翻译——2_Linear Regression and Support Vector Regression
上篇 1_Project Overview, Data Wrangling and Exploratory Analysis
使用不同的机器学习方法进行预测
线性回归
在这本笔记本中，将训练一个线性回归模型来预测基于历史能源数据、几个天气变量、一天中的小时、一周中的一天、周末和假期的电源能耗。
为了做到这一点，我们将把模型设定为从2012-01-01到2014-10-31的每日和每小时的能源和天气数据。
%matplotlib inline
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
pd.options.display.mpl_style = 'default'
from sklearn.linear_model import LinearRegression
dailyElectricity = pd.read_excel('Data/dailyElectricityWithFeatures.xlsx')
dailyElectricity = dailyElectricity.drop('startDay', 1).drop('endDay', 1)
dailyChilledWater = pd.read_excel('Data/dailyChilledWaterWithFeatures.xlsx')
dailyChilledWater = dailyChilledWater.drop('startDay', 1).drop('endDay', 1)
dailySteam = pd.read_excel('Data/dailySteamWithFeatures.xlsx')
dailySteam = dailySteam.drop('startDay', 1).drop('endDay', 1)
hourlyElectricity = pd.read_excel('Data/hourlyElectricityWithFeatures.xlsx')
hourlyElectricity = hourlyElectricity.drop('startTime', 1).drop('endTime', 1)
hourlyChilledWater = pd.read_excel('Data/hourlyChilledWaterWithFeatures.xlsx')
hourlyChilledWater = hourlyChilledWater.drop('startTime', 1).drop('endTime', 1)
hourlySteam = pd.read_excel('Data/hourlySteamWithFeatures.xlsx')
hourlySteam = hourlySteam.drop('startTime', 1).drop('endTime', 1)
#显示出dataframe
dailyElectricity.head()
| electricity-kWh | RH-% | T-C | Tdew-C | pressure-mbar | solarRadiation-W/m2 | windDirection | windSpeed-m/s | humidityRatio-kg/kg | coolingDegrees | heatingDegrees | dehumidification | occupancy | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 2012-01-01 | 2800.244977 | 76.652174 | 7.173913 | 3.073913 | 1004.956522 | 95.260870 | 236.086957 | 4.118361 | 0.004796 | 0.086957 | 7.826087 | 0 | 0.0 |
| 2012-01-02 | 3168.974047 | 55.958333 | 5.833333 | -2.937500 | 994.625000 | 87.333333 | 253.750000 | 5.914357 | 0.003415 | 0.000000 | 9.166667 | 0 | 0.3 |
| 2012-01-03 | 5194.533376 | 42.500000 | -3.208333 | -12.975000 | 1002.125000 | 95.708333 | 302.916667 | 6.250005 | 0.001327 | 0.000000 | 18.208333 | 0 | 0.3 |
| 2012-01-04 | 5354.861935 | 41.541667 | -7.083333 | -16.958333 | 1008.250000 | 98.750000 | 286.666667 | 5.127319 | 0.000890 | 0.000000 | 22.083333 | 0 | 0.3 |
| 2012-01-05 | 5496.223993 | 46.916667 | -0.583333 | -9.866667 | 1002.041667 | 90.750000 | 258.333333 | 5.162041 | 0.001746 | 0.000000 | 15.583333 | 0 | 0.3 |
每日预测
向dataframe添加新特征:工作日、一年中的一天和一周。
def addDailyTimeFeatures(df):
df['weekday'] = df.index.weekday
df['day'] = df.index.dayofyear
df['week'] = df.index.weekofyear
return df
dailyElectricity = addDailyTimeFeatures(dailyElectricity)
dailyChilledWater = addDailyTimeFeatures(dailyChilledWater)
dailySteam = addDailyTimeFeatures(dailySteam)
每日电力预测
df_elect = dailyElectricity[['weekday', 'day', 'week',
'occupancy', 'electricity-kWh']]
elect_train = pd.DataFrame(data=df_elect,
index=np.arange('2012-01', '2013-07',
dtype='datetime64[D]')).dropna()
elect_test = pd.DataFrame(data=df_elect,
index=np.arange('2013-07', '2014-11',
dtype='datetime64[D]')).dropna()
XX_elect_train = elect_train.drop('electricity-kWh',
axis = 1).reset_index().drop('index', axis = 1)
XX_elect_test = elect_test.drop('electricity-kWh',
axis = 1).reset_index().drop('index', axis = 1)
YY_elect_train = elect_train['electricity-kWh']
YY_elect_test = elect_test['electricity-kWh']
lr_elect = LinearRegression()
lr_elect.fit(XX_elect_train,YY_elect_train)
y_lr = lr_elect.predict(XX_elect_test)
print "The test score R2: ", lr_elect.score(XX_elect_test, YY_elect_test)
print "The Linear Regression coefficients are"
