技术标签: 图神经网络 GCN 深度学习 DGL pytorch
链接预测就是预测图中给定节点间是否存在边,常用于推荐系统。
形式化地,给定节点 u u u和 v v v,链接预测的任务就是得到它们间存在链接的概率 y u , v = ϕ ( u , v ) y_{u,v}=\phi \left ( u,v\right ) yu,v=ϕ(u,v)。具体到GNN上,我们通过L层的GNN得到节点 u u u和 v v v的表示 h u ( L ) h_{u}^{\left ( L\right )} hu(L)和 h v ( L ) h_{v}^{\left ( L\right )} hv(L),然后通过预测模型得到存在链接的概率 y u , v = ϕ ( h u ( L ) , h v ( L ) ) y_{u,v}=\phi \left ( h_{u}^{\left ( L\right )},h_{v}^{\left ( L\right )}\right ) yu,v=ϕ(hu(L),hv(L))。
链接预测的优化方式通常采用负采样。即给定一条链接 u u u和 v v v的边,我们希望 u u u与 v v v的得分(链接概率)高于 u u u与其他节点 v ′ {v}' v′的得分。而其他节点又太多了,为了提高效率,我们只从任意噪声分布 v ′ ∈ P n ( v ) {v}'\in P_{n}\left ( v\right ) v′∈Pn(v)采样一部分作为负样本。
常见的损失函数有:
依然使用DGL内置的数据集“Citeseer”:
dataset = dgl.data.CiteseerGraphDataset()
graph = dataset[0]
我们将节点间的得分(链接概率)视为节点间连边的边特征“score”,通过节点表示计算得到,这里采用最简单的内积函数。
class DotProductPredictor(nn.Module):
def forward(self, graph, h):
with graph.local_scope():
graph.ndata['h'] = h
graph.apply_edges(fn.u_dot_v('h', 'h', 'score'))
return graph.edata['score']
由上面的得分计算方式可知,得分的计算需要节点间存在连边。为了让节点与负样本间也存在连边,我们选择单独为负样本构建一个图。
def construct_negative_graph(graph, k):
src, dst = graph.edges()
neg_src = src.repeat_interleave(k)
neg_dst = torch.randint(0, graph.num_nodes(), (len(src) * k,))
return dgl.graph((neg_src, neg_dst), num_nodes=graph.num_nodes())
对于输入的原始图,我们将源节点复制k份,但目标节点由随机采样得到,如此,每条边有k个负样本,将它们连接起来构成负采样图。
还是使用两层GraphSAGE。
class SAGE(nn.Module):
def __init__(self, in_feats, hid_feats, out_feats):
super().__init__()
self.conv1 = dglnn.SAGEConv(
in_feats=in_feats, out_feats=hid_feats, aggregator_type='mean')
self.conv2 = dglnn.SAGEConv(
in_feats=hid_feats, out_feats=out_feats, aggregator_type='mean')
def forward(self, graph, inputs):
h = self.conv1(graph, inputs)
h = F.relu(h)
h = self.conv2(graph, h)
return h
通过“SAGE()”得到节点表示后,分别计算正样本的得分和负样本的得分。
class Model(nn.Module):
def __init__(self, in_features, hidden_features, out_features):
super().__init__()
self.sage = SAGE(in_features, hidden_features, out_features)
self.pred = DotProductPredictor()
def forward(self, g, neg_g, x):
h = self.sage(g, x)
return self.pred(g, h), self.pred(neg_g, h)
这里采用间隔损失,由于一个正样本对应多个负样本,所以这里调整了张量的shape,以利用广播机制。
def compute_loss(pos_score, neg_score):
n_edges = pos_score.shape[0]
return (1 - pos_score.unsqueeze(1) + neg_score.view(n_edges, -1)).clamp(min=0).mean()
node_features = graph.ndata['feat']
n_features = node_features.shape[1]
k = 5
model = Model(n_features, 100, 100)
opt = torch.optim.Adam(model.parameters())
for epoch in range(10):
negative_graph = construct_negative_graph(graph, k)
pos_score, neg_score = model(graph, negative_graph, node_features)
loss = compute_loss(pos_score, neg_score)
opt.zero_grad()
loss.backward()
opt.step()
print(loss.item())
如果想得到节点的表示,只需要调用模型的模型表示模块即可。
node_embeddings = model.sage(graph, node_features)
使用“跟着官方文档学DGL框架第八天”中人工构建的异构图数据集,包含两种类型的结点和六种类型的边。
n_users = 1000
n_items = 500
n_follows = 3000
n_clicks = 5000
n_dislikes = 500
n_hetero_features = 10
n_user_classes = 5
n_max_clicks = 10
follow_src = np.random.randint(0, n_users, n_follows)
follow_dst = np.random.randint(0, n_users, n_follows)
