波士顿房价预测
1.导入所需要的库
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import torch
import random
from sklearn.model_selection import train_test_split
2.读入数据
feature = pd.read_csv("../data/boston.csv")
feature
| CRIM | ZN | INDUS | CHAS | NOX | RM | AGE | DIS | RAD | TAX | PTRATIO | B | LSTAT | MEDV | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 0.00632 | 18.0 | 2.31 | 0 | 0.538 | 6.575 | 65.2 | 4.0900 | 1 | 296 | 15.3 | 396.90 | 4.98 | 24.0 |
| 1 | 0.02731 | 0.0 | 7.07 | 0 | 0.469 | 6.421 | 78.9 | 4.9671 | 2 | 242 | 17.8 | 396.90 | 9.14 | 21.6 |
| 2 | 0.02729 | 0.0 | 7.07 | 0 | 0.469 | 7.185 | 61.1 | 4.9671 | 2 | 242 | 17.8 | 392.83 | 4.03 | 34.7 |
| 3 | 0.03237 | 0.0 | 2.18 | 0 | 0.458 | 6.998 | 45.8 | 6.0622 | 3 | 222 | 18.7 | 394.63 | 2.94 | 33.4 |
| 4 | 0.06905 | 0.0 | 2.18 | 0 | 0.458 | 7.147 | 54.2 | 6.0622 | 3 | 222 | 18.7 | 396.90 | 5.33 | 36.2 |
| ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... |
| 501 | 0.06263 | 0.0 | 11.93 | 0 | 0.573 | 6.593 | 69.1 | 2.4786 | 1 | 273 | 21.0 | 391.99 | 9.67 | 22.4 |
| 502 | 0.04527 | 0.0 | 11.93 | 0 | 0.573 | 6.120 | 76.7 | 2.2875 | 1 | 273 | 21.0 | 396.90 | 9.08 | 20.6 |
| 503 | 0.06076 | 0.0 | 11.93 | 0 | 0.573 | 6.976 | 91.0 | 2.1675 | 1 | 273 | 21.0 | 396.90 | 5.64 | 23.9 |
| 504 | 0.10959 | 0.0 | 11.93 | 0 | 0.573 | 6.794 | 89.3 | 2.3889 | 1 | 273 | 21.0 | 393.45 | 6.48 | 22.0 |
| 505 | 0.04741 | 0.0 | 11.93 | 0 | 0.573 | 6.030 | 80.8 | 2.5050 | 1 | 273 | 21.0 | 396.90 | 7.88 | 11.9 |
506 rows × 14 columns
3.数据预处理
(1).将特征和标签分离
获取标签数据并转变成darray数据类型
label = feature['MEDV']
# label
label = np.array(label)
label,label.dtype,len(label)
(array([24. , 21.6, 34.7, 33.4, 36.2, 28.7, 22.9, 27.1, 16.5, 18.9, 15. ,
18.9, 21.7, 20.4, 18.2, 19.9, 23.1, 17.5, 20.2, 18.2, 13.6, 19.6,
15.2, 14.5, 15.6, 13.9, 16.6, 14.8, 18.4, 21. , 12.7, 14.5, 13.2,
13.1, 13.5, 18.9, 20. , 21. , 24.7, 30.8, 34.9, 26.6, 25.3, 24.7,
21.2, 19.3, 20. , 16.6, 14.4, 19.4, 19.7, 20.5, 25. , 23.4, 18.9,
35.4, 24.7, 31.6, 23.3, 19.6, 18.7, 16. , 22.2, 25. , 33. , 23.5,
19.4, 22. , 17.4, 20.9, 24.2, 21.7, 22.8, 23.4, 24.1, 21.4, 20. ,
20.8, 21.2, 20.3, 28. , 23.9, 24.8, 22.9, 23.9, 26.6, 22.5, 22.2,
23.6, 28.7, 22.6, 22. , 22.9, 25. , 20.6, 28.4, 21.4, 38.7, 43.8,
33.2, 27.5, 26.5, 18.6, 19.3, 20.1, 19.5, 19.5, 20.4, 19.8, 19.4,
21.7, 22.8, 18.8, 18.7, 18.5, 18.3, 21.2, 19.2, 20.4, 19.3, 22. ,
20.3, 20.5, 17.3, 18.8, 21.4, 15.7, 16.2, 18. , 14.3, 19.2, 19.6,