pd.DataFrame(zip(XX_elect_train.columns, lr_elect.coef_),
columns = ['elect_features', 'linearRegr_Coefficients'])
The test score R2: 0.608937488563
The Linear Regression coefficients are
| elect_features | linearRegr_Coefficients | |
|---|---|---|
| 0 | weekday | -125.392163 |
| 1 | day | 0.550121 |
| 2 | week | -11.553215 |
| 3 | occupancy | 2830.298384 |
#Plot observed and Predicted electricity value
fig = plt.figure(figsize=(15,7))
plt.scatter(XX_elect_test.index, YY_elect_test, label='Observed', color='k')
plt.plot(XX_elect_test.index, y_lr, label='Predicted', color='g')
plt.legend(loc='upper right')
# 图观察与线性回归预测使用。
fig = plt.figure(figsize=(6,6))
plt.plot(YY_elect_test, YY_elect_test, c='k')
plt.scatter(YY_elect_test, y_lr, c='g')
plt.xlabel('Observed Elec. Usage (kWh)')
plt.ylabel("Predicted Elec. Usage (kWh): $\hat{Y}_i$")
plt.title("Energy vs Predicted Elec.: $Y_i$ vs $\hat{Y}_i$")
每日冷水预报
chilledw_train = pd.DataFrame(data=dailyChilledWater, index=np.arange('2012-01', '2013-07', dtype='datetime64[D]')).dropna()
chilledw_test = pd.DataFrame(data=dailyChilledWater, index=np.arange('2013-07', '2014-11', dtype='datetime64[D]')).dropna()
XX_chilledw_train = chilledw_train.drop('chilledWater-TonDays', axis = 1).reset_index().drop('index', axis = 1)
XX_chilledw_test = chilledw_test.drop('chilledWater-TonDays', axis = 1).reset_index().drop('index', axis = 1)
YY_chilledw_train = chilledw_train['chilledWater-TonDays']
YY_chilledw_test = chilledw_test['chilledWater-TonDays']
lr_chilledw = LinearRegression()
lr_chilledw.fit(XX_chilledw_train,YY_chilledw_train)
print "The test score R2: ", lr_chilledw.score(XX_chilledw_test, YY_chilledw_test)
print "The Linear Regression coefficients are"
pd.DataFrame(zip(XX_chilledw_train.columns, lr_chilledw.coef_), columns = ['chilledw_features', 'linearRegr_Coefficients'])
The test score R2: 0.830709188732
The Linear Regression coefficients are
| chilledw_features | linearRegr_Coefficients | |
|---|---|---|
| 0 | RH-% | 0.464299 |
| 1 | T-C | 6.062113 |
| 2 | Tdew-C | -2.486768 |
| 3 | pressure-mbar | -0.095268 |
| 4 | solarRadiation-W/m2 | 0.042885 |
| 5 | windDirection | -0.025036 |
| 6 | windSpeed-m/s | -1.166902 |
| 7 | humidityRatio-kg/kg | 1673.166705 |
| 8 | coolingDegrees | 2.853128 |
| 9 | heatingDegrees | 4.421394 |
| 10 | dehumidification | 2999.125771 |
| 11 | occupancy | 0.571356 |
| 12 | weekday | -2.461900 |
| 13 | day | -0.010718 |
| 14 | week | 0.122757 |
# 实测和预测的电量值
y_lr = lr_chilledw.predict(XX_chilledw_test)
fig = plt.figure(figsize=(15,7))
plt.scatter(XX_chilledw_test.index, YY_chilledw_test, label='Observed', color='k')
plt.plot(XX_chilledw_test.index, y_lr, label='Predicted', color='r')
plt.legend(loc='upper right')
# 观察到的和预测的使用情况。
fig = plt.figure(figsize=(6,6))
plt.plot(YY_chilledw_test, YY_chilledw_test, c='k')
plt.scatter(YY_chilledw_test, y_lr, c='r')
plt.xlabel('Observed Chilled Water Usage (TonDays)')
plt.ylabel("Predicted Chilled Water Usage (TonDays): $\hat{Y}_i$")
plt.title("Observed vs Predicted Chilled Water: $Y_i$ vs $\hat{Y}_i$")
每日热水预测
steam_train = pd.DataFrame(data=dailySteam, index=np.arange('2012-01', '2013-07', dtype='datetime64[D]')).dropna()
steam_test = pd.DataFrame(data=dailySteam, index=np.arange('2013-07', '2014-11', dtype='datetime64[D]')).dropna()
XX_steam_train = steam_train.drop('steam-LBS', axis = 1).reset_index().drop('index', axis = 1)
XX_steam_test = steam_test.drop('steam-LBS', axis = 1).reset_index().drop('index', axis = 1)
YY_steam_train = steam_train['steam-LBS']
YY_steam_test = steam_test['steam-LBS']
