I am working on implementing a methodology described in a research paper that utilizes Graph Neural Networks (GNN) for processing electronic health records, Paper. Below is a simplified version of my code:

1. Does my code correctly follow the methodology described in the paper?

The paper outlines a process involving graph neural networks to process heterogeneous similarity matrices derived from different k-metapaths. I have tried to implement this by passing node features through a GNN for each similarity matrix, then aggregating the results. I also compute attention weights to create a final meta-adjacency matrix. Am I interpreting the methodology correctly? Are there any specific aspects of the paper that I might be overlooking in this implementation?

2. How can I handle feeding large numbers of nodes into one graph?

In my actual dataset, I need to work with graphs containing a large number of nodes, specifically summing up to 157,222 nodes (46520+58976+203+157+304+480+258+324 nodes) across different k-metapath based graphs. What would be the best approach to handle such large graphs considering the computational complexity, especially in terms of memory usage and processing time? How can I efficiently represent the features and edges for these nodes?

Any insights or suggestions on these points would be greatly appreciated!

I tried this. I made the code create a synthetic data for that purpose.

import torch
import torch.nn as nn
import torch.nn.functional as F
from torch_geometric.nn import GCNConv
import numpy as np
import scipy.sparse

# Define the GNN model
class GNN(nn.Module):
    def __init__(self, input_dim, output_dim):
        super(GNN, self).__init__()
        self.conv1 = GCNConv(input_dim, output_dim)

    def forward(self, x, edge_index):
        x = self.conv1(x, edge_index)
        return x

# Aggregation function
def aggregate_features(features_list, method='mean'):
    if method == 'mean':
        return torch.mean(torch.stack(features_list), dim=0)
    elif method == 'concat':
        return torch.cat(features_list, dim=1)
    elif method == 'max':
        return torch.max(torch.stack(features_list), dim=0).values
    else:
        raise ValueError("Unsupported aggregation method")

# Compute attention weights
def compute_attention_weights(f_meta):
    N = f_meta.shape[0]
    alpha = nn.Parameter(torch.randn(f_meta.shape[1] * 2, 1))
    attention_weights = torch.zeros(N, N)

    for i in range(N):
        for j in range(N):
            meta_concat = torch.cat([f_meta[i], f_meta[j]], dim=0)
            attention_weights[i, j] = torch.exp(F.relu(meta_concat @ alpha))

    attention_weights = attention_weights / attention_weights.sum(dim=1, keepdim=True)
    return attention_weights

# Main function to compute F_meta and A_meta
def compute_A_meta(features, similarity_matrices, output_dim, aggregation_method='mean'):
    N = features.shape[0]
    input_dim = features.shape[1]
    K = len(similarity_matrices)

    # Initialize GNN model
    gnn = GNN(input_dim, output_dim)
    
    # List to store node features from each similarity matrix
    features_list = []

    for A_k in similarity_matrices:
        edge_index = torch.tensor(A_k.nonzero(), dtype=torch.long)
        edge_index = torch.stack([edge_index[0], edge_index[1]])  # Ensure correct shape for edge_index
        x = features.clone().detach()
        features_list.append(gnn(x, edge_index))

    # Aggregate features to get F_meta
    f_meta = aggregate_features(features_list, method=aggregation_method)

    # Compute attention weights using F_meta
    attention_weights = compute_attention_weights(f_meta)

    # Compute A_meta
    A_meta = torch.zeros(N, N)
    for k in range(K):
        A_dense = torch.tensor(similarity_matrices[k].toarray(), dtype=torch.float32)  # Convert sparse matrix to dense tensor
        A_meta += attention_weights * A_dense  # Element-wise multiplication

    return f_meta, A_meta

# Example usage with synthetic data
N = 157,222 # Number of nodes
D = 32   # Dimension of node features
K = 20    # Number of similarity matrices
output_dim = 16  # Output dimension of GNN

features = torch.rand(N, D, dtype=torch.float32)

similarity_matrices = []
for _ in range(K):
    dense_matrix = np.random.rand(N, N)
    sparse_matrix = scipy.sparse.csr_matrix(dense_matrix > 0.95)  # Sparsify
    similarity_matrices.append(sparse_matrix)

f_meta, A_meta = compute_A_meta(features, similarity_matrices, output_dim, aggregation_method='max')

print("F_meta:", f_meta)
print("A_meta:", A_meta)