チェビシェフ多項式に基づく簡単なGCNネットワーク
論文『SEMI-SUPErVISED CLASSIFIFICATION WITH GRAPH CONVOLUTIONAL NETWORKS』の原理を用いて簡単なGCNテストを行い、具体的な原理はこの論文を見ることができる.
import torch
import torch.nn as nn
import torch.nn.functional as F
import networkx as nx
def normalize(A, symmetric=True):
# A = A+I
A = A + torch.eye(A.size(0))
d = A.sum(1)
if symmetric:
#D = D^-1/2
D = torch.diag(torch.pow(d , -0.5))
return D.mm(A).mm(D)
else:
# D=D^-1
D =torch.diag(torch.pow(d,-1))
return D.mm(A)
class GCN(nn.Module):
'''
Z = AXW
'''
def __init__(self , A, dim_in , dim_out):
super(GCN,self).__init__()
self.A = A
self.fc1 = nn.Linear(dim_in ,dim_in,bias=False)
self.fc2 = nn.Linear(dim_in,dim_in//2,bias=False)
self.fc3 = nn.Linear(dim_in//2,dim_out,bias=False)
def forward(self, X):
'''
gcn
'''
X = F.relu(self.fc1(self.A.mm(X)))
X = F.relu(self.fc2(self.A.mm(X)))
X = self.fc3(self.A.mm(X))
return F.softmax(X, dim=1)
#
G = nx.karate_club_graph()
A = nx.adjacency_matrix(G).todense()
A_normed = normalize(torch.FloatTensor(A.astype(int)),True)
N = len(A)
X_dim = N
# node features
X = torch.eye(N, X_dim)
# ,0 or 1
Y = torch.zeros(N, 1).long()
Y_mask = torch.zeros(N, 1, dtype=torch.uint8)
# 2 , ground truth label
#
Y[0][0] = 0
Y[N-1][0] = 1
#
Y_mask[0][0] = 1
Y_mask[N-1][0] = 1
# ground truth
Real = torch.zeros(34, dtype=torch.long)
for i in [1, 2, 3, 4, 5, 6, 7, 8, 11, 12, 13, 14, 17, 18, 20, 22]:
Real[i-1] = 0
for i in [9, 10, 15, 16, 19, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34]:
Real[i-1] = 1
gcn = GCN(A_normed, X_dim, 2)
gd = torch.optim.Adam(gcn.parameters())
for i in range(300):
y_pred = gcn(X)
# cross entropy
loss = (-y_pred.log().gather(1, Y.view(-1, 1)))
loss = loss.masked_select(Y_mask).mean() # mask 1
gd.zero_grad()
loss.backward()
gd.step()
if i % 20 == 0:
_, mi = y_pred.max(1)
print("loss: ", loss.item())
print(mi)
print("acc: ", (mi == Real).float().mean().item())