GraphSAGE

The problem, from first principles

GraphSAGE (Graph SAmple and aggreGatE) samples a neighborhood for each node and aggregates their features. Unlike GCN which uses all neighbors, GraphSAGE samples K neighbors for scalability.

Where S_i is a sampled neighborhood of node i.

From theory to code

Implement:

graphsage_layer(features, adj, weight, num_samples)

Samples neighbors, aggregates, applies weight, returns updated features.

Constraints

• features shape: (num_nodes, input_dim).
• adj shape: (num_nodes, num_nodes).
• weight shape: (input_dim, output_dim).
• num_samples: number of neighbors to sample.
• Return shape: (num_nodes, output_dim).