23. , 18.4, 15.6, 18.1, 17.4, 17.1, 13.3, 17.8, 14. , 14.4, 13.4,
15.6, 11.8, 13.8, 15.6, 14.6, 17.8, 15.4, 21.5, 19.6, 15.3, 19.4,
17. , 15.6, 13.1, 41.3, 24.3, 23.3, 27. , 50. , 50. , 50. , 22.7,
25. , 50. , 23.8, 23.8, 22.3, 17.4, 19.1, 23.1, 23.6, 22.6, 29.4,
23.2, 24.6, 29.9, 37.2, 39.8, 36.2, 37.9, 32.5, 26.4, 29.6, 50. ,
32. , 29.8, 34.9, 37. , 30.5, 36.4, 31.1, 29.1, 50. , 33.3, 30.3,
34.6, 34.9, 32.9, 24.1, 42.3, 48.5, 50. , 22.6, 24.4, 22.5, 24.4,
20. , 21.7, 19.3, 22.4, 28.1, 23.7, 25. , 23.3, 28.7, 21.5, 23. ,
26.7, 21.7, 27.5, 30.1, 44.8, 50. , 37.6, 31.6, 46.7, 31.5, 24.3,
31.7, 41.7, 48.3, 29. , 24. , 25.1, 31.5, 23.7, 23.3, 22. , 20.1,
22.2, 23.7, 17.6, 18.5, 24.3, 20.5, 24.5, 26.2, 24.4, 24.8, 29.6,
42.8, 21.9, 20.9, 44. , 50. , 36. , 30.1, 33.8, 43.1, 48.8, 31. ,
36.5, 22.8, 30.7, 50. , 43.5, 20.7, 21.1, 25.2, 24.4, 35.2, 32.4,
32. , 33.2, 33.1, 29.1, 35.1, 45.4, 35.4, 46. , 50. , 32.2, 22. ,
20.1, 23.2, 22.3, 24.8, 28.5, 37.3, 27.9, 23.9, 21.7, 28.6, 27.1,
20.3, 22.5, 29. , 24.8, 22. , 26.4, 33.1, 36.1, 28.4, 33.4, 28.2,
22.8, 20.3, 16.1, 22.1, 19.4, 21.6, 23.8, 16.2, 17.8, 19.8, 23.1,
21. , 23.8, 23.1, 20.4, 18.5, 25. , 24.6, 23. , 22.2, 19.3, 22.6,
19.8, 17.1, 19.4, 22.2, 20.7, 21.1, 19.5, 18.5, 20.6, 19. , 18.7,
32.7, 16.5, 23.9, 31.2, 17.5, 17.2, 23.1, 24.5, 26.6, 22.9, 24.1,
18.6, 30.1, 18.2, 20.6, 17.8, 21.7, 22.7, 22.6, 25. , 19.9, 20.8,
16.8, 21.9, 27.5, 21.9, 23.1, 50. , 50. , 50. , 50. , 50. , 13.8,
13.8, 15. , 13.9, 13.3, 13.1, 10.2, 10.4, 10.9, 11.3, 12.3, 8.8,
7.2, 10.5, 7.4, 10.2, 11.5, 15.1, 23.2, 9.7, 13.8, 12.7, 13.1,
12.5, 8.5, 5. , 6.3, 5.6, 7.2, 12.1, 8.3, 8.5, 5. , 11.9,
27.9, 17.2, 27.5, 15. , 17.2, 17.9, 16.3, 7. , 7.2, 7.5, 10.4,
8.8, 8.4, 16.7, 14.2, 20.8, 13.4, 11.7, 8.3, 10.2, 10.9, 11. ,
9.5, 14.5, 14.1, 16.1, 14.3, 11.7, 13.4, 9.6, 8.7, 8.4, 12.8,
10.5, 17.1, 18.4, 15.4, 10.8, 11.8, 14.9, 12.6, 14.1, 13. , 13.4,
15.2, 16.1, 17.8, 14.9, 14.1, 12.7, 13.5, 14.9, 20. , 16.4, 17.7,
19.5, 20.2, 21.4, 19.9, 19. , 19.1, 19.1, 20.1, 19.9, 19.6, 23.2,
29.8, 13.8, 13.3, 16.7, 12. , 14.6, 21.4, 23. , 23.7, 25. , 21.8,
20.6, 21.2, 19.1, 20.6, 15.2, 7. , 8.1, 13.6, 20.1, 21.8, 24.5,
23.1, 19.7, 18.3, 21.2, 17.5, 16.8, 22.4, 20.6, 23.9, 22. , 11.9]),
dtype('float64'),
506)
对特征进行提取并转为darray类型
feature = feature.drop('MEDV',axis=1)
data = np.array(feature)
data
array([[6.3200e-03, 1.8000e+01, 2.3100e+00, ..., 1.5300e+01, 3.9690e+02,
