Python和Numpy构建神经网络模型预测波士顿房价
代码所需文件housing.data
链接：https://pan.baidu.com/s/1oZbuUAtnEFf44w2tkUorpg
提取码：ntr1
构建一个基于下图13个因素进行房价预测的模型
# 导入需要用到的package
import numpy as np
import matplotlib.pyplot as plt
def load_data():
# 从文件导入数据
datafile = './housing.data'
data = np.fromfile(datafile, sep=' ')
# 每条数据包括14项，其中前面13项是影响因素，第14项是相应的房屋价格中位数
feature_names = [ 'CRIM', 'ZN', 'INDUS', 'CHAS', 'NOX', 'RM', 'AGE', \
'DIS', 'RAD', 'TAX', 'PTRATIO', 'B', 'LSTAT', 'MEDV' ]
feature_num = len(feature_names)
# 将原始数据进行Reshape，变成[N, 14]这样的形状
data = data.reshape([data.shape[0] // feature_num, feature_num])
# 将原数据集拆分成训练集和测试集
# 这里使用80%的数据做训练，20%的数据做测试
# 测试集和训练集必须是没有交集的
ratio = 0.8
offset = int(data.shape[0] * ratio)
training_data = data[:offset]
# 计算train数据集的最大值，最小值，平均值
maximums, minimums, avgs = training_data.max(axis=0),\
training_data.min(axis=0),\
training_data.sum(axis=0) / training_data.shape[0]
# 对数据进行归一化处理
for i in range(feature_num):
#print(maximums[i], minimums[i], avgs[i])
data[:, i] = (data[:, i] - avgs[i]) / (maximums[i] - minimums[i])
# 训练集和测试集的划分比例
training_data = data[:offset]
test_data = data[offset:]
return training_data, test_data
class Network(object):
def __init__(self, num_of_weights):
# 随机产生w的初始值
# 为了保持程序每次运行结果的一致性，此处设置固定的随机数种子
# np.random.seed(0)
self.w = np.random.randn(num_of_weights, 1)
self.b = 0.
def forward(self, x):
z = np.dot(x, self.w) + self.b
return z
def loss(self, z, y):
error = z - y
num_samples = error.shape[0]
cost = error * error
cost = np.sum(cost) / num_samples
return cost
def gradient(self, x, y):
z = self.forward(x)
N = x.shape[0]
gradient_w = 1. / N * np.sum((z - y) * x, axis=0)
gradient_w = gradient_w[:, np.newaxis]
gradient_b = 1. / N * np.sum(z - y)
return gradient_w, gradient_b
def update(self, gradient_w, gradient_b, eta=0.01):
self.w = self.w - eta * gradient_w
self.b = self.b - eta * gradient_b
def train(self, training_data, num_epoches, batch_size=10, eta=0.01):
n = len(training_data)
losses = []
for epoch_id in range(num_epoches):
# 在每轮迭代开始之前，将训练数据的顺序随机的打乱，
# 然后再按每次取batch_size条数据的方式取出
np.random.shuffle(training_data)
# 将训练数据进行拆分，每个mini_batch包含batch_size条的数据
mini_batches = [training_data[k:k + batch_size] for k in range(0, n, batch_size)]
for iter_id, mini_batch in enumerate(mini_batches):
# print(self.w.shape)
# print(self.b)
x = mini_batch[:, :-1]
y = mini_batch[:, -1:]
a = self.forward(x)
loss = self.loss(a, y)
gradient_w, gradient_b = self.gradient(x, y)
self.update(gradient_w, gradient_b, eta)
losses.append(loss)
print('Epoch {:3d} / iter {:3d}, loss = {:.4f}'.format(epoch_id, iter_id, loss))
return losses
# 获取数据
train_data, test_data = load_data()
# 创建网络
net = Network(13)
# 启动训练
losses = net.train(train_data, num_epoches=50, batch_size=100, eta=0.1)
# 画出损失函数的变化趋势
plot_x = np.arange(len(losses))
