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

Abstract

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% $\pm$ 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 $O\left(N^2\right)$ to $O\left(N\right)$. 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.