lr_steam = LinearRegression()
lr_steam.fit(XX_steam_train,YY_steam_train)
print "The test score R2: ", lr_steam.score(XX_steam_test, YY_steam_test)
print "The Linear Regression coefficients are"
pd.DataFrame(zip(XX_steam_train.columns, lr_steam.coef_), columns = ['steam_features', 'linearRegr_Coefficients'])
The test score R2: 0.942276415896
The Linear Regression coefficients are
| steam_features | linearRegr_Coefficients | |
|---|---|---|
| 0 | RH-% | 66.535470 |
| 1 | T-C | 458.096751 |
| 2 | Tdew-C | -951.521615 |
| 3 | pressure-mbar | -30.891470 |
| 4 | solarRadiation-W/m2 | -18.446292 |
| 5 | windDirection | -7.828922 |
| 6 | windSpeed-m/s | 251.824413 |
| 7 | humidityRatio-kg/kg | 857001.445663 |
| 8 | coolingDegrees | -99.989152 |
| 9 | heatingDegrees | 1794.351286 |
| 10 | dehumidification | -482120.622688 |
| 11 | occupancy | 3150.501909 |
| 12 | weekday | -531.583401 |
| 13 | day | -1.499061 |
| 14 | week | -43.000664 |
# 实测和预测的电量值
y_lr = lr_steam.predict(XX_steam_test)
fig = plt.figure(figsize=(15,7))
plt.scatter(XX_steam_test.index, YY_steam_test, label='Observed', color='k')
plt.plot(XX_steam_test.index, y_lr, label='Predicted', color='g')
plt.legend(loc='upper right')
# 绘制实际使用量与预测使用量。
fig = plt.figure(figsize=(6,6))
plt.plot(YY_steam_test, YY_steam_test, c='k')
plt.scatter(YY_steam_test, y_lr, c='g')
plt.xlabel('Observed Steam Usage (LBS)')
plt.ylabel("Predicted Steam Usage (LBS): $\hat{Y}_i$")
plt.title("Observed vs Predicted Steam: $Y_i$ vs $\hat{Y}_i$")
每小时预测
向dataframe添加新特征:小时、工作日、年中的一天和周。
def addHourlyTimeFeatures(df):
df['hour'] = df.index.hour
df['weekday'] = df.index.weekday
df['day'] = df.index.dayofyear
df['week'] = df.index.weekofyear
return df
hourlyElectricity = addHourlyTimeFeatures(hourlyElectricity)
每小时电力预测
df_hourlyelect = hourlyElectricity[['hour', 'weekday', 'day', 'week', 'cosHour',
'occupancy', 'electricity-kWh']]
hourlyelect_train = pd.DataFrame(data=df_hourlyelect, index=np.arange('2014-01-01 00:00:00', '2014-10-01 00:00:00', dtype='datetime64[h]')).dropna()
hourlyelect_test = pd.DataFrame(data=df_hourlyelect, index=np.arange('2014-10-01 00:00:00', '2014-11-01 00:00:00', dtype='datetime64[h]')).dropna()
XX_hourlyelect_train = hourlyelect_train.drop('electricity-kWh', axis = 1).reset_index().drop('index', axis = 1)
XX_hourlyelect_test = hourlyelect_test.drop('electricity-kWh', axis = 1).reset_index().drop('index', axis = 1)
YY_hourlyelect_train = hourlyelect_train['electricity-kWh']
YY_hourlyelect_test = hourlyelect_test['electricity-kWh']
lr_hourlyelect = LinearRegression()
lr_hourlyelect.fit(XX_hourlyelect_train,YY_hourlyelect_train)
y_hourlyelect_lr = lr_hourlyelect.predict(XX_hourlyelect_test)
print "The test score R2: ", lr_hourlyelect.score(XX_hourlyelect_test, YY_hourlyelect_test)
print "The Linear Regression coefficients are"
pd.DataFrame(zip(XX_hourlyelect_train.columns, lr_hourlyelect.coef_), columns = ['hourlyelect_features', 'linearRegr_Coefficients'])
The test score R2: 0.714713369958
The Linear Regression coefficients are
| hourlyelect_features | linearRegr_Coefficients | |
|---|---|---|
| 0 | hour | -0.287362 |
| 1 | weekday | -6.995868 |
| 2 | day | -0.309981 |
| 3 | week | 0.955127 |
| 4 | cosHour | -81.049080 |
| 5 | occupancy | 114.803110 |
# 实测和预测的电量值
fig = plt.figure(figsize=(25,7))
plt.scatter(XX_hourlyelect_test.index, YY_hourlyelect_test, label='Observed', color='k')
plt.plot(XX_hourlyelect_test.index, y_hourlyelect_lr, label='Predicted', color='r')
plt.legend(loc='upper right')
#Plot Observed vs. Predicted usage.
