加州房價預測模型

原創 小哲嗨数 2020-06-16 01:19 
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

%matplotlib
%matplotlib inline
%config InlineBackend.figure_format = 'retina'

Using matplotlib backend: MacOSX

讀取數據集並觀察數據特點

字段意義和數據觀察結果

  • longitude: 經度
  • latitude: 緯度
  • housing_median_age: 房齡中位數
  • total_rooms: 房間總數
  • total_bedrooms: 臥室總數
  • population: 人口數
  • households: 家庭戶數
  • median_income: 收入中位數
  • median_house_value: 房價中位數
  • ocean_proximity: 距離海邊的距離

數據加載

# 讀取數據，原數據可查看 https://github.com/ageron/handson-ml/tree/master/datasets/housing
housing_df = pd.read_csv('https://query.data.world/s/yffqqcx3rsjlzspztxr6zt5iqd45kn')

# 查看數據結構
housing_df.head(10)
longitude latitude housing_median_age total_rooms total_bedrooms population households median_income median_house_value ocean_proximity
0 -122.23 37.88 41.0 880.0 129.0 322.0 126.0 8.3252 452600.0 NEAR BAY
1 -122.22 37.86 21.0 7099.0 1106.0 2401.0 1138.0 8.3014 358500.0 NEAR BAY
2 -122.24 37.85 52.0 1467.0 190.0 496.0 177.0 7.2574 352100.0 NEAR BAY
3 -122.25 37.85 52.0 1274.0 235.0 558.0 219.0 5.6431 341300.0 NEAR BAY
4 -122.25 37.85 52.0 1627.0 280.0 565.0 259.0 3.8462 342200.0 NEAR BAY
5 -122.25 37.85 52.0 919.0 213.0 413.0 193.0 4.0368 269700.0 NEAR BAY
6 -122.25 37.84 52.0 2535.0 489.0 1094.0 514.0 3.6591 299200.0 NEAR BAY
7 -122.25 37.84 52.0 3104.0 687.0 1157.0 647.0 3.1200 241400.0 NEAR BAY
8 -122.26 37.84 42.0 2555.0 665.0 1206.0 595.0 2.0804 226700.0 NEAR BAY
9 -122.25 37.84 52.0 3549.0 707.0 1551.0 714.0 3.6912 261100.0 NEAR BAY

數據的描述性統計

數據屬性

# 查看數據信息
# 1. 通過以下數據可發現除了total_bedrooms字段數據缺失(非空20433,總數爲20640)，其他字段數據都是完整的。
# 2. 除了ocean_proximity，其他都是float64類型，可以進一步查看ocean_proximity非枚舉值分佈
housing_df.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 20640 entries, 0 to 20639
Data columns (total 10 columns):
longitude             20640 non-null float64
latitude              20640 non-null float64
housing_median_age    20640 non-null float64
total_rooms           20640 non-null float64
total_bedrooms        20433 non-null float64
population            20640 non-null float64
households            20640 non-null float64
median_income         20640 non-null float64
median_house_value    20640 non-null float64
ocean_proximity       20640 non-null object
dtypes: float64(9), object(1)
memory usage: 1.6+ MB

# 查看ocean_proximity枚舉值分佈
housing_df['ocean_proximity'].value_counts()

<1H OCEAN     9136
INLAND        6551
NEAR OCEAN    2658
NEAR BAY      2290
ISLAND           5
Name: ocean_proximity, dtype: int64

枚舉值釋義:

  • INLAND: 內地，內陸
  • NEAR OCEAN: 靠海
  • NEAR BAY: 靠海
  • ISLAND: 島上

數據的描述性統計

# 統計信息
housing_df.describe()
longitude latitude housing_median_age total_rooms total_bedrooms population households median_income median_house_value
count 20640.000000 20640.000000 20640.000000 20640.000000 20433.000000 20640.000000 20640.000000 20640.000000 20640.000000
mean -119.569704 35.631861 28.639486 2635.763081 537.870553 1425.476744 499.539680 3.870671 206855.816909
std 2.003532 2.135952 12.585558 2181.615252 421.385070 1132.462122 382.329753 1.899822 115395.615874
min -124.350000 32.540000 1.000000 2.000000 1.000000 3.000000 1.000000 0.499900 14999.000000
25% -121.800000 33.930000 18.000000 1447.750000 296.000000 787.000000 280.000000 2.563400 119600.000000
50% -118.490000 34.260000 29.000000 2127.000000 435.000000 1166.000000 409.000000 3.534800 179700.000000
75% -118.010000 37.710000 37.000000 3148.000000 647.000000 1725.000000 605.000000 4.743250 264725.000000
max -114.310000 41.950000 52.000000 39320.000000 6445.000000 35682.000000 6082.000000 15.000100 500001.000000

數據分佈

# 各個屬性的數據分佈
housing_df.hist(bins=50, figsize=(20,15))

array([[<matplotlib.axes._subplots.AxesSubplot object at 0x10d8efd68>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x10e45d198>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x10e48e748>],
       [<matplotlib.axes._subplots.AxesSubplot object at 0x118efccf8>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x118f392e8>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x118f6a898>],
       [<matplotlib.axes._subplots.AxesSubplot object at 0x119283e48>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x1192bf470>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x1192bf4a8>]],
      dtype=object)

png

地理數據可視化

參考：https://www.bigendiandata.com/2017-06-27-Mapping_in_Jupyter/

housing_df.plot(kind='scatter', x='longitude', y='latitude', 
                s=housing_df['population']/100, c='median_house_value', cmap=plt.get_cmap('jet'),
                colorbar=True, alpha=0.1, figsize=(10,10))

<matplotlib.axes._subplots.AxesSubplot at 0x1199350b8>

png

https://public.tableau.com/views/1990_15748722575690/1990?:display_count=y&publish=yes&:origin=viz_share_link

尋找相關性

探索每個屬性與房價中位數(median_house_value)的相關性

使用相關性矩陣

由於數據集不大，這裏使用皮爾遜係數。可使用dataframe自帶有corr(method=‘pearson’)函數

直接使用現成字段

corr = housing_df.corr(method='pearson')
corr
longitude latitude housing_median_age total_rooms total_bedrooms population households median_income median_house_value
longitude 1.000000 -0.924664 -0.108197 0.044568 0.069608 0.099773 0.055310 -0.015176 -0.045967
latitude -0.924664 1.000000 0.011173 -0.036100 -0.066983 -0.108785 -0.071035 -0.079809 -0.144160
housing_median_age -0.108197 0.011173 1.000000 -0.361262 -0.320451 -0.296244 -0.302916 -0.119034 0.105623
total_rooms 0.044568 -0.036100 -0.361262 1.000000 0.930380 0.857126 0.918484 0.198050 0.134153
total_bedrooms 0.069608 -0.066983 -0.320451 0.930380 1.000000 0.877747 0.979728 -0.007723 0.049686
population 0.099773 -0.108785 -0.296244 0.857126 0.877747 1.000000 0.907222 0.004834 -0.024650
households 0.055310 -0.071035 -0.302916 0.918484 0.979728 0.907222 1.000000 0.013033 0.065843
median_income -0.015176 -0.079809 -0.119034 0.198050 -0.007723 0.004834 0.013033 1.000000 0.688075
median_house_value -0.045967 -0.144160 0.105623 0.134153 0.049686 -0.024650 0.065843 0.688075 1.000000 
# 只查看median_house_value與其他屬性的皮爾遜係數。相關係數的數值範圍 -1~1.
# 1.趨近於1表示正相關性越強；2.趨近於-1表示負相關性越強；3. 趨近於0表示沒有任何關係
corr['median_house_value'].sort_values(ascending=False)

median_house_value    1.000000
median_income         0.688075
total_rooms           0.134153
housing_median_age    0.105623
households            0.065843
total_bedrooms        0.049686
population           -0.024650
longitude            -0.045967
latitude             -0.144160
Name: median_house_value, dtype: float64