click_src = np.random.randint(0, n_users, n_clicks)
click_dst = np.random.randint(0, n_items, n_clicks)
dislike_src = np.random.randint(0, n_users, n_dislikes)
dislike_dst = np.random.randint(0, n_items, n_dislikes)
hetero_graph = dgl.heterograph({
('user', 'follow', 'user'): (follow_src, follow_dst),
('user', 'followed-by', 'user'): (follow_dst, follow_src),
('user', 'click', 'item'): (click_src, click_dst),
('item', 'clicked-by', 'user'): (click_dst, click_src),
('user', 'dislike', 'item'): (dislike_src, dislike_dst),
('item', 'disliked-by', 'user'): (dislike_dst, dislike_src)})
hetero_graph.nodes['user'].data['feature'] = torch.randn(n_users, n_hetero_features)
hetero_graph.nodes['item'].data['feature'] = torch.randn(n_items, n_hetero_features)
hetero_graph.nodes['user'].data['label'] = torch.randint(0, n_user_classes, (n_users,))
hetero_graph.edges['click'].data['label'] = torch.randint(1, n_max_clicks, (n_clicks,)).float()
# randomly generate training masks on user nodes and click edges
hetero_graph.nodes['user'].data['train_mask'] = torch.zeros(n_users, dtype=torch.bool).bernoulli(0.6)
hetero_graph.edges['click'].data['train_mask'] = torch.zeros(n_clicks, dtype=torch.bool).bernoulli(0.6)
与同构图不同的是,计算得分时需要指定边的类型,我们只计算一种边上的得分。
class HeteroDotProductPredictor(nn.Module):
def forward(self, graph, h, etype):
with graph.local_scope():
graph.ndata['h'] = h
graph.apply_edges(fn.u_dot_v('h', 'h', 'score'), etype=etype)
return graph.edges[etype].data['score']
对要进行链接预测的边类型构造一个负采样图。
def construct_negative_graph(graph, k, etype):
utype, _, vtype = etype
src, dst = graph.edges(etype=etype)
neg_src = src.repeat_interleave(k)
neg_dst = torch.randint(0, graph.num_nodes(vtype), (len(src) * k,))
return dgl.heterograph(
{
etype: (neg_src, neg_dst)},
num_nodes_dict={
ntype: graph.num_nodes(ntype) for ntype in graph.ntypes})
老办法,“RGCN()”:
class RGCN(nn.Module):
def __init__(self, in_feats, hid_feats, out_feats, rel_names):
super().__init__()
self.conv1 = dglnn.HeteroGraphConv({
rel: dglnn.GraphConv(in_feats, hid_feats)
for rel in rel_names}, aggregate='sum')
self.conv2 = dglnn.HeteroGraphConv({
rel: dglnn.GraphConv(hid_feats, out_feats)
for rel in rel_names}, aggregate='sum')
def forward(self, graph, inputs):
h = self.conv1(graph, inputs)
h = {
k: F.relu(v) for k, v in h.items()}
h = self.conv2(graph, h)
return h
class Model(nn.Module):
def __init__(self, in_features, hidden_features, out_features, rel_names):
super().__init__()
self.sage = RGCN(in_features, hidden_features, out_features, rel_names)
self.pred = HeteroDotProductPredictor()
def forward(self, g, neg_g, x, etype):
h = self.sage(g, x)
return self.pred(g, h, etype), self.pred(neg_g, h, etype)
def compute_loss(pos_score, neg_score):
n_edges = pos_score.shape[0]
return (1 - pos_score.unsqueeze(1) + neg_score.view(n_edges, -1)).clamp(min=0).mean()
model = Model(10, 20, 5, hetero_graph.etypes)
user_feats = hetero_graph.nodes['user'].data['feature']
item_feats = hetero_graph.nodes['item'].data['feature']
node_features = {
