GNN邻接矩阵归一化

诸神缄默不语-个人优快云博文目录

特征归一化见这篇博文：特征工程/数据预处理超全面总结（持续更新ing…）

1. 对称归一化$D^{-\frac{1}{2}}A{D}^{-\frac{1}{2}}$

代码参考自R-former：

def normalize_adj(adj):
    """Symmetrically normalize adjacency matrix."""
    rowsum = np.array(adj.sum(1))
    with np.errstate(divide='ignore'):
        d_inv_sqrt = np.power(rowsum, -0.5).flatten()
    d_inv_sqrt[np.isinf(d_inv_sqrt)] = 0.
    d_mat_inv_sqrt = np.diag(d_inv_sqrt)
    return adj.dot(d_mat_inv_sqrt).transpose().dot(d_mat_inv_sqrt)

2. $D^{-1}A$

代码参考自GL-GIN：

def normalize_adj(mx):
    """
    Row-normalize matrix  D^{-1}A
    torch.diag_embed: https://github.com/pytorch/pytorch/pull/12447
    """
    mx = mx.float()
    rowsum = mx.sum(2)
    r_inv = torch.pow(rowsum, -1)
    r_inv[torch.isinf(r_inv)] = 0.
    r_mat_inv = torch.diag_embed(r_inv, 0)
    mx = r_mat_inv.matmul(mx)
    return mx