fig = plt.figure(figsize=(6,6))
plt.plot(YY_hourlyelect_test, YY_hourlyelect_test, c='k')
plt.scatter(YY_hourlyelect_test, y_hourlyelect_lr, c='r')
plt.xlabel('Observed Elec. Usage (kWh)')
plt.ylabel("Predicted Elec. Usage (kWh): $\hat{Y}_i$")
plt.title("Energy vs Predicted Elec.: $Y_i$ vs $\hat{Y}_i$")
每小时冷水预报
hourlychilledw_train = pd.DataFrame(data=hourlyChilledWater,
index=np.arange('2014-01-01 00:00:00',
'2014-09-01 00:00:00',
dtype='datetime64[h]')).dropna()
hourlychilledw_test = pd.DataFrame(data=hourlyChilledWater,
index=np.arange('2014-09-01 00:00:00',
'2014-11-01 00:00:00',
dtype='datetime64[h]')).dropna()
XX_hourlychilledw_train =
hourlychilledw_train.drop('chilledWater-TonDays',
axis = 1).reset_index().drop('index', axis = 1)
XX_hourlychilledw_test =
hourlychilledw_test.drop('chilledWater-TonDays',
axis = 1).reset_index().drop('index', axis = 1)
YY_hourlychilledw_train = hourlychilledw_train['chilledWater-TonDays']
YY_hourlychilledw_test = hourlychilledw_test['chilledWater-TonDays']
lr_hourlychilledw = LinearRegression()
lr_hourlychilledw.fit(XX_hourlychilledw_train,YY_hourlychilledw_train)
y_hourlychilledw_lr = lr_hourlychilledw.predict(XX_hourlychilledw_test)
print "The test score R2: ", lr_hourlychilledw.score(XX_hourlychilledw_test, YY_hourlychilledw_test)
print "The Linear Regression coefficients are"
pd.DataFrame(zip(XX_hourlychilledw_train.columns,
lr_hourlychilledw.coef_),
columns = ['hourlychilledw_features', 'linearRegr_Coefficients'])
The test score R2: 0.709930521875
The Linear Regression coefficients are
| hourlychilledw_features | linearRegr_Coefficients | |
|---|---|---|
| 0 | RH-% | -0.028198 |
| 1 | T-C | 0.459533 |
| 2 | Tdew-C | 0.166999 |
| 3 | pressure-mbar | -0.007099 |
| 4 | solarRadiation-W/m2 | 0.001003 |
| 5 | windDirection | -0.000382 |
| 6 | windSpeed-m/s | 0.004837 |
| 7 | humidityRatio-kg/kg | -91.425425 |
| 8 | coolingDegrees | -0.172407 |
| 9 | heatingDegrees | 0.603195 |
| 10 | dehumidification | 226.397306 |
| 11 | occupancy | 0.483000 |
| 12 | cosHour | -0.562715 |
#Plot Observed and Predicted electricity value
fig = plt.figure(figsize=(15,7))
plt.scatter(XX_hourlychilledw_test.index,
YY_hourlychilledw_test,
label='Observed',
color='k')
plt.plot(XX_hourlychilledw_test.index,
y_hourlychilledw_lr,
label='Predicted',
color='g')
plt.legend(loc='upper right')
# 观察到的和预测的使用情况。
fig = plt.figure(figsize=(6,6))
plt.plot(YY_hourlychilledw_test, YY_hourlychilledw_test, c='k')
plt.scatter(YY_hourlychilledw_test, y_hourlychilledw_lr, c='g')
plt.xlabel('Observed Chilled Water Usage (TonDays)')
plt.ylabel("Predicted Chilled Water Usage (TonDays): $\hat{Y}_i$")
plt.title("Observed vs Predicted Chilled Water: $Y_i$ vs $\hat{Y}_i$")
每小时热水预测
hourlysteam_train = pd.DataFrame(data=hourlySteam,
index=np.arange('2012-01-01 00:00:00',
'2014-02-01 00:00:00',
dtype='datetime64[h]')).dropna()
hourlysteam_test = pd.DataFrame(data=hourlySteam,
index=np.arange('2014-02-01 00:00:00',
'2014-11-01 00:00:00',
dtype='datetime64[h]')).dropna()
XX_hourlysteam_train =
hourlysteam_train.drop('steam-LBS',
axis = 1).reset_index().drop('index', axis = 1)
XX_hourlysteam_test =
hourlysteam_test.drop('steam-LBS',
axis = 1).reset_index().drop('index', axis = 1)
YY_hourlysteam_train = hourlysteam_train['steam-LBS']
YY_hourlysteam_test = hourlysteam_test['steam-LBS']
