数据归一化
除了·边界比较明显的数据集（像素），一般用均值方差归一化。
测试数据集要用训练集的平均数和标准差进行归一化
import numpy as np
import matplotlib.pyplot as plt
最值归一化 normalization
x=np.random.randint(0,100,100)
x
array([84, 5, 7, 97, 16, 15, 64, 71, 55, 58, 12, 0, 73, 41, 27, 92, 97,
21, 29, 69, 46, 7, 70, 68, 61, 59, 65, 2, 70, 30, 34, 45, 86, 29,
17, 21, 41, 50, 5, 51, 3, 27, 68, 25, 53, 76, 15, 9, 16, 63, 62,
65, 39, 78, 76, 82, 83, 67, 51, 6, 32, 30, 99, 56, 65, 80, 31, 12,
4, 33, 54, 95, 63, 87, 62, 55, 86, 27, 84, 96, 35, 54, 64, 88, 8,
36, 99, 27, 50, 53, 95, 56, 20, 70, 15, 70, 27, 40, 4, 54])
(x-np.min(x))/(np.max(x)-np.min(x))
array([0.84848485, 0.05050505, 0.07070707, 0.97979798, 0.16161616,
0.15151515, 0.64646465, 0.71717172, 0.55555556, 0.58585859,
0.12121212, 0. , 0.73737374, 0.41414141, 0.27272727,
0.92929293, 0.97979798, 0.21212121, 0.29292929, 0.6969697 ,
0.46464646, 0.07070707, 0.70707071, 0.68686869, 0.61616162,
0.5959596 , 0.65656566, 0.02020202, 0.70707071, 0.3030303 ,
0.34343434, 0.45454545, 0.86868687, 0.29292929, 0.17171717,
0.21212121, 0.41414141, 0.50505051, 0.05050505, 0.51515152,
0.03030303, 0.27272727, 0.68686869, 0.25252525, 0.53535354,
0.76767677, 0.15151515, 0.09090909, 0.16161616, 0.63636364,
0.62626263, 0.65656566, 0.39393939, 0.78787879, 0.76767677,
0.82828283, 0.83838384, 0.67676768, 0.51515152, 0.06060606,
0.32323232, 0.3030303 , 1. , 0.56565657, 0.65656566,
0.80808081, 0.31313131, 0.12121212, 0.04040404, 0.33333333,
0.54545455, 0.95959596, 0.63636364, 0.87878788, 0.62626263,
0.55555556, 0.86868687, 0.27272727, 0.84848485, 0.96969697,
0.35353535, 0.54545455, 0.64646465, 0.88888889, 0.08080808,
0.36363636, 1. , 0.27272727, 0.50505051, 0.53535354,
0.95959596, 0.56565657, 0.2020202 , 0.70707071, 0.15151515,
0.70707071, 0.27272727, 0.4040404 , 0.04040404, 0.54545455])
X=np.random.randint(0,100,(50,2))
X[:10,:]
array([[55, 33],
[51, 53],
[40, 14],
[10, 24],
[90, 36],
[76, 34],
[45, 48],
[86, 89],
[88, 68],
[ 4, 39]])
X=np.array(X,dtype=float)
X[:10,:]
array([[55., 33.],
[51., 53.],
[40., 14.],
[10., 24.],
[90., 36.],
[76., 34.],
[45., 48.],
[86., 89.],
[88., 68.],
[ 4., 39.]])
