GraphSAGE

SAmple and aggreGatE — Hamilton, Ying & Leskovec, NeurIPS 2017 (arXiv:1706.02216).

The best mean rank in graphnetz's own findings, on a design whose distinguishing feature is that it keeps a node separate from its neighbourhood.

What it computes

\[h_i' \;=\; W_{\text{self}}\,h_i \;+\; W_{\text{neigh}} \cdot \mathrm{AGG}\big(\{h_j : j \in \mathcal{N}(i)\}\big)\]

The two weight matrices are the whole idea. GCN folds a node into its own neighbourhood average via the added self-loop, so a node's representation and its neighbours' are transformed identically. GraphSAGE gives the node its own parameters, which lets the model learn contrast between a node and its surroundings rather than only agreement.

AGG is configurable — mean by default, with max, lstm and sum available through PyG.

Architecture as shipped

Two SAGEConv layers with ReLU and dropout between them:

GraphSAGE(in_channels, hidden_channels, out_channels, aggr="mean", dropout=0.5)

layers	2
aggregation	"mean" (aggr=)
activation	ReLU
dropout	0.5, between the layers
supported tasks	all four, via adapters

Where it does well, and why

The separate self-transform is what makes GraphSAGE robust on heterophilic graphs — those where connected nodes tend to have different labels. Averaging a node into its neighbourhood, as GCN does, destroys exactly the signal such a graph carries. Keeping the two apart preserves it.

In the ten-category sweep GraphSAGE wins outright only once (Combinatorial, TSP-random, 0.890) but is rarely bad, and that consistency gives it the best mean rank of the four: 2.10, ahead of GCN's 2.20. It is a useful illustration of the difference between winning categories and ranking well — GCN takes four rows to GraphSAGE's one and still ranks second.

The best mean rank is still not a win

GraphSAGE's 2.10 against GraphTransformer's 2.90 is a gap of 0.80, well inside the Nemenyi critical difference of 1.483 at \(N = 10\), and the Friedman omnibus does not reject (\(p = 0.392\)). The ordering is not evidence. See Comparison.

The original paper's other contribution — neighbourhood sampling for inductive learning on graphs too large to fit in memory — is not exercised by the built-in, which does full-neighbourhood aggregation. The catalogue's largest graphs arrive through the OGB loaders, where sampling would be the natural next step.

Usage

from graphnetz import GraphSAGE, run_benchmark
from graphnetz.datasets.social import roman_empire

# Heterophilic node classification, where the separate self-weights matter.
ds = roman_empire("data/roman_empire")
model = GraphSAGE(ds.num_features, 64, ds.num_classes, aggr="max")

report = run_benchmark(
    "social",
    {"GraphSAGE": GraphSAGE},
    seeds=range(10),
    task_type="node_cls",
)

API

Full signature, parameters and source: graphnetz.models.GraphSAGE.