4.9800e+00],
[2.7310e-02, 0.0000e+00, 7.0700e+00, ..., 1.7800e+01, 3.9690e+02,
9.1400e+00],
[2.7290e-02, 0.0000e+00, 7.0700e+00, ..., 1.7800e+01, 3.9283e+02,
4.0300e+00],
...,
[6.0760e-02, 0.0000e+00, 1.1930e+01, ..., 2.1000e+01, 3.9690e+02,
5.6400e+00],
[1.0959e-01, 0.0000e+00, 1.1930e+01, ..., 2.1000e+01, 3.9345e+02,
6.4800e+00],
[4.7410e-02, 0.0000e+00, 1.1930e+01, ..., 2.1000e+01, 3.9690e+02,
7.8800e+00]])
(2).对数据做归一化处理
由于输入的数据中不同的特征值数值大小差异很大，所以神经网络会认为数值大的特征更重要，以此影响了预测结果。
因此我们需要归一化处理，让不同的特征值大小在一个级别上
# !pip install scikit-learn
from sklearn import preprocessing
data = preprocessing.StandardScaler().fit_transform(data)
data
array([[-0.41978194, 0.28482986, -1.2879095 , ..., -1.45900038,
0.44105193, -1.0755623 ],
[-0.41733926, -0.48772236, -0.59338101, ..., -0.30309415,
0.44105193, -0.49243937],
[-0.41734159, -0.48772236, -0.59338101, ..., -0.30309415,
0.39642699, -1.2087274 ],
...,
[-0.41344658, -0.48772236, 0.11573841, ..., 1.17646583,
0.44105193, -0.98304761],
[-0.40776407, -0.48772236, 0.11573841, ..., 1.17646583,
0.4032249 , -0.86530163],
[-0.41500016, -0.48772236, 0.11573841, ..., 1.17646583,
0.44105193, -0.66905833]])
(3).划分训练集和测试集
train_data,test_data,train_label,test_label = train_test_split(data,label,test_size=0.2)
# train_data
test_data,test_label
(array([[-0.40301721, -0.48772236, 2.11761463, ..., 0.29797709,
0.14950964, 1.78818809],
[ 2.59827406, -0.48772236, 1.01599907, ..., 0.80657583,
-2.51428122, 1.96060184],
[ 1.32780421, -0.48772236, 1.01599907, ..., 0.80657583,
-0.07887794, 1.7181012 ],
...,
[-0.39825173, 0.45650813, -0.76993132, ..., 0.29797709,
0.35585887, 0.8139803 ],
[-0.41613247, 2.94584308, -1.40317788, ..., -2.70737911,
0.38951945, -0.8456773 ],
[-0.32270106, -0.48772236, -0.43725801, ..., 1.17646583,
-0.58389629, 0.54064142]]),
array([17.3, 10.4, 12. , 26.4, 24.4, 20.8, 28.7, 18.3, 14.5, 22.6, 21.2,
15.2, 29.1, 22.9, 13.1, 21.4, 21.4, 24.1, 11.8, 21.7, 17.8, 23.2,
19.5, 23.3, 33.1, 14.1, 26.7, 36.5, 14.1, 16.8, 7. , 17.7, 24.8,
22.2, 21. , 29.1, 8.7, 27.1, 9.7, 20.4, 15.2, 16.5, 33.2, 19.8,
35.4, 22. , 21.2, 20.7, 10.9, 20.9, 8.8, 10.5, 31.5, 21.9, 28.7,
25. , 17.9, 7.2, 19.4, 29. , 14. , 42.3, 22.8, 29.9, 14.5, 17.5,
22.6, 7. , 36. , 21.2, 20.6, 15. , 9.5, 10.8, 24.8, 50. , 16.4,
19.6, 23.7, 24.5, 15.6, 17.8, 16.2, 20.6, 19.9, 19.6, 19. , 8.5,
22.8, 21. , 21.7, 34.9, 48.5, 15.6, 11.7, 12.5, 17.1, 17.5, 28.4,
18.5, 34.6, 13.9]))