lr_hourlysteam = LinearRegression()
lr_hourlysteam.fit(XX_hourlysteam_train,YY_hourlysteam_train)
y_hourlysteam_lr = lr_hourlysteam.predict(XX_hourlysteam_test)
print "The test score R2: ", lr_hourlysteam.score(XX_hourlysteam_test,
YY_hourlysteam_test)
print "The coefficients Linear Regression are"
pd.DataFrame(zip(XX_hourlysteam_train.columns,
lr_hourlysteam.coef_),
columns = ['hourlysteam_features', 'linearRegr_Coefficients'])
The test score R2: 0.764295430491
The coefficients Linear Regression are
| hourlysteam_features | linearRegr_Coefficients | |
|---|---|---|
| 0 | RH-% | 5.367666 |
| 1 | T-C | 8.577206 |
| 2 | Tdew-C | -54.743326 |
| 3 | pressure-mbar | -0.279591 |
| 4 | solarRadiation-W/m2 | 0.138138 |
| 5 | windDirection | 0.041451 |
| 6 | windSpeed-m/s | 13.943372 |
| 7 | humidityRatio-kg/kg | 75847.104324 |
| 8 | coolingDegrees | -31.597421 |
| 9 | heatingDegrees | 57.903822 |
| 10 | dehumidification | -8088.312347 |
| 11 | occupancy | 131.534596 |
| 12 | cosHour | -343.896782 |
# 图观测值和预测值
fig = plt.figure(figsize=(15,7))
plt.scatter(XX_hourlysteam_test.index,
YY_hourlysteam_test,
label='Observed',
color='k')
plt.plot(XX_hourlysteam_test.index, y_hourlysteam_lr, label='Predicted', color='r')
plt.legend(loc='upper right')
#Plot Observed vs. Predicted usage.
fig = plt.figure(figsize=(6,6))
plt.plot(YY_hourlysteam_test, YY_hourlysteam_test, c='k')
plt.scatter(YY_hourlysteam_test, y_hourlysteam_lr, c='r')
plt.xlabel('Observed Steam Usage (LBS)')
plt.ylabel("Predicted Steam Usage (LBS): $\hat{Y}_i$")
plt.title("Observed vs Predicted Steam: $Y_i$ vs $\hat{Y}_i$")
支持向量回归和交叉验证
在这本笔记本中，将训练一个支持向量回归(SVR)模型来预测基于历史能源数据、几个天气变量、一天中的小时、一周中的一天、周末和假期的能源能耗。
为了做到这一点，我们将模型与2012年01月01日至2014年10月31日的每日和每小时的能源和天气数据进行拟合，并计算预测的平均残差平方。
在设计期间，我们使用交叉验证来微调SVR参数。由于SVR需要太多的时间来计算，在最后的笔记本中，将设置参数为交叉验证找到的最优值。仍然会显示作为交叉验证输入的参数范围。
%matplotlib inline
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sklearn.svm import SVR
from sklearn.grid_search import GridSearchCV
from sklearn import cross_validation
from sklearn import grid_search
pd.options.display.mpl_style = 'default'
dailyElectricity = pd.read_excel('Data/dailyElectricityWithFeatures.xlsx')
dailyElectricity = dailyElectricity.drop('startDay', 1).drop('endDay', 1)
dailyChilledWater = pd.read_excel('Data/dailyChilledWaterWithFeatures.xlsx')
dailyChilledWater = dailyChilledWater.drop('startDay', 1).drop('endDay', 1)
dailySteam = pd.read_excel('Data/dailySteamWithFeatures.xlsx')
dailySteam = dailySteam.drop('startDay', 1).drop('endDay', 1)
hourlyElectricity = pd.read_excel('Data/hourlyElectricityWithFeatures.xlsx')
hourlyElectricity = hourlyElectricity.drop('startTime', 1).drop('endTime', 1)
hourlyChilledWater = pd.read_excel('Data/hourlyChilledWaterWithFeatures.xlsx')
hourlyChilledWater = hourlyChilledWater.drop('startTime', 1).drop('endTime', 1)
hourlySteam = pd.read_excel('Data/hourlySteamWithFeatures.xlsx')
hourlySteam = hourlySteam.drop('startTime', 1).drop('endTime', 1)
#显示dataframe
dailyElectricity.head()
| electricity-kWh | RH-% | T-C | Tdew-C | pressure-mbar | solarRadiation-W/m2 | windDirection | windSpeed-m/s | humidityRatio-kg/kg | coolingDegrees | heatingDegrees | dehumidification | occupancy | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 2012-01-01 | 2800.244977 | 76.652174 | 7.173913 | 3.073913 | 1004.956522 | 95.260870 | 236.086957 | 4.118361 | 0.004796 | 0.086957 | 7.826087 | 0 | 0.0 |