X[:,0]=(X[:,0]-np.min(X[:,0]))/(np.max(X[:,0])-np.min(X[:,0]))
X[:,1]=(X[:,1]-np.min(X[:,1]))/(np.max(X[:,1])-np.min(X[:,1]))
X[:10,]
array([[0.55102041, 0.33333333],
[0.51020408, 0.54166667],
[0.39795918, 0.13541667],
[0.09183673, 0.23958333],
[0.90816327, 0.36458333],
[0.76530612, 0.34375 ],
[0.44897959, 0.48958333],
[0.86734694, 0.91666667],
[0.8877551 , 0.69791667],
[0.03061224, 0.39583333]])
plt.scatter(X[:,0],X[:,1])
<matplotlib.collections.PathCollection at 0x2070630a988>
数据均值
np.mean(X[:,0])
0.540204081632653
np.mean(X[:,1])
0.5147916666666666
数据标准差
np.std(X[:,0])
0.28443891736063087
np.std(X[:,1])
0.28634346181639975
均值方差归一化
X2=np.random.randint(0,100,(50,2))
X2=np.array(X2,dtype=float)
X2[:,0]=(X2[:,0]-np.mean(X2[:,0]))/np.std(X2[:,0])
X2[:,1]=(X2[:,1]-np.mean(X2[:,1]))/np.std(X2[:,1])
X2[:10,]
array([[-1.24848758, -1.00045396],
[ 0.55550544, -1.47236621],
[ 1.39529529, -0.60719376],
[ 1.36419196, -0.41056365],
[ 0.83543539, 0.4546088 ],
[ 1.11536534, 0.49393482],
[-1.27959091, 1.47708533],
[-1.27959091, -0.17460753],
[ 0.55550544, -1.079106 ],
[-0.78193766, -0.84314988]])
plt.scatter(X2[:,0],X2[:,1])
<matplotlib.collections.PathCollection at 0x207064e8a48>
np.mean(X2[:,0])
-6.106226635438361e-17
np.std(X2[:,0])
1.0
np.mean(X2[:1])
-1.1244707714628714
np.std(X2[:1])
0.12401681156731514
scikit_learn中的scater
import numpy as np
from sklearn import datasets
iris=datasets.load_iris()
X=iris.data
y=iris.target
X[:10,]
array([[5.1, 3.5, 1.4, 0.2],
[4.9, 3. , 1.4, 0.2],
[4.7, 3.2, 1.3, 0.2],
[4.6, 3.1, 1.5, 0.2],
[5. , 3.6, 1.4, 0.2],
[5.4, 3.9, 1.7, 0.4],
[4.6, 3.4, 1.4, 0.3],
[5. , 3.4, 1.5, 0.2],
[4.4, 2.9, 1.4, 0.2],
[4.9, 3.1, 1.5, 0.1]])
from sklearn.model_selection import train_test_split
X_train,X_test,y_train,y_test=train_test_split(X,y,test_size=0.2,random_state=666)
scikit-learn 中的StandardScater
from sklearn.preprocessing import StandardScaler
stdScater=StandardScaler()
stdScater.fit(X_train)
StandardScaler(copy=True, with_mean=True, with_std=True)
stdScater.mean_
array([5.83416667, 3.08666667, 3.70833333, 1.17 ])
scale_表示标准差
stdScater.scale_
array([0.81019502, 0.44327067, 1.76401924, 0.75317107])
进行数据归一transform
X_train=stdScater.transform(X_train)
stdScater.fit(X_test)
X_test_std=stdScater.transform(X_test)
X_train[:10,]
array([[-0.90616043, 0.93246262, -1.30856471, -1.28788802],
[-1.15301457, -0.19551636, -1.30856471, -1.28788802],
[-0.16559799, -0.64670795, 0.22203084, 0.17260355],
[ 0.45153738, 0.70686683, 0.95898425, 1.50032315],
[-0.90616043, -1.32349533, -0.40154513, -0.09294037],
[ 1.43895396, 0.25567524, 0.56216318, 0.30537551],
[ 0.3281103 , -1.09789954, 1.0723617 , 0.30537551],
[ 2.1795164 , -0.19551636, 1.63924894, 1.23477923],
[-0.78273335, 2.2860374 , -1.25187599, -1.42065998],
[ 0.45153738, -2.00028272, 0.44878573, 0.43814747]])
X_test_std[:10,]