'user': user_feats, 'item': item_feats}
opt = torch.optim.Adam(model.parameters())
for epoch in range(10):
negative_graph = construct_negative_graph(hetero_graph, k, ('user', 'click', 'item'))
pos_score, neg_score = model(hetero_graph, negative_graph, node_features, ('user', 'click', 'item'))
loss = compute_loss(pos_score, neg_score)
opt.zero_grad()
loss.backward()
opt.step()
print(loss.item())
import dgl
import dgl.nn as dglnn
import dgl.function as fn
import torch.nn as nn
import torch.nn.functional as F
import torch
class DotProductPredictor(nn.Module):
def forward(self, graph, h):
with graph.local_scope():
graph.ndata['h'] = h
graph.apply_edges(fn.u_dot_v('h', 'h', 'score'))
return graph.edata['score']
def construct_negative_graph(graph, k):
src, dst = graph.edges()
neg_src = src.repeat_interleave(k)
neg_dst = torch.randint(0, graph.num_nodes(), (len(src) * k,))
return dgl.graph((neg_src, neg_dst), num_nodes=graph.num_nodes())
class SAGE(nn.Module):
def __init__(self, in_feats, hid_feats, out_feats):
super().__init__()
self.conv1 = dglnn.SAGEConv(
in_feats=in_feats, out_feats=hid_feats, aggregator_type='mean')
self.conv2 = dglnn.SAGEConv(
in_feats=hid_feats, out_feats=out_feats, aggregator_type='mean')
def forward(self, graph, inputs):
h = self.conv1(graph, inputs)
h = F.relu(h)
h = self.conv2(graph, h)
return h
class Model(nn.Module):
def __init__(self, in_features, hidden_features, out_features):
super().__init__()
self.sage = SAGE(in_features, hidden_features, out_features)
self.pred = DotProductPredictor()
def forward(self, g, neg_g, x):
h = self.sage(g, x)
return self.pred(g, h), self.pred(neg_g, h)
def compute_loss(pos_score, neg_score):
n_edges = pos_score.shape[0]
return (1 - pos_score.unsqueeze(1) + neg_score.view(n_edges, -1)).clamp(min=0).mean()
dataset = dgl.data.CiteseerGraphDataset()
graph = dataset[0]
node_features = graph.ndata['feat']
n_features = node_features.shape[1]
k = 5
model = Model(n_features, 100, 100)
opt = torch.optim.Adam(model.parameters())
for epoch in range(10):
negative_graph = construct_negative_graph(graph, k)
pos_score, neg_score = model(graph, negative_graph, node_features)
loss = compute_loss(pos_score, neg_score)
opt.zero_grad()
loss.backward()
opt.step()
print(loss.item())
node_embeddings = model.sage(graph, node_features)
import dgl
import dgl.nn as dglnn
import dgl.function as fn
import torch.nn as nn
import torch.nn.functional as F
import torch
import numpy as np
n_users = 1000
n_items = 500
n_follows = 3000
n_clicks = 5000
n_dislikes = 500
n_hetero_features = 10
n_user_classes = 5
n_max_clicks = 10
follow_src = np.random.randint(0, n_users, n_follows)
follow_dst = np.random.randint(0, n_users, n_follows)
click_src = np.random.randint(0, n_users, n_clicks)
click_dst = np.random.randint(0, n_items, n_clicks)
dislike_src = np.random.randint(0, n_users, n_dislikes)
dislike_dst = np.random.randint(0, n_items, n_dislikes)
hetero_graph = dgl.heterograph({
('user', 'follow', 'user'): (follow_src, follow_dst),
('user', 'followed-by', 'user'): (follow_dst, follow_src),