| 2012-01-02 | 3168.974047 | 55.958333 | 5.833333 | -2.937500 | 994.625000 | 87.333333 | 253.750000 | 5.914357 | 0.003415 | 0.000000 | 9.166667 | 0 | 0.3 |
| 2012-01-03 | 5194.533376 | 42.500000 | -3.208333 | -12.975000 | 1002.125000 | 95.708333 | 302.916667 | 6.250005 | 0.001327 | 0.000000 | 18.208333 | 0 | 0.3 |
| 2012-01-04 | 5354.861935 | 41.541667 | -7.083333 | -16.958333 | 1008.250000 | 98.750000 | 286.666667 | 5.127319 | 0.000890 | 0.000000 | 22.083333 | 0 | 0.3 |
| 2012-01-05 | 5496.223993 | 46.916667 | -0.583333 | -9.866667 | 1002.041667 | 90.750000 | 258.333333 | 5.162041 | 0.001746 | 0.000000 | 15.583333 | 0 | 0.3 |
每日预测
向dataframe添加新特征:工作日、一年中的一天和一周。
def addDailyTimeFeatures(df):
df['weekday'] = df.index.weekday
df['day'] = df.index.dayofyear
df['week'] = df.index.weekofyear
return df
dailyElectricity = addDailyTimeFeatures(dailyElectricity)
dailyChilledWater = addDailyTimeFeatures(dailyChilledWater)
dailySteam = addDailyTimeFeatures(dailySteam)
每日电力预测
df_elect = dailyElectricity[['weekday', 'day', 'week',
'occupancy', 'electricity-kWh']]
elect_train = pd.DataFrame(data=df_elect,
index=np.arange('2012-01', '2013-07',
dtype='datetime64[D]')).dropna()
elect_test = pd.DataFrame(data=df_elect,
index=np.arange('2013-07', '2014-11',
dtype='datetime64[D]')).dropna()
XX_elect_train = elect_train.drop('electricity-kWh',
axis = 1).reset_index().drop('index', axis = 1)
XX_elect_test = elect_test.drop('electricity-kWh',
axis = 1).reset_index().drop('index', axis = 1)
YY_elect_train = elect_train['electricity-kWh']
YY_elect_test = elect_test['electricity-kWh']
# 输入参数范围交叉验证
gamma_range = [0.01, 0.001, 0.0001]
epsilon_range = [x * 0.1 for x in range(0, 2)]
C_range = range(1, 2500, 500)
# 为了加快速度，首先找到C和gamma的最佳解析器，然后在方法调用中直接设置它们
tuned_parameters = [{
'kernel': ['rbf', 'linear'],
# 'C': C_range,
# 'gamma': gamma_range,
'epsilon': epsilon_range}]
# 使用交叉验证搜索最佳参数。
svr_elect = GridSearchCV(SVR(C=2000, gamma=0.01), param_grid = tuned_parameters, verbose = 0)
# 选择合适的回归模型
y_elect = svr_elect.fit(XX_elect_train, YY_elect_train).predict(XX_elect_test)
print 'Optimum parameters C=2000 and gamma=0.01 for SVR'
print 'Optimum parameters epsilon and kernel for SVR: ', svr_elect.best_params_
print "The test score R2 for SVR: ", svr_elect.score(XX_elect_test, YY_elect_test)
print("SVR mean squared error: %.2f"
% np.mean((YY_elect_test - svr_elect.predict(XX_elect_test)) ** 2))
Optimum parameters C=2000 and gamma=0.01 for SVR
Optimum parameters epsilon and kernel for SVR: {'epsilon': 0.1, 'kernel': 'rbf'}
The test score R2 for RBF: 0.691753544427
RBF mean squared error: 391582.21
# 在测试期间观测和预测的电力需求的时间序列。
fig = plt.figure(figsize=(15,7))
plt.scatter(XX_elect_test.index, YY_elect_test, c='k', label='Observed')
plt.plot(XX_elect_test.index, y_elect, c='r', label='Predicted')
plt.xlabel('data')
plt.ylabel('target')
plt.title('Support Vector Regression')
plt.legend()
plt.show()
# 观察到的和预测的使用情况。
fig = plt.figure(figsize=(6,6))
plt.scatter(YY_elect_test, YY_elect_test, c='k')
plt.scatter(YY_elect_test, y_elect, c='r')
plt.xlabel('Observed Elec. Usage (kWh)')
plt.ylabel("Predicted Elec. Usage (kWh): $\hat{Y}_i$")
plt.title("Energy vs Predicted Energy: $Y_i$ vs $\hat{Y}_i$")
每日冷水预测
chilledw_train = pd.DataFrame(data=dailyChilledWater,
