[Sparse] Add HGNN example (#4917)

* hgnn example

* desc

* update example index

* address

* replace naming

* address comments

examples/README.md

@@ -247,6 +247,10 @@ To quickly locate the examples of your interest, search for the tagged keywords
     - Example code: [pytorch](../examples/pytorch/dtgrnn)
     - Tags: Static discrete temporal graph, traffic forecasting
 
+- <a name="hgnn"></a> Feng et al. Hypergraph Neural Networks. [Paper link](https://arxiv.org/abs/1809.09401).
+    - Example code: [pytorch](../examples/sparse/hgnn)
+    - Tags: hypergraph
+
 ## 2017
 
 - <a name="gcn"></a> Kipf and Welling. Semi-Supervised Classification with Graph Convolutional Networks. [Paper link](https://arxiv.org/abs/1609.02907). 

examples/sparse/hgnn.py

+"""
+Hypergraph Neural Networks (https://arxiv.org/pdf/1809.09401.pdf)
+"""
+import dgl
+import dgl.data
+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
+
+class HGNN(nn.Module):
+    def __init__(self, H, in_size, out_size, hidden_dims=16):
+        super().__init__()
+
+        self.Theta1 = nn.Linear(in_size, hidden_dims)
+        self.Theta2 = nn.Linear(hidden_dims, out_size)
+        self.dropout = nn.Dropout(0.5)
+
+        ###########################################################
+        # (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))
+        self.laplacian = D_V_invsqrt @ H @ W @ D_E_inv @ H.T @ D_V_invsqrt
+
+    def forward(self, X):
+        X = self.laplacian @ self.Theta1(self.dropout(X))
+        X = F.relu(X)
+        X = self.laplacian @ self.Theta2(self.dropout(X))
+        return X
+
+def train(model, optimizer, X, Y, train_mask):
+    model.train()
+    Y_hat = model(X)
+    loss = F.cross_entropy(Y_hat[train_mask], Y[train_mask])
+    optimizer.zero_grad()
+    loss.backward()
+    optimizer.step()
+
+def evaluate(model, X, Y, val_mask, test_mask):
+    model.eval()
+    Y_hat = model(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 = HGNN(H, X.shape[1], num_classes)
+    optimizer = torch.optim.Adam(model.parameters(), lr=0.001)
+
+    with tqdm.trange(500) as tq:
+        for epoch in tq:
+            train(model, optimizer, X, Y, train_mask)
+            val_acc, test_acc = evaluate(model, X, Y, val_mask, test_mask)
+            tq.set_postfix(
+                {
+                    "Val acc": f"{val_acc:.5f}",
+                    "Test acc": f"{test_acc:.5f}",
+                },
+                refresh=False,
+            )
+
+if __name__ == '__main__':
+    main()