plot_y = np.array(losses)
plt.plot(plot_x, plot_y)
plt.show()
运行结果：
Epoch 0 / iter 0, loss = 0.3777
Epoch 0 / iter 1, loss = 0.3285
Epoch 0 / iter 2, loss = 0.2757
Epoch 0 / iter 3, loss = 0.3729
Epoch 0 / iter 4, loss = 0.1333
Epoch 1 / iter 0, loss = 0.3939
Epoch 1 / iter 1, loss = 0.2654
Epoch 1 / iter 2, loss = 0.2978
Epoch 1 / iter 3, loss = 0.3355
Epoch 1 / iter 4, loss = 0.6185
Epoch 2 / iter 0, loss = 0.4056
Epoch 2 / iter 1, loss = 0.2857
Epoch 2 / iter 2, loss = 0.2786
Epoch 2 / iter 3, loss = 0.2712
Epoch 2 / iter 4, loss = 0.5689
Epoch 3 / iter 0, loss = 0.2229
Epoch 3 / iter 1, loss = 0.3562
Epoch 3 / iter 2, loss = 0.3143
Epoch 3 / iter 3, loss = 0.3225
Epoch 3 / iter 4, loss = 0.0956
Epoch 4 / iter 0, loss = 0.3202
Epoch 4 / iter 1, loss = 0.2770
Epoch 4 / iter 2, loss = 0.3372
Epoch 4 / iter 3, loss = 0.2469
Epoch 4 / iter 4, loss = 0.1560
Epoch 5 / iter 0, loss = 0.2791
Epoch 5 / iter 1, loss = 0.2548
Epoch 5 / iter 2, loss = 0.3007
Epoch 5 / iter 3, loss = 0.3109
Epoch 5 / iter 4, loss = 0.1631
Epoch 6 / iter 0, loss = 0.3691
Epoch 6 / iter 1, loss = 0.3011
Epoch 6 / iter 2, loss = 0.2135
Epoch 6 / iter 3, loss = 0.2157
Epoch 6 / iter 4, loss = 0.4304
Epoch 7 / iter 0, loss = 0.2703
Epoch 7 / iter 1, loss = 0.2913
Epoch 7 / iter 2, loss = 0.2247
Epoch 7 / iter 3, loss = 0.2806
Epoch 7 / iter 4, loss = 0.3282
Epoch 8 / iter 0, loss = 0.2186
Epoch 8 / iter 1, loss = 0.2956
Epoch 8 / iter 2, loss = 0.2893
Epoch 8 / iter 3, loss = 0.2334
Epoch 8 / iter 4, loss = 0.1080
Epoch 9 / iter 0, loss = 0.2720
Epoch 9 / iter 1, loss = 0.2500
Epoch 9 / iter 2, loss = 0.2554
Epoch 9 / iter 3, loss = 0.2230
Epoch 9 / iter 4, loss = 0.3167
Epoch 10 / iter 0, loss = 0.2516
Epoch 10 / iter 1, loss = 0.2183
Epoch 10 / iter 2, loss = 0.2480
Epoch 10 / iter 3, loss = 0.2532
Epoch 10 / iter 4, loss = 0.2529
Epoch 11 / iter 0, loss = 0.2471
Epoch 11 / iter 1, loss = 0.1995
Epoch 11 / iter 2, loss = 0.2431
Epoch 11 / iter 3, loss = 0.2603
Epoch 11 / iter 4, loss = 0.0497
Epoch 12 / iter 0, loss = 0.2953
Epoch 12 / iter 1, loss = 0.2202
Epoch 12 / iter 2, loss = 0.1838
Epoch 12 / iter 3, loss = 0.2122
Epoch 12 / iter 4, loss = 0.4517
Epoch 13 / iter 0, loss = 0.2460
Epoch 13 / iter 1, loss = 0.2652
Epoch 13 / iter 2, loss = 0.1917
Epoch 13 / iter 3, loss = 0.1824
Epoch 13 / iter 4, loss = 0.5421
Epoch 14 / iter 0, loss = 0.2678
Epoch 14 / iter 1, loss = 0.1879
Epoch 14 / iter 2, loss = 0.2311
Epoch 14 / iter 3, loss = 0.1936
Epoch 14 / iter 4, loss = 0.0858
Epoch 15 / iter 0, loss = 0.2504
Epoch 15 / iter 1, loss = 0.2325
Epoch 15 / iter 2, loss = 0.1389
Epoch 15 / iter 3, loss = 0.2258
Epoch 15 / iter 4, loss = 0.3085
Epoch 16 / iter 0, loss = 0.1968
Epoch 16 / iter 1, loss = 0.2143
Epoch 16 / iter 2, loss = 0.1871