index=np.arange('2012-01', '2013-07',
dtype='datetime64[D]')).dropna()
chilledw_test = pd.DataFrame(data=dailyChilledWater,
index=np.arange('2013-07', '2014-11',
dtype='datetime64[D]')).dropna()
XX_chilledw_train =
chilledw_train.drop('chilledWater-TonDays',
axis = 1).reset_index().drop('index', axis = 1)
XX_chilledw_test =
chilledw_test.drop('chilledWater-TonDays',
axis = 1).reset_index().drop('index', axis = 1)
YY_chilledw_train = chilledw_train['chilledWater-TonDays']
YY_chilledw_test = chilledw_test['chilledWater-TonDays']
# SVR回归器的最优参数
gamma_range = [0.1, 0.01, 0.001, 0.0001]
epsilon_range = [x * 0.1 for x in range(0, 3)]
C_range = range(1, 5, 2)
tuned_parameters = [{
'kernel': ['rbf', 'linear'],
# 'C': C_range,
# 'gamma': gamma_range,
'epsilon': epsilon_range}]
svr_chilledw = GridSearchCV(SVR(C=3, gamma=0.0001), param_grid = tuned_parameters, verbose = 0)
y_chilledw = svr_chilledw.fit(XX_chilledw_train, YY_chilledw_train).predict(XX_chilledw_test)
print 'Optimum parameters C=3 and gamma=0.1 for SVR'
print 'Optimum epsilon and kernel: ', svr_chilledw.best_params_
print "The test score R2 for SVR: ", svr_chilledw.score(XX_chilledw_test, YY_chilledw_test)
print("SVR mean squared error: %.2f"
% np.mean((YY_chilledw_test - svr_chilledw.predict(XX_chilledw_test)) ** 2))
Optimum parameters C=3 and gamma=0.1 for SVR
Optimum epsilon and kernel: {'epsilon': 0.1, 'kernel': 'linear'}
The test score R2 for SVR: 0.764904375769
SVR mean squared error: 443.92
# 使用SVR绘制观察和预测的冷水值
fig = plt.figure(figsize=(15,10))
plt.scatter(XX_chilledw_test.index, YY_chilledw_test, c='k', label='Observed')
plt.plot(XX_chilledw_test.index, y_chilledw, c='g', label='Predicted')
plt.xlabel('data')
plt.ylabel('target')
plt.title('Support Vector Regression')
plt.legend()
plt.show()
# 观察到的和预测的使用情况。
fig = plt.figure(figsize=(6,6))
plt.scatter(YY_chilledw_test, YY_chilledw_test, c='k')
plt.scatter(YY_chilledw_test, y_chilledw, c='g')
plt.xlabel('Observed Chilled Water Usage (TonDays)')
plt.ylabel("Predicted Chilled Water Usage (TonDays): $\hat{Y}_i$")
plt.title("Observed vs Predicted Energy: $Y_i$ vs $\hat{Y}_i$")
每日热水预测
steam_train = pd.DataFrame(data=dailySteam,
index=np.arange('2012-01', '2013-07',
dtype='datetime64[D]')).dropna()
steam_test = pd.DataFrame(data=dailySteam,
index=np.arange('2013-07', '2014-11',
dtype='datetime64[D]')).dropna()
XX_steam_train = steam_train.drop('steam-LBS',
axis = 1).reset_index().drop('index', axis = 1)
XX_steam_test = steam_test.drop('steam-LBS',
axis = 1).reset_index().drop('index', axis = 1)
YY_steam_train = steam_train['steam-LBS']
YY_steam_test = steam_test['steam-LBS']
gamma_range = [0.1, 0.01, 0.001, 0.0001]
epsilon_range = [x * 0.1 for x in range(0, 3)]
C_range = range(1, 500, 50)
tuned_parameters = [{
'kernel': ['rbf', 'linear'],
# 'C': C_range,
'gamma': gamma_range,
'epsilon': epsilon_range}]
svr_steam = GridSearchCV(SVR(C=50), param_grid = tuned_parameters, verbose = 0)
y_steam = svr_steam.fit(XX_steam_train, YY_steam_train).predict(XX_steam_test)
print 'Optimum parameters C=50 for SVR'
print 'Optimum epsilon, gamma and kernel: ', svr_steam.best_params_
print "The test score R2 for SVR: ", svr_steam.score(XX_steam_test, YY_steam_test)
print("SVR mean squared error: %.2f"
% np.mean((YY_steam_test - svr_steam.predict(XX_steam_test)) ** 2))