組合字段

  • population_per_household: 每個家庭的人口數
  • rooms_household: 每個家庭的房間數
  • bedrooms_per_room: 臥室的佔比
tmp_df = housing_df.copy()
tmp_df['population_per_household'] = tmp_df['population'] / tmp_df['households']
tmp_df['rooms_per_household'] = tmp_df['total_rooms'] / tmp_df['households']
tmp_df['bedrooms_per_room'] = tmp_df['total_bedrooms'] / tmp_df['total_rooms']

tmp_df.head(10)
longitude latitude housing_median_age total_rooms total_bedrooms population households median_income median_house_value ocean_proximity population_per_household rooms_per_household bedrooms_per_room
0 -122.23 37.88 41.0 880.0 129.0 322.0 126.0 8.3252 452600.0 NEAR BAY 2.555556 6.984127 0.146591
1 -122.22 37.86 21.0 7099.0 1106.0 2401.0 1138.0 8.3014 358500.0 NEAR BAY 2.109842 6.238137 0.155797
2 -122.24 37.85 52.0 1467.0 190.0 496.0 177.0 7.2574 352100.0 NEAR BAY 2.802260 8.288136 0.129516
3 -122.25 37.85 52.0 1274.0 235.0 558.0 219.0 5.6431 341300.0 NEAR BAY 2.547945 5.817352 0.184458
4 -122.25 37.85 52.0 1627.0 280.0 565.0 259.0 3.8462 342200.0 NEAR BAY 2.181467 6.281853 0.172096
5 -122.25 37.85 52.0 919.0 213.0 413.0 193.0 4.0368 269700.0 NEAR BAY 2.139896 4.761658 0.231774
6 -122.25 37.84 52.0 2535.0 489.0 1094.0 514.0 3.6591 299200.0 NEAR BAY 2.128405 4.931907 0.192899
7 -122.25 37.84 52.0 3104.0 687.0 1157.0 647.0 3.1200 241400.0 NEAR BAY 1.788253 4.797527 0.221327
8 -122.26 37.84 42.0 2555.0 665.0 1206.0 595.0 2.0804 226700.0 NEAR BAY 2.026891 4.294118 0.260274
9 -122.25 37.84 52.0 3549.0 707.0 1551.0 714.0 3.6912 261100.0 NEAR BAY 2.172269 4.970588 0.199211 
corr = tmp_df.corr(method='pearson')
corr['median_house_value'].sort_values(ascending=False)

median_house_value          1.000000
median_income               0.688075
rooms_per_household         0.151948
total_rooms                 0.134153
housing_median_age          0.105623
households                  0.065843
total_bedrooms              0.049686
population_per_household   -0.023737
population                 -0.024650
longitude                  -0.045967
latitude                   -0.144160
bedrooms_per_room          -0.255880
Name: median_house_value, dtype: float64

可以看出bedrooms_per_room在負數最小，於房價呈負相關。population_per_household比較接近於0，與房價的關係不大

數據清理與特徵工程

  1. total_bedrooms字段數據缺失(非空20433,總數爲20640)，使用sklearn自帶的缺失值處理函數imputer
  2. ocean_proximity文本信息處理；
  3. 轉化數據流，定義任務步驟，自動順序執行；

缺失值處理

from sklearn.impute import SimpleImputer

tmp_df = housing_df.copy()
# axis=0代表drop索引，axis=1代表drop列
imputer = SimpleImputer(strategy='median')
tmp_df['total_bedrooms'] = imputer.fit_transform(tmp_df[['total_bedrooms']])
tmp_df.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 20640 entries, 0 to 20639
Data columns (total 10 columns):
longitude             20640 non-null float64
latitude              20640 non-null float64
housing_median_age    20640 non-null float64
total_rooms           20640 non-null float64
total_bedrooms        20640 non-null float64
population            20640 non-null float64
households            20640 non-null float64
median_income         20640 non-null float64
median_house_value    20640 non-null float64
ocean_proximity       20640 non-null object
dtypes: float64(9), object(1)
memory usage: 1.6+ MB

