectively in accuracy over state-of-the-art methods, with the dilated layer alone achieving 98.05% ± 0.99% accuracy at seven layers in the colorectal dataset. Additionally, SA-GCN offers significant computational advantages: by optimising graph construction, we reduce complexity from O(N²) to O(N). Theoretical analyses further guarantee preserved graph signal diversity, ensuring robust performance on both sparse and dense tissue structures. Overall, SA-GCN advances the state of the art by delivering higher accuracy, deeper architectures, and the ability to scale to large datasets, a problem other oversmoothing mitigating techniques face.