Optimum parameters C=50 for SVR
Optimum epsilon, gamma and kernel: {'epsilon': 0.2, 'gamma': 0.1, 'kernel': 'linear'}
The test score R2 for SVR: 0.938467924325
SVR mean squared error: 20632451.77
# 图观测值和预测值
fig,ax = plt.subplots(1, 1,figsize=(20,10))
plt.scatter(XX_steam_test.index, YY_steam_test, c='k', label='Observed')
plt.plot(XX_steam_test.index, y_steam, c='r', label='Predicted')
plt.xlabel('data')
plt.ylabel('target')
plt.title('Support Vector Regression')
plt.legend()
plt.show()
# 图观测值和预测值
fig = plt.figure(figsize=(6,6))
plt.scatter(YY_steam_test, YY_steam_test, c='k')
plt.scatter(YY_steam_test, y_steam, c='r')
plt.xlabel('Observed Steam Usage (LBS)')
plt.ylabel("Predicted Steam Usage (LBS): $\hat{Y}_i$")
plt.title("Observed vs Predicted Energy: $Y_i$ vs $\hat{Y}_i$")
每小时预测
每小时电力预测
向dataframe添加新特征:小时、工作日、年中的一天和周。
def addHourlyTimeFeatures(df):
df['hour'] = df.index.hour
df['weekday'] = df.index.weekday
df['day'] = df.index.dayofyear
df['week'] = df.index.weekofyear
return df
hourlyElectricity = addHourlyTimeFeatures(hourlyElectricity)
df_hourlyelect = hourlyElectricity[['hour', 'weekday', 'day', 'week',
'cosHour', 'occupancy', 'electricity-kWh']]
hourlyelect_train = pd.DataFrame(data=df_hourlyelect,
index=np.arange('2014-01-01 00:00:00',
'2014-10-01 00:00:00',
dtype='datetime64[h]')).dropna()
hourlyelect_test = pd.DataFrame(data=df_hourlyelect,
index=np.arange('2014-10-01 00:00:00',
'2014-11-01 00:00:00',
dtype='datetime64[h]')).dropna()
XX_hourlyelect_train =
hourlyelect_train.drop('electricity-kWh',
axis = 1).reset_index().drop('index', axis = 1)
XX_hourlyelect_test =
hourlyelect_test.drop('electricity-kWh',
axis = 1).reset_index().drop('index', axis = 1)
YY_hourlyelect_train = hourlyelect_train['electricity-kWh']
YY_hourlyelect_test = hourlyelect_test['electricity-kWh']
gamma_range = [0.01, 0.001, 0.0001]
epsilon_range = [x * 0.1 for x in range(0, 2)]
C_range = range(1, 5, 1)
tuned_parameters = [{
'kernel': ['rbf', 'linear'],
# 'C': C_range,
# 'gamma': gamma_range,
'epsilon': epsilon_range}]
svr_hourlyelect = GridSearchCV(SVR(C=1, gamma=0.01), param_grid = tuned_parameters, verbose = 0)
y_hourlyelect = svr_hourlyelect.fit(XX_hourlyelect_train, YY_hourlyelect_train).predict(XX_hourlyelect_test)
print 'Optimum parameters C=1 and gamma=0.01 for SVR'
print 'Optimum epsilon and kernel for SVR: ', svr_hourlyelect.best_params_
print "The test score R2: ", svr_hourlyelect.score(XX_hourlyelect_test, YY_hourlyelect_test)
print("SVR mean squared error: %.2f"
% np.mean((YY_hourlyelect_test -
svr_hourlyelect.predict(XX_hourlyelect_test)) ** 2))
Optimum parameters C=1 and gamma=0.01 for SVR
Optimum epsilon and kernel for SVR: {'epsilon': 0.1, 'kernel': 'linear'}
The test score R2: 0.747282383852
SVR mean squared error: 1561.24
# 实测和预测的电量值
fig = plt.figure(figsize=(20,10))
plt.scatter(XX_hourlyelect_test.index,
YY_hourlyelect_test,
label='Observed',
color='k')
plt.plot(XX_hourlyelect_test.index, y_hourlyelect, label='Predicted', color='g')
plt.legend(loc='upper right')
# 观察到的和预测的使用情况。
fig = plt.figure(figsize=(6,6))
plt.plot(YY_hourlyelect_test, YY_hourlyelect_test, c='k')
plt.scatter(YY_hourlyelect_test, y_hourlyelect, c='g')
plt.xlabel('Observed Elec. Usage (kWh)')
plt.ylabel("Predicted Elec. Usage (kWh): $\hat{Y}_i$")
plt.title("Observed vs Predicted Elec.: $Y_i$ vs $\hat{Y}_i$")
