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论文名称：Diffusion Convolutional Recurrent Neural Network: Data-Driven Traffic Forecasting

论文下载：https://arxiv.org/abs/1707.01926

论文解读： 论文翻译。由于我们这里主要进行论文代码的展示，论文的解读就不进行详细的讲解。

代码

  PyG Temporal中提供了大量已经编译好的图卷积递归神经网络模型，DCRNN模型对应的部分如下：

in_channels：代表输入模型进行处理的数据特征的维度，比如想要基于T个历史时间预测T+1时刻道路的交通流量，这里的in_channels=T。

out_channels：经过DCRNN模型处理后输出特征的维度。

K：扩散过程通过在图G上进行随机游走，来聚合节点之间的特征，这个K相当于扩散程度，与GCN中的K相似。

  模型主要进行节点的预测任务，给定节点T个时刻的历史特征，通过DCRNN模型来对T+1时刻的节点特征进行预测。节点数为10，节点之间的拓扑结构为随机生成的拓扑结构，通过邻接矩阵A来表示。具体代码实现如下：

import numpy as np
import pandas as pd
import torch
import torch.nn.functional as F
import matplotlib.pyplot as plt
from sklearn.preprocessing import StandardScaler
from sklearn.preprocessing import MinMaxScaler
from torch_geometric_temporal.nn.recurrent import DCRNN
from torch_geometric_temporal import StaticGraphTemporalSignal
from tqdm import tqdm


TRAINING_LENGTH = 72
# 载入节点信息并进行预处理
node_cpu0 = pd.read_csv(r'v.2_data/v.2_CPU.csv', header=None)#(10, 1008)
node_cpu0 = node_cpu0.transpose()#(1008, 10)
node_cpu = np.zeros(node_cpu0.shape, dtype=float)
for j in range(node_cpu0.shape[1]):
    for i in range(len(node_cpu0)):
        if i == 0:
            node_cpu[i, j] = node_cpu0.iloc[i, j]
        elif i == len(node_cpu0):
            node_cpu[i, j] = node_cpu0.iloc[i, j]
        else:
            node_cpu[i, j] = np.mean(node_cpu0.iloc[i - 1:i + 2, j])

def clean_train_test_data(traindata, testdata):
    # sc = MinMaxScaler()
    sc = StandardScaler()
    train_data= sc.fit_transform(traindata)
    test_data = sc.transform(testdata)  # 利用训练集的属性对测试集进行归一化
    return train_data, test_data


# 将数据划分为训练集与测试集,前80%的数据作为训练集，后20%的数据作为测试集
train_size = int(len(node_cpu)*0.8)
test_size = len(node_cpu) - train_size
train_data = node_cpu[0:train_size, :]
test_data = node_cpu[train_size:len(node_cpu), :]
train_data, test_data = clean_train_test_data(train_data, test_data)
# print(train_data.shape)(806, 10)
# print(test_data.shape)(202, 10)
train_data = np.array(train_data).transpose()
test_data = np.array(test_data).transpose()
# print(train_data.shape)#(10, 806)
def create_dataset(data, n_sequence):
    '''
    对数据进行处理
    '''
    train_X, train_Y = [], []
    for i in range(data.shape[1] - n_sequence - 1):
        a = data[:, i:(i + n_sequence)]
        train_X.append(a)
        b = data[:, (i + n_sequence):(i + n_sequence + 1)]
        train_Y.append(b.T)

    return train_X, train_Y

train_feature, train_target = create_dataset(train_data, 72)
test_feature, test_target = create_dataset(test_data, 72)

edge_index = np.array([[0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 7, 1, 2, 1, 6, 2, 3, 2, 8, 2, 9, 3, 4, 3, 5, 3, 6, 3, 7, 5, 9, 7, 8],
                       [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 7, 0, 2, 1, 6, 1, 3, 2, 8, 2, 9, 2, 4, 3, 5, 3, 6, 3, 7, 3, 9, 5, 8, 7]])
train_dataset = StaticGraphTemporalSignal(edge_index=edge_index, edge_weight=np.ones(edge_index.shape[1]), features=train_feature, targets=train_target)
test_dataset = StaticGraphTemporalSignal(edge_index=edge_index, edge_weight=np.ones(edge_index.shape[1]), features=test_feature, targets=test_target)
# train_dataset, test_dataset = temporal_signal_split(dataset, train_ratio=0.75)
# print("Number of train buckets: ", len(set(train_dataset)))
# print("Number of test buckets: ", len(set(test_dataset)))


class RecurrentGCN(torch.nn.Module):
    def __init__(self, in_channel, out_channel, K):
        super(RecurrentGCN, self).__init__()
        self.recurrent = DCRNN(in_channel, out_channel, K)
        self.linear = torch.nn.Sequential(
            torch.nn.Linear(out_channel, out_channel // 2),
            torch.nn.ReLU(inplace=True),
            torch.nn.Linear(out_channel // 2, out_channel // 4),
            torch.nn.ReLU(inplace=True),
            torch.nn.Linear(out_channel // 4, 1))


    def forward(self, x, edge_index, edge_weight):
        h = self.recurrent(x, edge_index, edge_weight)
        h = F.relu(h)
        h = F.dropout(h, training=self.training)
        h = self.linear(h)
        return h


model = RecurrentGCN(in_channel=72, out_channel=36, K=1)
optimizer = torch.optim.Adam(model.parameters(), lr=0.01, weight_decay=5e-4)
cost_list = []
model.train()
'''time为train size'''
for epoch in tqdm(range(300)):
    cost = 0
    for time, snapshot in enumerate(train_dataset):

        y_hat = model(snapshot.x, snapshot.edge_index, snapshot.edge_attr)
        y_hat = y_hat.T
        cost = cost + torch.mean((y_hat - snapshot.y) ** 2)
        # cost = cost + regular_loss(model, lamda=1.5e-3)
    cost = cost / (time + 1)
    cost_list.append(cost.item())
    cost.backward()
    optimizer.step()
    optimizer.zero_grad()
cost = cost.item()
print("training MSE: {:.4f}".format(cost))

plt.plot(cost_list)
plt.xlabel("Epoch")
plt.ylabel("MSE")
plt.title("average of Training cost for 10 nodes")
plt.show()

model.eval()
cost = 0
test_real = []
test_pre = []
cha = []
for time, snapshot in enumerate(test_dataset):
    y_hat = model(snapshot.x, snapshot.edge_index, snapshot.edge_attr)
    y_hat = y_hat.T
    test_pre.append(y_hat.detach().numpy())
    test_real.append(snapshot.y.detach().numpy())
    cost = cost + torch.mean((y_hat - snapshot.y) ** 2)
cost = cost / (time + 1)
cost = cost.item()
print("test MSE: {:.4f}".format(cost))
test_real = np.array(test_real)
test_real = test_real.reshape([test_real.shape[0], test_real.shape[2]])
test_pre = np.array(test_pre)
test_pre = test_pre.reshape([test_pre.shape[0], test_pre.shape[2]])
plt.figure(1)
for i in range(test_real.shape[1]):
    plt.subplot(3, 4, 1+i)
    plt.plot(test_real[:, i].T, label='real data')
    plt.plot(test_pre[:, i].T, label='pre data')
    plt.xlabel("Time steps")
    plt.ylabel("Normalized Value")
    plt.suptitle("prediction against truth")
    plt.legend()
plt.show()

损失函数：

预测结果：

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新闻名称：基于PyGTemporal的DCRNN（扩散卷积递归神经网络）代码实现-创新互联
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