[Example] Hypergraph attention (#4941)

* hypergraph attention

* address comments

examples/sparse/hypergraphatt.py

+"""
+Hypergraph Convolution and Hypergraph Attention
+(https://arxiv.org/pdf/1901.08150.pdf).
+"""
+import dgl
+import dgl.mock_sparse as dglsp
+import torch
+import torch.nn as nn
+import torch.nn.functional as F
+from torchmetrics.functional import accuracy
+import tqdm
+
+def hypergraph_laplacian(H):
+    ###########################################################
+    # (HIGHLIGHT) Compute the Laplacian with Sparse Matrix API
+    ###########################################################
+    d_V = H.sum(1)  # node degree
+    d_E = H.sum(0)  # edge degree
+    n_edges = d_E.shape[0]
+    D_V_invsqrt = dglsp.diag(d_V ** -0.5)  # D_V ** (-1/2)
+    D_E_inv = dglsp.diag(d_E ** -1)  # D_E ** (-1)
+    W = dglsp.identity((n_edges, n_edges))
+    return D_V_invsqrt @ H @ W @ D_E_inv @ H.T @ D_V_invsqrt
+
+class HypergraphAttention(nn.Module):
+    """Hypergraph Attention module as in the paper
+    `Hypergraph Convolution and Hypergraph Attention
+    <https://arxiv.org/pdf/1901.08150.pdf>`_.
+    """
+    def __init__(self, in_size, out_size):
+        super().__init__()
+
+        self.P = nn.Linear(in_size, out_size)
+        self.a = nn.Linear(2 * out_size, 1)
+
+    def forward(self, H, X, X_edges):
+        Z = self.P(X)
+        Z_edges = self.P(X_edges)
+        sim = self.a(torch.cat([Z[H.row], Z_edges[H.col]], 1))
+        sim = F.leaky_relu(sim, 0.2).squeeze(1)
+        # Reassign the hypergraph new weights.
+        H_att = dglsp.create_from_coo(H.row, H.col, sim, shape=H.shape)
+        H_att = H_att.softmax()
+        return hypergraph_laplacian(H_att) @ Z
+
+class Net(nn.Module):
+    def __init__(self, in_size, out_size, hidden_size=16):
+        super().__init__()
+
+        self.layer1 = HypergraphAttention(in_size, hidden_size)
+        self.layer2 = HypergraphAttention(hidden_size, out_size)
+
+    def forward(self, H, X):
+        Z = self.layer1(H, X, X)
+        Z = F.elu(Z)
+        Z = self.layer2(H, Z, Z)
+        return Z
+
+def train(model, optimizer, H, X, Y, train_mask):
+    model.train()
+    Y_hat = model(H, X)
+    loss = F.cross_entropy(Y_hat[train_mask], Y[train_mask])
+    optimizer.zero_grad()
+    loss.backward()
+    optimizer.step()
+    return loss.item()
+
+def evaluate(model, H, X, Y, val_mask, test_mask):
+    model.eval()
+    Y_hat = model(H, X)
+    val_acc = accuracy(Y_hat[val_mask], Y[val_mask])
+    test_acc = accuracy(Y_hat[test_mask], Y[test_mask])
+    return val_acc, test_acc
+
+def load_data():
+    dataset = dgl.data.CoraGraphDataset()
+
+    graph = dataset[0]
+    # The paper created a hypergraph from the original graph. For each node in
+    # the original graph, a hyperedge in the hypergraph is created to connect
+    # its neighbors and itself. In this case, the incidence matrix of the
+    # hypergraph is the same as the adjacency matrix of the original graph (with
+    # self-loops).
+    # We follow the paper and assume that the rows of the incidence matrix
+    # are for nodes and the columns are for edges.
+    src, dst = graph.edges()
+    H = dglsp.create_from_coo(dst, src)
+    H = H + dglsp.identity(H.shape)
+
+    X = graph.ndata["feat"]
+    Y = graph.ndata["label"]
+    train_mask = graph.ndata["train_mask"]
+    val_mask = graph.ndata["val_mask"]
+    test_mask = graph.ndata["test_mask"]
+    return H, X, Y, dataset.num_classes, train_mask, val_mask, test_mask
+
+def main():
+    H, X, Y, num_classes, train_mask, val_mask, test_mask = load_data()
+    model = Net(X.shape[1], num_classes)
+    optimizer = torch.optim.Adam(model.parameters(), lr=0.001)
+
+    with tqdm.trange(500) as tq:
+        for epoch in tq:
+            loss = train(model, optimizer, H, X, Y, train_mask)
+            val_acc, test_acc = evaluate(model, H, X, Y, val_mask, test_mask)
+            tq.set_postfix(
+                {
+                    "Loss": f"{loss:.5f}",
+                    "Val acc": f"{val_acc:.5f}",
+                    "Test acc": f"{test_acc:.5f}",
+                },
+                refresh=False,
+            )
+
+if __name__ == '__main__':
+    main()