/
normalization.py
115 lines (94 loc) · 3.67 KB
/
normalization.py
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import numpy as np
import scipy.sparse as sp
def normalized_laplacian(adj):
adj = sp.coo_matrix(adj)
row_sum = np.array(adj.sum(1))
d_inv_sqrt = np.power(row_sum, -0.5).flatten()
d_inv_sqrt[np.isinf(d_inv_sqrt)] = 0.
d_mat_inv_sqrt = sp.diags(d_inv_sqrt)
return (sp.eye(adj.shape[0]) - d_mat_inv_sqrt.dot(adj).dot(d_mat_inv_sqrt)).tocoo()
def laplacian(adj):
adj = sp.coo_matrix(adj)
row_sum = np.array(adj.sum(1)).flatten()
d_mat = sp.diags(row_sum)
return (d_mat - adj).tocoo()
def gcn(adj):
adj = sp.coo_matrix(adj)
row_sum = np.array(adj.sum(1))
d_inv_sqrt = np.power(row_sum, -0.5).flatten()
d_inv_sqrt[np.isinf(d_inv_sqrt)] = 0.
d_mat_inv_sqrt = sp.diags(d_inv_sqrt)
return (sp.eye(adj.shape[0]) + d_mat_inv_sqrt.dot(adj).dot(d_mat_inv_sqrt)).tocoo()
def aug_normalized_adjacency(adj):
adj = adj + sp.eye(adj.shape[0])
adj = sp.coo_matrix(adj)
row_sum = np.array(adj.sum(1))
d_inv_sqrt = np.power(row_sum, -0.5).flatten()
d_inv_sqrt[np.isinf(d_inv_sqrt)] = 0.
d_mat_inv_sqrt = sp.diags(d_inv_sqrt)
return d_mat_inv_sqrt.dot(adj).dot(d_mat_inv_sqrt).tocoo()
def bingge_norm_adjacency(adj):
adj = adj + sp.eye(adj.shape[0])
adj = sp.coo_matrix(adj)
row_sum = np.array(adj.sum(1))
d_inv_sqrt = np.power(row_sum, -0.5).flatten()
d_inv_sqrt[np.isinf(d_inv_sqrt)] = 0.
d_mat_inv_sqrt = sp.diags(d_inv_sqrt)
return (d_mat_inv_sqrt.dot(adj).dot(d_mat_inv_sqrt) + sp.eye(adj.shape[0])).tocoo()
def normalized_adjacency(adj):
adj = sp.coo_matrix(adj)
row_sum = np.array(adj.sum(1))
d_inv_sqrt = np.power(row_sum, -0.5).flatten()
d_inv_sqrt[np.isinf(d_inv_sqrt)] = 0.
d_mat_inv_sqrt = sp.diags(d_inv_sqrt)
return (d_mat_inv_sqrt.dot(adj).dot(d_mat_inv_sqrt)).tocoo()
def random_walk_laplacian(adj):
adj = sp.coo_matrix(adj)
row_sum = np.array(adj.sum(1))
d_inv = np.power(row_sum, -1.0).flatten()
d_mat = sp.diags(d_inv)
return (sp.eye(adj.shape[0]) - d_mat.dot(adj)).tocoo()
def aug_random_walk(adj):
adj = adj + sp.eye(adj.shape[0])
adj = sp.coo_matrix(adj)
row_sum = np.array(adj.sum(1))
d_inv = np.power(row_sum, -1.0).flatten()
d_mat = sp.diags(d_inv)
return (d_mat.dot(adj)).tocoo()
def random_walk(adj):
adj = sp.coo_matrix(adj)
row_sum = np.array(adj.sum(1))
d_inv = np.power(row_sum, -1.0).flatten()
d_mat = sp.diags(d_inv)
return d_mat.dot(adj).tocoo()
def no_norm(adj):
adj = sp.coo_matrix(adj)
return adj
def i_norm(adj):
adj = adj + sp.eye(adj.shape[0])
adj = sp.coo_matrix(adj)
return adj
def fetch_normalization(type):
switcher = {
'NormLap': normalized_laplacian, # A' = I - D^-1/2 * A * D^-1/2
'Lap': laplacian, # A' = D - A
'RWalkLap': random_walk_laplacian, # A' = I - D^-1 * A
'FirstOrderGCN': gcn, # A' = I + D^-1/2 * A * D^-1/2
'AugNormAdj': aug_normalized_adjacency, # A' = (D + I)^-1/2 * ( A + I ) * (D + I)^-1/2
'BingGeNormAdj': bingge_norm_adjacency, # A' = I + (D + I)^-1/2 * (A + I) * (D + I)^-1/2
'NormAdj': normalized_adjacency, # D^-1/2 * A * D^-1/2
'RWalk': random_walk, # A' = D^-1*A
'AugRWalk': aug_random_walk, # A' = (D + I)^-1*(A + I)
'NoNorm': no_norm, # A' = A
'INorm': i_norm, # A' = A + I
}
func = switcher.get(type, lambda: "Invalid normalization technique.")
return func
def row_normalize(mx):
"""Row-normalize sparse matrix"""
rowsum = np.array(mx.sum(1))
r_inv = np.power(rowsum, -1).flatten()
r_inv[np.isinf(r_inv)] = 0.
r_mat_inv = sp.diags(r_inv)
mx = r_mat_inv.dot(mx)
return mx