處理文本信息

  • 方法一：使用LabelEncoder文本轉化爲整數，再使用OneHotEncode將整數one-hot編碼
  • 方法二：使用LabelBinarizer直接完成這兩步驟
from sklearn.preprocessing import LabelBinarizer

encode = LabelBinarizer()
encode.fit_transform(housing_df['ocean_proximity'])

array([[0, 0, 0, 1, 0],
       [0, 0, 0, 1, 0],
       [0, 0, 0, 1, 0],
       ...,
       [0, 1, 0, 0, 0],
       [0, 1, 0, 0, 0],
       [0, 1, 0, 0, 0]])

轉化流水線

定義數據轉化任務的步驟，讓任務流水化執行.

from sklearn.base import BaseEstimator, TransformerMixin

class DataFrameSelector(BaseEstimator, TransformerMixin):
    """
    sklearn庫主要使用numpy數組, 所以將dataframe全部轉化爲numpy數組.
    自定義轉化器需添加基類：BaseEstimator, TransformerMixin
    """
    def __init__(self, attribute_names):
        self.attribute_names=attribute_names
    def fit(self, x, y=None):
        return self
    def transform(self, x):
        """返回numpy數組"""
        return x[self.attribute_names].values

def get_columns_index(df, columns):
    return [list(df.columns).index(column) for column in list(columns)]

def add_extra_features(x, rooms_ix, bedrooms_ix, population_ix, household_ix):    
    """補充字段"""
    population_per_household = x[:, population_ix] / x[:, household_ix]
    rooms_per_household = x[:, rooms_ix] / x[:, household_ix]
    bedrooms_per_room = x[:, bedrooms_ix] / x[:, rooms_ix]
    return np.c_[x, population_per_household, rooms_per_household, bedrooms_per_room]


# 轉化流水線
from sklearn.pipeline import Pipeline
from sklearn.pipeline import FeatureUnion
from sklearn.preprocessing import FunctionTransformer
from sklearn.preprocessing import StandardScaler
from sklearn.preprocessing import OneHotEncoder


# 數值類型流水線
num_attribute_names = ['longitude', 'latitude', 'housing_median_age', 'total_rooms', 'total_bedrooms', 'population',
              'households', 'median_income']
rooms_ix, bedrooms_ix, population_ix, household_ix = get_columns_index(housing_df, ['total_rooms', 'total_bedrooms', 'population', 'households'])
num_pipline = Pipeline([
    ('selector', DataFrameSelector(num_attribute_names)),
    ('imputer', SimpleImputer(strategy='median')),
    ('attribs_adder', FunctionTransformer(add_extra_features, kw_args={'rooms_ix':rooms_ix, 'bedrooms_ix':bedrooms_ix, 
                                                                       'population_ix':population_ix, 'household_ix':household_ix})),
    ('std_scaler', StandardScaler())
])

# 文本類型流水線
text_pipline = Pipeline([
    ('selector', DataFrameSelector(['ocean_proximity'])),
    ('text_encoder', OneHotEncoder(sparse=False)),
])

# 合併
union_pipplines = FeatureUnion(transformer_list=[
    ('num_pipline', num_pipline),
    ('text_pipline', text_pipline),
])

housing_prepares = union_pipplines.fit_transform(housing_df)
print('shape: ', housing_prepares.shape)
print('data head 5: \n', housing_prepares[0:5, :])

