import pandas as pd
import numpy as np
df = pd.read_csv(
'../data/wine_data.csv', #葡萄酒数据集
header=None, #用哪行当做列名，我们自己来指定
usecols=[0,1,2] #返回一个子集，我们拿部分特征举例就可以了
)
df.columns=['Class label', 'Alcohol', 'Malic acid']
df.head()
在数据中，Alcohol和Malic acid 衡量的标准应该是不同的，特征之间数值差异较大
Standardization and Min-Max scaling
from sklearn import preprocessing
std_scale = preprocessing.StandardScaler().fit(df[['Alcohol', 'Malic acid']])
df_std = std_scale.transform(df[['Alcohol', 'Malic acid']])
minmax_scale = preprocessing.MinMaxScaler().fit(df[['Alcohol', 'Malic acid']])
df_minmax = minmax_scale.transform(df[['Alcohol', 'Malic acid']])
print('Mean after standardization:\nAlcohol={:.2f}, Malic acid={:.2f}'
.format(df_std[:,0].mean(), df_std[:,1].mean()))
print('\nStandard deviation after standardization:\nAlcohol={:.2f}, Malic acid={:.2f}'
.format(df_std[:,0].std(), df_std[:,1].std()))
输出 ：
Mean after standardization:
Alcohol=-0.00, Malic acid=-0.00
Standard deviation after standardization:
Alcohol=1.00, Malic acid=1.00
print('Min-value after min-max scaling:\nAlcohol={:.2f}, Malic acid={:.2f}'
.format(df_minmax[:,0].min(), df_minmax[:,1].min()))
print('\nMax-value after min-max scaling:\nAlcohol={:.2f}, Malic acid={:.2f}'
.format(df_minmax[:,0].max(), df_minmax[:,1].max()))
输出 ：
Min-value after min-max scaling:
Alcohol=0.00, Malic acid=0.00
Max-value after min-max scaling:
Alcohol=1.00, Malic acid=1.00
Plotting
%matplotlib inline
from matplotlib import pyplot as plt
def plot():
plt.figure(figsize=(8,6))
plt.scatter(df['Alcohol'], df['Malic acid'],
color='green', label='input scale', alpha=0.5)
plt.scatter(df_std[:,0], df_std[:,1], color='red',
label='Standardized [$N (\mu=0, \; \sigma=1)$]', alpha=0.3)
plt.scatter(df_minmax[:,0], df_minmax[:,1],
color='blue', label='min-max scaled [min=0, max=1]', alpha=0.3)
plt.title('Alcohol and Malic Acid content of the wine dataset')
plt.xlabel('Alcohol')
plt.ylabel('Malic Acid')
plt.legend(loc='upper left')
plt.grid()
plt.tight_layout()
plot()
plt.show()
我们将原始的和变换后都放到了同一个图上，观察下结果吧！接下来我们再看看数据是否被打乱了呢？
fig, ax = plt.subplots(3, figsize=(6,14))
for a,d,l in zip(range(len(ax)),
(df[['Alcohol', 'Malic acid']].values, df_std, df_minmax),
('Input scale',
'Standardized [$N (\mu=0, \; \sigma=1)$]',
'min-max scaled [min=0, max=1]')
):
for i,c in zip(range(1,4), ('red', 'blue', 'green')):
ax[a].scatter(d[df['Class label'].values == i, 0],
d[df['Class label'].values == i, 1],
alpha=0.5,
color=c,
label='Class %s' %i
)
ax[a].set_title(l)
ax[a].set_xlabel('Alcohol')
ax[a].set_ylabel('Malic Acid')
ax[a].legend(loc='upper left')
ax[a].grid()
plt.tight_layout()
plt.show()
在机器学习中，如果我们对训练集做了上述处理，那么同样的对测试集也必须要经过相同的处理
std_scale = preprocessing.StandardScaler().fit(X_train)
X_train = std_scale.transform(X_train)
X_test = std_scale.transform(X_test)
标准化处理对PCA主成分分析的影响
主成分分析（PCA）和一个非常有用的套路，接下来，咱们来看看数据经过标准化处理和未经标准化处理后使用PCA的效果
Reading in the dataset
import pandas as pd
df = pd.read_csv(
'../data/wine_data.csv',
header=None,
)
df.head()
Dividing the dataset into a separate training and test dataset
In this step, we will randomly divide the wine dataset into a training dataset and a test dataset where the training dataset will contain 70% of the samples and the test dataset will contain 30%, respectively.
from sklearn.model_selection import train_test_split
X_wine = df.values[:,1:]
y_wine = df.values[:,0]
X_train, X_test, y_train, y_test = train_test_split(X_wine, y_wine,
test_size=0.30, random_state=12345)
Feature Scaling - Standardization
from sklearn import preprocessing
std_scale = preprocessing.StandardScaler().fit(X_train)
X_train_std = std_scale.transform(X_train)
X_test_std = std_scale.transform(X_test)
使用PCA进行降维
现在，我们在标准化和非标准化数据集上执行PCA，将数据集转换成二维特征子空间。
from sklearn.decomposition import PCA
# on non-standardized data
pca = PCA(n_components=2).fit(X_train)
X_train = pca.transform(X_train)
X_test = pca.transform(X_test)
# om standardized data
pca_std = PCA(n_components=2).fit(X_train_std)
X_train_std = pca_std.transform(X_train_std)
X_test_std = pca_std.transform(X_test_std)
来看看效果咋样吧
%matplotlib inline
from matplotlib import pyplot as plt
fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(10,4))
for l,c,m in zip(range(1,4), ('blue', 'red', 'green'), ('^', 's', 'o')):
ax1.scatter(X_train[y_train==l, 0], X_train[y_train==l, 1],
color=c,
label='class %s' %l,
alpha=0.5,
marker=m
)
for l,c,m in zip(range(1,4), ('blue', 'red', 'green'), ('^', 's', 'o')):
ax2.scatter(X_train_std[y_train==l, 0], X_train_std[y_train==l, 1],
color=c,
label='class %s' %l,
alpha=0.5,
marker=m
)
ax1.set_title('Transformed NON-standardized training dataset after PCA')
ax2.set_title('Transformed standardized training dataset after PCA')
for ax in (ax1, ax2):
ax.set_xlabel('1st principal component')
ax.set_ylabel('2nd principal component')
ax.legend(loc='upper right')
ax.grid()
plt.tight_layout()
plt.show()
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