(4).转换为tensor张量
# train_data = torch.tensor(train_data,dtype=torch.float32)
# train_label = torch.tensor(train_label,dtype=torch.float32)
# test_data = torch.tensor(test_data,dtype=torch.float32)
# test_label = torch.tensor(test_label,dtype=torch.float32)
train_data=torch.tensor(train_data,dtype=float,requires_grad=True).to(torch.float32)
train_label=torch.tensor(train_label,dtype=float,requires_grad=True).to(torch.float32).reshape(-1,1)
test_data=torch.tensor(test_data,dtype=float,requires_grad=True).to(torch.float32)
test_label=torch.tensor(test_label,dtype=float,requires_grad=True).to(torch.float32).reshape(-1,1)
train_data.size(),train_label.shape,test_data.shape,test_label.shape,train_data.type(),train_label
(torch.Size([404, 13]),
torch.Size([404, 1]),
torch.Size([102, 13]),
torch.Size([102, 1]),
'torch.FloatTensor',
tensor([[19.1000],
[33.3000],
[15.1000],
[15.4000],
[22.5000],
[19.9000],
[30.7000],
[19.5000],
[31.2000],
[19.3000],
[13.1000],
[31.6000],
[43.8000],
[15.6000],
[50.0000],
[29.6000],
[19.3000],
[20.2000],
[15.4000],
[19.8000],
[12.8000],
[21.7000],
[18.5000],
[21.2000],
[34.9000],
[31.5000],
[21.1000],
[23.6000],
[19.1000],
[ 5.0000],
[10.2000],
[20.5000],
[15.0000],
[13.4000],
[24.5000],
[18.7000],
[21.4000],
[29.4000],
[20.4000],
[27.9000],
[42.8000],
[23.1000],
[33.4000],
[ 9.6000],
[22.2000],
[17.4000],
[22.3000],
[14.3000],
[24.4000],
[20.0000],
[18.4000],
[18.5000],
[27.0000],
[11.9000],
[22.6000],
[50.0000],
[13.1000],
[23.3000],
[16.1000],
[17.2000],
[ 8.5000],
[17.2000],
[13.0000],
[29.6000],
[25.0000],
[22.4000],
[20.1000],
[16.6000],
[50.0000],
[20.5000],
[22.3000],
[19.2000],
[17.4000],
[30.1000],
[ 7.2000],
[13.8000],
[14.8000],
[19.4000],
[19.3000],
[22.0000],
[28.6000],
[18.7000],
[13.2000],
[11.9000],
[32.9000],
[50.0000],
[20.3000],
[22.9000],
[20.1000],
[30.1000],
[36.1000],
[15.3000],
[18.9000],
[17.8000],
[27.1000],
[34.7000],
[28.7000],
[18.2000],
[18.5000],
[13.4000],
[18.7000],
[16.3000],
[28.0000],
[19.1000],
[45.4000],
[18.4000],
[13.5000],
[21.9000],
[18.9000],
[10.2000],
[23.7000],
[19.9000],
[22.8000],
[37.9000],
[24.6000],
[19.6000],
[23.7000],
[18.2000],
[22.7000],
[24.5000],
[19.6000],
[16.8000],
[50.0000],
[13.3000],
[20.8000],
[23.3000],
[24.0000],
[ 8.3000],
[50.0000],
[24.7000],
[41.7000],
[17.8000],
[16.0000],
[19.9000],
[26.6000],
[36.4000],
[13.8000],
[29.0000],
[ 6.3000],
[19.0000],
[22.0000],