shape:  (20640, 16)
data head 5: 
 [[-1.32783522  1.05254828  0.98214266 -0.8048191  -0.97247648 -0.9744286
  -0.97703285  2.34476576 -0.04959654  0.62855945 -1.02998783  0.
   0.          0.          1.          0.        ]
 [-1.32284391  1.04318455 -0.60701891  2.0458901   1.35714343  0.86143887
   1.66996103  2.33223796 -0.09251223  0.32704136 -0.8888972   0.
   0.          0.          1.          0.        ]
 [-1.33282653  1.03850269  1.85618152 -0.53574589 -0.82702426 -0.82077735
  -0.84363692  1.7826994  -0.02584253  1.15562047 -1.29168566  0.
   0.          0.          1.          0.        ]
 [-1.33781784  1.03850269  1.85618152 -0.62421459 -0.71972345 -0.76602806
  -0.73378144  0.93296751 -0.0503293   0.15696608 -0.4496128   0.
   0.          0.          1.          0.        ]
 [-1.33781784  1.03850269  1.85618152 -0.46240395 -0.61242263 -0.75984669
  -0.62915718 -0.012881   -0.08561576  0.3447108  -0.63908657  0.
   0.          0.          1.          0.        ]]


/Users/cleland/.pyenv/versions/3.7.1/envs/base/lib/python3.7/site-packages/sklearn/preprocessing/_function_transformer.py:97: FutureWarning: The default validate=True will be replaced by validate=False in 0.22.
  "validate=False in 0.22.", FutureWarning)
/Users/cleland/.pyenv/versions/3.7.1/envs/base/lib/python3.7/site-packages/sklearn/preprocessing/_function_transformer.py:97: FutureWarning: The default validate=True will be replaced by validate=False in 0.22.
  "validate=False in 0.22.", FutureWarning)

模型訓練

medain_housing_values 25%~75%: 119600~264725 美元

訓練數據集和測試數據集劃分

from sklearn.model_selection import train_test_split


housing_label = housing_df['median_house_value'].values
x_train, x_test, y_train, y_test = train_test_split(housing_prepares, housing_label)

線性迴歸

測試數據集最好得分67906。而實際數據大部分分佈在119600~264725 美元，預測偏差較大。

from sklearn.linear_model import LinearRegression
from sklearn.model_selection import GridSearchCV
from sklearn.metrics import mean_squared_error

estimator = LinearRegression()
estimator.fit(x_train, y_train)

estimator = GridSearchCV(estimator, param_grid={}, cv=5)
estimator.fit(x_train, y_train)

y_test_predict = estimator.predict(x_test)

print('MSE: ', mean_squared_error(y_test, y_test_predict))
print('RMSE: ', np.sqrt(mean_squared_error(y_test, y_test_predict)))

# 最佳參數
print(u'最佳參數: \n', estimator.best_params_)
# 最佳結果
print(u'結果: \n', estimator.best_score_)
# 最佳估計器
print(u'估計器: \n', estimator.best_estimator_)
# 交叉驗證結果
print(u'交叉驗證結果: \n', estimator.cv_results_)

MSE:  4543924391.051387
RMSE:  67408.63736236913
最佳參數: 
 {}
結果: 
 0.6432229836429453
估計器: 
 LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)
交叉驗證結果: 
 {'mean_fit_time': array([0.14581642]), 'std_fit_time': array([0.04799657]), 'mean_score_time': array([0.00797019]), 'std_score_time': array([0.00313379]), 'params': [{}], 'split0_test_score': array([0.65722112]), 'split1_test_score': array([0.64810884]), 'split2_test_score': array([0.65080866]), 'split3_test_score': array([0.62162591]), 'split4_test_score': array([0.63835039]), 'mean_test_score': array([0.64322298]), 'std_test_score': array([0.01238981]), 'rank_test_score': array([1], dtype=int32)}

決策樹

from sklearn.tree import DecisionTreeRegressor
from sklearn.model_selection import GridSearchCV
from sklearn.metrics import mean_squared_error

estimator = DecisionTreeRegressor()
estimator.fit(x_train, y_train)

estimator = GridSearchCV(estimator, param_grid={}, cv=5)
estimator.fit(x_train, y_train)

y_test_predict = estimator.predict(x_test)

print('MSE: ', mean_squared_error(y_test, y_test_predict))
print('RMSE: ', np.sqrt(mean_squared_error(y_test, y_test_predict)))