('user', 'click', 'item'): (click_src, click_dst),
('item', 'clicked-by', 'user'): (click_dst, click_src),
('user', 'dislike', 'item'): (dislike_src, dislike_dst),
('item', 'disliked-by', 'user'): (dislike_dst, dislike_src)})
hetero_graph.nodes['user'].data['feature'] = torch.randn(n_users, n_hetero_features)
hetero_graph.nodes['item'].data['feature'] = torch.randn(n_items, n_hetero_features)
hetero_graph.nodes['user'].data['label'] = torch.randint(0, n_user_classes, (n_users,))
hetero_graph.edges['click'].data['label'] = torch.randint(1, n_max_clicks, (n_clicks,)).float()
# randomly generate training masks on user nodes and click edges
hetero_graph.nodes['user'].data['train_mask'] = torch.zeros(n_users, dtype=torch.bool).bernoulli(0.6)
hetero_graph.edges['click'].data['train_mask'] = torch.zeros(n_clicks, dtype=torch.bool).bernoulli(0.6)
class HeteroDotProductPredictor(nn.Module):
def forward(self, graph, h, etype):
with graph.local_scope():
graph.ndata['h'] = h
graph.apply_edges(fn.u_dot_v('h', 'h', 'score'), etype=etype)
return graph.edges[etype].data['score']
def construct_negative_graph(graph, k, etype):
utype, _, vtype = etype
src, dst = graph.edges(etype=etype)
neg_src = src.repeat_interleave(k)
neg_dst = torch.randint(0, graph.num_nodes(vtype), (len(src) * k,))
return dgl.heterograph(
{
etype: (neg_src, neg_dst)},
num_nodes_dict={
ntype: graph.num_nodes(ntype) for ntype in graph.ntypes})
class RGCN(nn.Module):
def __init__(self, in_feats, hid_feats, out_feats, rel_names):
super().__init__()
self.conv1 = dglnn.HeteroGraphConv({
rel: dglnn.GraphConv(in_feats, hid_feats)
for rel in rel_names}, aggregate='sum')
self.conv2 = dglnn.HeteroGraphConv({
rel: dglnn.GraphConv(hid_feats, out_feats)
for rel in rel_names}, aggregate='sum')
def forward(self, graph, inputs):
h = self.conv1(graph, inputs)
h = {
k: F.relu(v) for k, v in h.items()}
h = self.conv2(graph, h)
return h
class Model(nn.Module):
def __init__(self, in_features, hidden_features, out_features, rel_names):
super().__init__()
self.sage = RGCN(in_features, hidden_features, out_features, rel_names)
self.pred = HeteroDotProductPredictor()
def forward(self, g, neg_g, x, etype):
h = self.sage(g, x)
return self.pred(g, h, etype), self.pred(neg_g, h, etype)
def compute_loss(pos_score, neg_score):
n_edges = pos_score.shape[0]
return (1 - pos_score.unsqueeze(1) + neg_score.view(n_edges, -1)).clamp(min=0).mean()
k = 5
model = Model(10, 20, 5, hetero_graph.etypes)
user_feats = hetero_graph.nodes['user'].data['feature']
item_feats = hetero_graph.nodes['item'].data['feature']
node_features = {
'user': user_feats, 'item': item_feats}
opt = torch.optim.Adam(model.parameters())
for epoch in range(10):
negative_graph = construct_negative_graph(hetero_graph, k, ('user', 'click', 'item'))
pos_score, neg_score = model(hetero_graph, negative_graph, node_features, ('user', 'click', 'item'))
loss = compute_loss(pos_score, neg_score)
opt.zero_grad()
loss.backward()
opt.step()
print(loss.item())
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