[20.4000],
[25.2000],
[23.4000],
[29.8000],
[21.4000],
[22.6000],
[23.1000],
[14.4000],
[21.7000],
[21.6000],
[28.5000],
[21.8000],
[18.3000],
[ 7.4000],
[14.1000],
[17.1000],
[26.6000],
[21.8000],
[19.1000],
[14.6000],
[13.8000],
[16.6000],
[20.1000],
[13.3000],
[48.8000],
[21.0000],
[34.9000],
[11.8000],
[23.9000],
[32.5000],
[20.0000],
[25.1000],
[28.4000],
[23.7000],
[13.6000],
[12.7000],
[21.9000],
[24.4000],
[26.5000],
[18.6000],
[50.0000],
[37.2000],
[31.1000],
[20.3000],
[20.4000],
[22.5000],
[24.3000],
[20.1000],
[14.5000],
[23.1000],
[32.0000],
[23.0000],
[13.8000],
[18.1000],
[22.2000],
[14.3000],
[23.1000],
[19.7000],
[21.1000],
[22.5000],
[ 8.1000],
[20.7000],
[22.4000],
[38.7000],
[21.7000],
[25.3000],
[46.7000],
[19.5000],
[19.8000],
[14.9000],
[17.6000],
[26.2000],
[ 7.5000],
[15.2000],
[12.3000],
[13.4000],
[23.2000],
[23.9000],
[20.0000],
[20.3000],
[50.0000],
[23.0000],
[20.3000],
[23.0000],
[14.4000],
[29.8000],
[ 5.6000],
[20.9000],
[30.8000],
[24.0000],
[24.8000],
[22.0000],
[23.4000],
[16.7000],
[23.8000],
[25.0000],
[22.0000],
[26.4000],
[30.3000],
[19.4000],
[50.0000],
[15.0000],
[19.3000],
[21.4000],
[12.7000],
[18.8000],
[13.3000],
[23.9000],
[25.0000],
[24.6000],
[50.0000],
[14.6000],
[20.0000],
[37.3000],
[ 8.4000],
[32.2000],
[16.1000],
[28.2000],
[20.6000],
[31.7000],
[18.8000],
[27.9000],
[21.5000],
[23.9000],
[11.0000],
[20.0000],
[19.3000],
[18.2000],
[13.1000],
[32.7000],
[31.0000],
[18.9000],
[10.2000],
[15.7000],
[17.5000],
[20.2000],
[27.5000],
[20.6000],
[19.4000],
[18.0000],
[20.6000],
[22.0000],
[33.1000],
[25.0000],
[19.6000],
[ 8.3000],
[36.2000],
[14.9000],
[17.1000],
[23.1000],
[50.0000],
[27.5000],
[17.8000],
[19.4000],
[19.2000],
[27.5000],
[33.2000],
[24.4000],
[22.9000],
[22.0000],
[31.6000],
[41.3000],
[17.4000],
[22.1000],
[24.7000],
[17.2000],
[48.3000],
[10.5000],
[32.4000],
[10.4000],
[35.1000],
[22.8000],
[19.4000],
[22.6000],
[16.2000],
[20.6000],
[13.8000],
[13.6000],
[23.0000],
[24.2000],
[44.8000],
[25.0000],
[50.0000],
[23.8000],
[16.1000],
[18.6000],
[19.5000],
[18.4000],
[20.5000],
[24.7000],
[25.0000],
[28.1000],
[19.7000],
[39.8000],
[25.0000],
[11.3000],
[26.6000],
[23.1000],
[21.5000],
[13.9000],
[27.5000],
[15.6000],
[36.2000],
[ 8.4000],
[13.4000],
[32.0000],
[50.0000],
[23.2000],
[33.0000],
[13.5000],
[16.5000],
[ 8.8000],
[18.9000],
[ 5.0000],
[23.8000],
[23.8000],
[14.2000],
[43.1000],
[46.0000],
