Graph Neural Network WSI

Each cell nucleus or superpixel region is instantiated as a node in the graph. A feature vector is computed for every node using a pre-trained encoder or handcrafted features such as morphology (area, eccentricity), texture (GLCM, LBP), and color (H&E channel statistics). This transforms unstructured pixel data into a structured set of vertex embeddings that serve as input to the GNN.

Edges are defined based on spatial proximity to capture the tissue topology. Common strategies include:

• K-Nearest Neighbors (k-NN): Connect each node to its k closest centroids.
• Radius Graphs: Connect all node pairs within a fixed distance threshold (e.g., 50 microns).
• Delaunay Triangulation: Creates a mesh that naturally respects tissue boundaries. Edge features may encode the Euclidean distance vector between connected cells.

The core operation where nodes iteratively update their representations by aggregating information from their neighbors. A Graph Isomorphism Network (GIN) or Graph Attention Network (GAT) layer applies a permutation-invariant function (sum, mean, or attention-weighted sum) to neighbor states. This allows a cell's embedding to incorporate its local tissue context after multiple hops, learning higher-order architectural motifs.

To generate a slide-level representation, the graph must be coarsened. Differentiable pooling layers (e.g., DiffPool, SAGPool) learn to cluster nodes into sub-graphs hierarchically, mimicking the pathologist's zoom-out process. Alternatively, global mean/max pooling or a Set Transformer can be applied to all node embeddings after message passing to produce a single graph-level feature vector for classification.

A gated attention mechanism computes a weighted sum of node embeddings for the final prediction, allowing the model to identify diagnostically relevant regions without pixel-level annotations. The attention score for node v is calculated as: α_v = softmax(w^T tanh(V h_v)). This provides inherent interpretability, as attention weights can be visualized as a heatmap over the tissue to highlight which cell clusters drove the diagnosis.

Tissue architecture exists at multiple scales, from nuclear pleomorphism to glandular formation. A robust architecture constructs separate graphs at different magnifications (e.g., 20x for cytology, 5x for tissue architecture) using multi-resolution patch extraction. Features from each graph are processed by independent GNN branches and fused via concatenation or cross-attention before final classification, capturing both fine cellular detail and global tissue organization.