Epoch 16 / iter 3, loss = 0.2282
Epoch 16 / iter 4, loss = 0.0626
Epoch 17 / iter 0, loss = 0.2001
Epoch 17 / iter 1, loss = 0.2177
Epoch 17 / iter 2, loss = 0.1988
Epoch 17 / iter 3, loss = 0.1888
Epoch 17 / iter 4, loss = 0.1423
Epoch 18 / iter 0, loss = 0.2279
Epoch 18 / iter 1, loss = 0.2517
Epoch 18 / iter 2, loss = 0.1425
Epoch 18 / iter 3, loss = 0.1638
Epoch 18 / iter 4, loss = 0.1511
Epoch 19 / iter 0, loss = 0.2041
Epoch 19 / iter 1, loss = 0.1792
Epoch 19 / iter 2, loss = 0.1684
Epoch 19 / iter 3, loss = 0.2202
Epoch 19 / iter 4, loss = 0.1024
Epoch 20 / iter 0, loss = 0.1829
Epoch 20 / iter 1, loss = 0.1547
Epoch 20 / iter 2, loss = 0.1689
Epoch 20 / iter 3, loss = 0.2449
Epoch 20 / iter 4, loss = 0.1568
Epoch 21 / iter 0, loss = 0.1654
Epoch 21 / iter 1, loss = 0.1765
Epoch 21 / iter 2, loss = 0.1631
Epoch 21 / iter 3, loss = 0.2279
Epoch 21 / iter 4, loss = 0.1282
Epoch 22 / iter 0, loss = 0.1716
Epoch 22 / iter 1, loss = 0.1853
Epoch 22 / iter 2, loss = 0.2120
Epoch 22 / iter 3, loss = 0.1486
Epoch 22 / iter 4, loss = 0.1048
Epoch 23 / iter 0, loss = 0.1944
Epoch 23 / iter 1, loss = 0.1901
Epoch 23 / iter 2, loss = 0.1447
Epoch 23 / iter 3, loss = 0.1686
Epoch 23 / iter 4, loss = 0.1152
Epoch 24 / iter 0, loss = 0.1904
Epoch 24 / iter 1, loss = 0.1510
Epoch 24 / iter 2, loss = 0.1516
Epoch 24 / iter 3, loss = 0.1830
Epoch 24 / iter 4, loss = 0.4108
Epoch 25 / iter 0, loss = 0.2076
Epoch 25 / iter 1, loss = 0.1427
Epoch 25 / iter 2, loss = 0.2165
Epoch 25 / iter 3, loss = 0.0994
Epoch 25 / iter 4, loss = 0.0347
Epoch 26 / iter 0, loss = 0.1714
Epoch 26 / iter 1, loss = 0.1893
Epoch 26 / iter 2, loss = 0.1221
Epoch 26 / iter 3, loss = 0.1699
Epoch 26 / iter 4, loss = 0.0563
Epoch 27 / iter 0, loss = 0.2228
Epoch 27 / iter 1, loss = 0.1105
Epoch 27 / iter 2, loss = 0.1266
Epoch 27 / iter 3, loss = 0.1767
Epoch 27 / iter 4, loss = 0.1282
Epoch 28 / iter 0, loss = 0.1914
Epoch 28 / iter 1, loss = 0.1426
Epoch 28 / iter 2, loss = 0.1306
Epoch 28 / iter 3, loss = 0.1622
Epoch 28 / iter 4, loss = 0.0444
Epoch 29 / iter 0, loss = 0.1888
Epoch 29 / iter 1, loss = 0.1400
Epoch 29 / iter 2, loss = 0.1674
Epoch 29 / iter 3, loss = 0.1185
Epoch 29 / iter 4, loss = 0.0511
Epoch 30 / iter 0, loss = 0.1351
Epoch 30 / iter 1, loss = 0.1429
Epoch 30 / iter 2, loss = 0.1674
Epoch 30 / iter 3, loss = 0.1355
Epoch 30 / iter 4, loss = 0.6274
Epoch 31 / iter 0, loss = 0.1871
Epoch 31 / iter 1, loss = 0.1476
Epoch 31 / iter 2, loss = 0.1210
Epoch 31 / iter 3, loss = 0.1181
Epoch 31 / iter 4, loss = 0.2849
Epoch 32 / iter 0, loss = 0.1416
Epoch 32 / iter 1, loss = 0.1233
Epoch 32 / iter 2, loss = 0.1400
Epoch 32 / iter 3, loss = 0.1589
Epoch 32 / iter 4, loss = 0.2137
Epoch 33 / iter 0, loss = 0.1274
