Reference: Neural Graph Collaborative Filtering. In SIGIR 2019.
使用用户-物品隐式交互数据来构建用户-物品二分图，然后使用图卷积的方法来更新图中每一个节点的embedding，使得每一个节点中都包含着高阶邻居的信息，在推荐的场景下，这样的卷积操作相当于将协同过滤信号编码进了每一个节点的embedding函数中，如果堆叠多次这样的卷积操作，就可以捕获更高阶的交互关系。
- 利用交互数据来生成评分矩阵R
R = sp.dok_matrix((n_users, n_items), dtype=np.float32)
with open(train_file) as f_train:
for l in f_train.readline():
items = [int(i) for i in l.strip('\n').split(' ')]
uid, train_items = items[0], itms[1:]
for i in train_items:
R[uid, i] = 1
- 将评分矩阵转化为邻接矩阵
def create_adj_matrix(R):
adj_mat = sp.dok_matrix((n_users + n_items, n_users + n_items), dtype=np.float32)
adj_mat = adj_mat.tolil()
R = R.tolil()
adj_mat[:n_users, n_users:] = R
adj_mat[n_users:, :n_users] = R.T
adj_mat = adj_mat.todok()
print('already create adjacency matrix', adj_mat.shape)
- 将邻接矩阵进行标准化
添加自环(第3代GCN)：adj_mat = adj_mat + sp.eye(adj_mat.shape[0])
不添加自环：adj_mat
可以使用L1标准化 将邻接矩阵乘度矩阵的逆(适用于单边标准化-第1代GCN)，也可以使用开根号的方式，将度矩阵上每一个元素开根号之后求逆(适用于双边标准化-第2代GCN，效果更好).
def normalize_adj_single(adj):
rowsum = np.array(adj.sum(1))
d_inv = np.power(rowsum, -1).flatten()
d_inv[np.isinf(d_inv)] = 0.
d_mat_inv = sp.diags(d_inv)
norm_adj = d_mat_inv.dot(adj)
print('generate single-normalized adjacency matrix.')
return norm_adj.tocoo()
def normalize_adj_symetric(adj):
adj = sp.coo_matrix(adj)
rowsum = np.array(adj.sum(1))
d_inv_sqrt = np.power(rowsum, -0.5).flatten()
d_inv_sqrt[np.isinf(d_inv_sqrt)] = 0.
d_mat_inv_sqrt = sp.diags(d_inv_sqrt)
return adj.dot(d_mat_inv_sqrt).transpose().dot(d_mat_inv_sqrt).tocoo()
mean_adj_1 = normalize_adj_single(adj_mat) # 单边标准化
norm_adj_1 = normalize_adj_symteric(adj_mat) # 双边标准化
mean_adj_2 = normalize_adj_single(adj_mat + sp.eye(adj_mat.shape[0])) # 单边标准化+自环
norm_adj_2 = normalize_adj_symteric(adj_mat + sp.eye(adj_mat.shape[0])) # 双边标准化+自环
- 一般较大的邻接矩阵无法直接和别的矩阵相乘（内存不足），需要将邻接矩阵切片后每部分单独运算，最后将结果组合在一起。
def _split_A_hat( X):
A_fold_hat = []
fold_len = (n_users + n_items) // n_fold
for i_fold in range(n_fold):
start = i_fold * fold_len
if i_fold == n_fold - 1:
end = n_users + n_items
else:
end = (i_fold + 1) * fold_len
A_fold_hat.append(_convert_sp_mat_to_sp_tensor(X[start:end]))
return A_fold_hat
# 将稀疏矩阵转化为tensor格式
def _convert_sp_mat_to_sp_tensor(self, X):
coo = X.tocoo().astype(np.float32)
indices = np.mat([coo.row, coo.col]).transpose()
return tf.SparseTensor(indices, coo.data, coo.shape)
- 利用GCN来更新节点的embedding
def create_gcn_embed():
A_fold_hat = _split_A_hat(adj_mat)
node_embeddings = tf.concat([user_embeddings, item_embeddings], axis=0)
all_embeddings = [node_embedding]
for k in range(n_layers):
temp_emb = []
for f in range(n_fold):
# 稀疏tensor和稠密tensor相乘的 方法
temp_embed.append(tf.sparse_tensor_dense_matmul(A_fold_hat[f], eu_embeddings))
sum_embeddings = tf.concat(temp_embed, 0)
node_embeddings = sum_embeddings
all_embeddings += [node_embeddings]
all_embeddings = tf.concat(all_embeddings, 1)
user_embeddings, item_embeddings = tf.split(all_embeddings, [n_users, n_items], 0)
return user_embeddings, item_embeddings
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