[20.1000],
[24.3000],
[33.8000],
[21.7000],
[15.6000],
[35.2000],
[22.7000],
[24.1000],
[30.1000],
[12.1000],
[12.7000],
[43.5000],
[23.9000],
[22.2000],
[21.7000],
[24.1000],
[11.5000],
[20.8000],
[14.9000],
[16.7000],
[23.2000],
[23.5000],
[21.2000],
[ 7.2000],
[10.9000],
[35.4000],
[24.3000],
[21.6000],
[23.6000],
[11.7000],
[17.0000],
[50.0000],
[44.0000],
[33.4000],
[30.5000],
[24.8000],
[37.6000],
[37.0000],
[12.6000],
[22.2000],
[22.9000],
[50.0000],
[23.1000],
[23.3000]], grad_fn=<ReshapeAliasBackward0>))
4.定义模型
class LinearModel(torch.nn.Module):
def __init__(self):
super(LinearModel,self).__init__()
self.linear = torch.nn.Linear(13, 1)
def forward(self, x):
y_pred = self.linear(x)
return y_pred
model1 = LinearModel()
model1
LinearModel(
(linear): Linear(in_features=13, out_features=1, bias=True)
)
criterion = torch.nn.MSELoss(reduction='mean')
optimizer = torch.optim.SGD(model1.parameters(), lr =0.005)
5.训练
epoch_loss = []
for epoch in range(300):
y_pred = model1(train_data)
loss = criterion(y_pred,train_label)
print(epoch,loss.item())
optimizer.zero_grad()
loss.backward()
optimizer.step()
# print('epoch',epoch,'loss=',loss.item())
epoch_loss.append(loss.item())
0 624.7080688476562
1 608.4896240234375
2 593.03759765625
3 578.2877197265625
4 564.1824951171875
5 550.6704711914062
6 537.7056274414062
7 525.24658203125
8 513.2561645507812
9 501.7012023925781
10 490.5516052246094
11 479.7803955078125
12 469.3631591796875
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画出损失和训练次数的图
from pylab import mpl
# 设置显示中文字体
mpl.rcParams["font.sans-serif"] = ["SimHei"]
plt.plot([i for i in range(len(epoch_loss))],epoch_loss)
plt.xlabel('训练次数')
plt.ylabel('损失值')
plt.grid(True, linestyle='--', alpha=0.5)
plt.title("训练次数和损失值关系图", fontsize=12)
plt.show()
6.预测
y_pred = model1(test_data).detach().numpy()
test_label_numpy = test_label.detach().numpy()
plt.plot(y_pred ,color='b',label="预测值")
plt.plot(test_label_numpy,color='r',label="真实值")
plt.xlabel('预测样本点')
plt.ylabel('预测值')
plt.title("预测值和真实值拟合检验图", fontsize=12)
plt.grid(True, linestyle='--', alpha=0.5)
plt.legend(loc="best")
plt.show()
F:\SoftWare\ProgramFiles\anaconda3\envs\pytorch\lib\site-packages\IPython\core\pylabtools.py:151: UserWarning: Glyph 8722 (\N{MINUS SIGN}) missing from current font.
fig.canvas.print_figure(bytes_io, **kw)
7.总结
在训练的过程中，发现损失值一直为80.不下降。经过一上午的调试，发现问题在于：标签的维度是一维的，导致训练有问题，经过改正，训练正常。
并且预测值和真实值基本吻合。