# 最佳參數
print(u'最佳參數: \n', estimator.best_params_)
# 最佳結果
print(u'結果: \n', estimator.best_score_)
# 最佳估計器
print(u'估計器: \n', estimator.best_estimator_)
# 交叉驗證結果
print(u'交叉驗證結果: \n', estimator.cv_results_)

MSE:  4484788001.235852
RMSE:  66968.5597966378
最佳參數: 
 {}
結果: 
 0.6330416409343302
估計器: 
 DecisionTreeRegressor(criterion='mse', max_depth=None, max_features=None,
                      max_leaf_nodes=None, min_impurity_decrease=0.0,
                      min_impurity_split=None, min_samples_leaf=1,
                      min_samples_split=2, min_weight_fraction_leaf=0.0,
                      presort=False, random_state=None, splitter='best')
交叉驗證結果: 
 {'mean_fit_time': array([0.36660266]), 'std_fit_time': array([0.02361012]), 'mean_score_time': array([0.00709462]), 'std_score_time': array([0.00589681]), 'params': [{}], 'split0_test_score': array([0.64208581]), 'split1_test_score': array([0.63046887]), 'split2_test_score': array([0.64717912]), 'split3_test_score': array([0.60435885]), 'split4_test_score': array([0.64111556]), 'mean_test_score': array([0.63304164]), 'std_test_score': array([0.01533738]), 'rank_test_score': array([1], dtype=int32)}

隨機森林

from sklearn.ensemble import RandomForestRegressor
from sklearn.model_selection import GridSearchCV
from sklearn.metrics import mean_squared_error

estimator = RandomForestRegressor()
estimator.fit(x_train, y_train)

estimator = GridSearchCV(estimator, param_grid={}, cv=5)
estimator.fit(x_train, y_train)

y_test_predict = estimator.predict(x_test)

print('MSE: ', mean_squared_error(y_test, y_test_predict))
print('RMSE: ', np.sqrt(mean_squared_error(y_test, y_test_predict)))

# 最佳參數
print(u'最佳參數: \n', estimator.best_params_)
# 最佳結果
print(u'結果: \n', estimator.best_score_)
# 最佳估計器
print(u'估計器: \n', estimator.best_estimator_)
# 交叉驗證結果
print(u'交叉驗證結果: \n', estimator.cv_results_)

/Users/cleland/.pyenv/versions/3.7.1/envs/base/lib/python3.7/site-packages/sklearn/ensemble/forest.py:245: FutureWarning: The default value of n_estimators will change from 10 in version 0.20 to 100 in 0.22.
  "10 in version 0.20 to 100 in 0.22.", FutureWarning)


MSE:  2599366029.248785
RMSE:  50983.97816225
最佳參數: 
 {}
結果: 
 0.7895634451066635
估計器: 
 RandomForestRegressor(bootstrap=True, criterion='mse', max_depth=None,
                      max_features='auto', max_leaf_nodes=None,
                      min_impurity_decrease=0.0, min_impurity_split=None,
                      min_samples_leaf=1, min_samples_split=2,
                      min_weight_fraction_leaf=0.0, n_estimators=10,
                      n_jobs=None, oob_score=False, random_state=None,
                      verbose=0, warm_start=False)
交叉驗證結果: 
 {'mean_fit_time': array([2.7657424]), 'std_fit_time': array([0.1215011]), 'mean_score_time': array([0.02362027]), 'std_score_time': array([0.00405571]), 'params': [{}], 'split0_test_score': array([0.79759449]), 'split1_test_score': array([0.78053044]), 'split2_test_score': array([0.80471751]), 'split3_test_score': array([0.77450088]), 'split4_test_score': array([0.79047391]), 'mean_test_score': array([0.78956345]), 'std_test_score': array([0.01098588]), 'rank_test_score': array([1], dtype=int32)}

參考

  • 機器學習實戰-基於Scikit-Learn和TensorFlow
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