[Sparse] SIGN example. (#4908)

Co-authored-by: Steve <ubuntu@ip-172-31-34-29.ap-northeast-1.compute.internal>
Co-authored-by: Mufei Li <mufeili1996@gmail.com>

examples/sparse/sign.py

+"""
+[SIGN: Scalable Inception Graph Neural Networks]
+(https://arxiv.org/abs/2004.11198)
+
+This example shows a simplified version of SIGN: a precomputed 2-hops diffusion
+operator on top of symmetrically normalized adjacency matrix A_hat.
+"""
+
+import torch
+import torch.nn as nn
+import torch.nn.functional as F
+from torch.optim import Adam
+
+from dgl.data import CoraGraphDataset
+from dgl.mock_sparse import create_from_coo, diag, identity
+
+################################################################################
+# (HIGHLIGHT) Take the advantage of DGL sparse APIs to implement the feature
+# diffusion in SIGN laconically.
+################################################################################
+def sign_diffusion(A, X, r):
+    # Perform the r-hop diffusion operation.
+    X_sign = [X]
+    for _ in range(r):
+        X = A @ X
+        X_sign.append(X)
+    return X_sign
+
+
+class SIGN(nn.Module):
+    def __init__(self, in_size, out_size, r, hidden_size=256):
+        super().__init__()
+        # Note that theta and omega refer to the learnable matrices in the
+        # original paper correspondingly. The variable r refers to subscript to
+        # theta.
+        self.theta = nn.ModuleList(
+            [nn.Linear(in_size, hidden_size) for _ in range(r + 1)]
+        )
+        self.omega = nn.Linear(hidden_size * (r + 1), out_size)
+
+    def forward(self, X_sign):
+        results = []
+        for i in range(len(X_sign)):
+            results.append(self.theta[i](X_sign[i]))
+        Z = F.relu(torch.cat(results, dim=1))
+        return self.omega(Z)
+
+
+def evaluate(g, pred):
+    label = g.ndata["label"]
+    val_mask = g.ndata["val_mask"]
+    test_mask = g.ndata["test_mask"]
+
+    # Compute accuracy on validation/test set.
+    val_acc = (pred[val_mask] == label[val_mask]).float().mean()
+    test_acc = (pred[test_mask] == label[test_mask]).float().mean()
+    return val_acc, test_acc
+
+
+def train(g, model):
+    labels = g.ndata["label"]
+    train_mask = g.ndata["train_mask"]
+    optimizer = Adam(model.parameters(), lr=3e-3)
+
+    for epoch in range(10):
+        # Forward.
+        logits = model(X_sign)
+
+        # Compute loss with nodes in training set.
+        loss = F.cross_entropy(logits[train_mask], labels[train_mask])
+
+        # Backward.
+        optimizer.zero_grad()
+        loss.backward()
+        optimizer.step()
+
+        # Compute prediction.
+        pred = logits.argmax(1)
+
+        # Evaluate the prediction.
+        val_acc, test_acc = evaluate(g, pred)
+        print(
+            f"In epoch {epoch}, loss: {loss:.3f}, val acc: {val_acc:.3f}, test"
+            f" acc: {test_acc:.3f}"
+        )
+
+
+if __name__ == "__main__":
+    # If CUDA is available, use GPU to accelerate the training, use CPU
+    # otherwise.
+    dev = torch.device("cuda:0" if torch.cuda.is_available() else "cpu")
+
+    # Load graph from the existing dataset.
+    dataset = CoraGraphDataset()
+    g = dataset[0].to(dev)
+
+    # Create the sparse adjacency matrix A (note that W was used as the notation
+    # for adjacency matrix in the original paper).
+    src, dst = g.edges()
+    N = g.num_nodes()
+    A = create_from_coo(dst, src, shape=(N, N))
+
+    # Calculate the symmetrically normalized adjacency matrix.
+    I = identity(A.shape, device=dev)
+    A_hat = A + I
+    D_hat = diag(A_hat.sum(dim=1)) ** -0.5
+    A_hat = D_hat @ A_hat @ D_hat
+
+    # 2-hop diffusion.
+    r = 2
+    X = g.ndata["feat"]
+    X_sign = sign_diffusion(A_hat, X, r)
+
+    # Create SIGN model.
+    in_size = X.shape[1]
+    out_size = dataset.num_classes
+    model = SIGN(in_size, out_size, r).to(dev)
+
+    # Kick off training.
+    train(g, model)