GraphSAGE Mean Aggregation

Write one GraphSAGE layer with the mean aggregator.

A GCN mixes a node's own features into the same average as its neighbours. GraphSAGE keeps them apart. It transforms the node's own features with one weight matrix and the mean of its neighbours' features with another, then adds the two:

neigh_mean[v] = mean of H[u] over the neighbours u of v
H_new[v]      = relu(H[v] @ W_self + neigh_mean[v] @ W_neigh)

Because it only needs a node's neighbours, GraphSAGE can embed nodes that were not in the training graph.

A node with no neighbours has a neighbour mean of zero.

Function signature

def sage_layer(A, H, W_self, W_neigh):

Example

Input

A = np.array([[0, 1, 0],
              [1, 0, 1],
              [0, 1, 0]])
H = np.array([[1.0, 0.0],
              [0.0, 1.0],
              [1.0, 1.0]])
W_self  = np.eye(2)
W_neigh = np.array([[0.5, 0.0],
                    [0.0, -1.0]])
sage_layer(A, H, W_self, W_neigh)

Output

array([[1. , 0. ],
       [0.5, 0.5],
       [1. , 0. ]])

Reasoning

Node 1 has neighbours 0 and 2, so its neighbour mean is [1, 0.5]. That maps to [0.5, -0.5], and adding its own [0, 1] gives [0.5, 0.5]. Node 0 has only node 1, with mean [0, 1], which maps to [0, -1]. Adding [1, 0] gives [1, -1], and the ReLU makes it [1, 0].

Constraints and notes

• A is a 0/1 adjacency matrix with zeros on the diagonal. Do not add self loops.
• H has shape (n, d_in), and both weight matrices have shape (d_in, d_out).
• Do not divide by zero for isolated nodes.