Epoch 33 / iter 1, loss = 0.1675
Epoch 33 / iter 2, loss = 0.1450
Epoch 33 / iter 3, loss = 0.1224
Epoch 33 / iter 4, loss = 0.1024
Epoch 34 / iter 0, loss = 0.1329
Epoch 34 / iter 1, loss = 0.1472
Epoch 34 / iter 2, loss = 0.1628
Epoch 34 / iter 3, loss = 0.0992
Epoch 34 / iter 4, loss = 0.3712
Epoch 35 / iter 0, loss = 0.1419
Epoch 35 / iter 1, loss = 0.1507
Epoch 35 / iter 2, loss = 0.1386
Epoch 35 / iter 3, loss = 0.1102
Epoch 35 / iter 4, loss = 0.0792
Epoch 36 / iter 0, loss = 0.1259
Epoch 36 / iter 1, loss = 0.1685
Epoch 36 / iter 2, loss = 0.1326
Epoch 36 / iter 3, loss = 0.0859
Epoch 36 / iter 4, loss = 0.4206
Epoch 37 / iter 0, loss = 0.1141
Epoch 37 / iter 1, loss = 0.1527
Epoch 37 / iter 2, loss = 0.1300
Epoch 37 / iter 3, loss = 0.1128
Epoch 37 / iter 4, loss = 0.0758
Epoch 38 / iter 0, loss = 0.1438
Epoch 38 / iter 1, loss = 0.1239
Epoch 38 / iter 2, loss = 0.0929
Epoch 38 / iter 3, loss = 0.1391
Epoch 38 / iter 4, loss = 0.1156
Epoch 39 / iter 0, loss = 0.1265
Epoch 39 / iter 1, loss = 0.0943
Epoch 39 / iter 2, loss = 0.1143
Epoch 39 / iter 3, loss = 0.1518
Epoch 39 / iter 4, loss = 0.1370
Epoch 40 / iter 0, loss = 0.1220
Epoch 40 / iter 1, loss = 0.1379
Epoch 40 / iter 2, loss = 0.1167
Epoch 40 / iter 3, loss = 0.1046
Epoch 40 / iter 4, loss = 0.0347
Epoch 41 / iter 0, loss = 0.1424
Epoch 41 / iter 1, loss = 0.1198
Epoch 41 / iter 2, loss = 0.0876
Epoch 41 / iter 3, loss = 0.1216
Epoch 41 / iter 4, loss = 0.0984
Epoch 42 / iter 0, loss = 0.1110
Epoch 42 / iter 1, loss = 0.0929
Epoch 42 / iter 2, loss = 0.1213
Epoch 42 / iter 3, loss = 0.1384
Epoch 42 / iter 4, loss = 0.0717
Epoch 43 / iter 0, loss = 0.1180
Epoch 43 / iter 1, loss = 0.1312
Epoch 43 / iter 2, loss = 0.0810
Epoch 43 / iter 3, loss = 0.1263
Epoch 43 / iter 4, loss = 0.0319
Epoch 44 / iter 0, loss = 0.1297
Epoch 44 / iter 1, loss = 0.1299
Epoch 44 / iter 2, loss = 0.0984
Epoch 44 / iter 3, loss = 0.0881
Epoch 44 / iter 4, loss = 0.0838
Epoch 45 / iter 0, loss = 0.1049
Epoch 45 / iter 1, loss = 0.1272
Epoch 45 / iter 2, loss = 0.0955
Epoch 45 / iter 3, loss = 0.1153
Epoch 45 / iter 4, loss = 0.0400
Epoch 46 / iter 0, loss = 0.1068
Epoch 46 / iter 1, loss = 0.0776
Epoch 46 / iter 2, loss = 0.1252
Epoch 46 / iter 3, loss = 0.1186
Epoch 46 / iter 4, loss = 0.1686
Epoch 47 / iter 0, loss = 0.0918
Epoch 47 / iter 1, loss = 0.1058
Epoch 47 / iter 2, loss = 0.1187
Epoch 47 / iter 3, loss = 0.1058
Epoch 47 / iter 4, loss = 0.0958
Epoch 48 / iter 0, loss = 0.0771
Epoch 48 / iter 1, loss = 0.0963
Epoch 48 / iter 2, loss = 0.1055
Epoch 48 / iter 3, loss = 0.1288
Epoch 48 / iter 4, loss = 0.2914
Epoch 49 / iter 0, loss = 0.1209
Epoch 49 / iter 1, loss = 0.0658
Epoch 49 / iter 2, loss = 0.1141
Epoch 49 / iter 3, loss = 0.0974
Epoch 49 / iter 4, loss = 0.2922