array([[-0.31739042, 0.16012815, 0.3146853 , 0.23680294],
[-0.09068298, -0.37363236, 0.66219054, 1.3992901 ],
[-0.99751275, -1.70803364, -0.38032518, -0.40902326],
[-0.09068298, -0.64051262, 0.66219054, 0.7534639 ],
[-1.45092764, 0.42700841, -1.42284091, -1.44234518],
[-0.43074414, -1.17427313, 0.0250976 , -0.02152754],
[-0.2040367 , -0.37363236, 0.3146853 , -0.02152754],
[ 0.70279308, 0.16012815, 0.72010808, 0.88262914],
[ 0.47608563, -1.70803364, 0.25676776, -0.02152754],
[-0.43074414, -0.90739287, 0.25676776, -0.15069278]])
KNN进行分类
from sklearn.neighbors import KNeighborsClassifier
knn_clf=KNeighborsClassifier(n_neighbors=3)
knn_clf.fit(X_train,y_train)
KNeighborsClassifier(algorithm='auto', leaf_size=30, metric='minkowski',
metric_params=None, n_jobs=None, n_neighbors=3, p=2,
weights='uniform')
必须用归一化处理后的测试数据集X_test_std进行预测
knn_clf.score(X_test_std,y_test)
0.9666666666666667
knn_clf.score(X_test,y_test)
0.3333333333333333
MinMaxScater
import numpy as np
from sklearn import datasets
iris=datasets.load_iris()
X=iris.data
y=iris.target
from sklearn.model_selection import train_test_split
X_train,X_test,y_train,y_test=train_test_split(X,y,test_size=0.2,random_state=666)
from sklearn.preprocessing import MinMaxScaler
minmaxscater=MinMaxScaler()
minmaxscater.fit(X_train)
minmaxscater.fit(X_test)
X_train=minmaxscater.transform(X_train)
Y_test_std=minmaxscater.transform(X_test)
from sklearn.neighbors import KNeighborsClassifier
knn_clf=KNeighborsClassifier(n_neighbors=3)
knn_clf.fit(X_train,y_train)
knn_clf.score(X_test_std,y_test)
0.9666666666666667
knn_clf.score(X_test,y_test)
0.3333333333333333
自己瞎写
for i in range(X.shape[1]):
X_train[:,i]=(X_train[:,i]-np.mean(X_train[:,i]))/np.std(X_train[:,i])
for i in range(X.shape[1]):
X_test[:,i]=(X_test[:,i]-np.mean(X_train[:,i]))/np.std(X_train[:,i])
X_train[:10,]
array([[-0.90616043, 0.93246262, -1.30856471, -1.28788802],
[-1.15301457, -0.19551636, -1.30856471, -1.28788802],
[-0.16559799, -0.64670795, 0.22203084, 0.17260355],
[ 0.45153738, 0.70686683, 0.95898425, 1.50032315],
[-0.90616043, -1.32349533, -0.40154513, -0.09294037],
[ 1.43895396, 0.25567524, 0.56216318, 0.30537551],
[ 0.3281103 , -1.09789954, 1.0723617 , 0.30537551],
[ 2.1795164 , -0.19551636, 1.63924894, 1.23477923],
[-0.78273335, 2.2860374 , -1.25187599, -1.42065998],
[ 0.45153738, -2.00028272, 0.44878573, 0.43814747]])
X_test[:10]
array([[5.6, 3. , 4.5, 1.5],
[5.8, 2.8, 5.1, 2.4],
[5. , 2.3, 3.3, 1. ],
[5.8, 2.7, 5.1, 1.9],
[4.6, 3.1, 1.5, 0.2],
[5.5, 2.5, 4. , 1.3],
[5.7, 2.8, 4.5, 1.3],
[6.5, 3. , 5.2, 2. ],
[6.3, 2.3, 4.4, 1.3],
[5.5, 2.6, 4.4, 1.2]])
X_train_mean=np.array([np.mean(X_train[:,i]) for i in range (X.shape[1])])
X_train_std=np.array([np.std(X_train[:10,i]) for i in range (X.shape[1])])
X_train_mean
array([ 2.07241631e-16, 4.81096644e-16, -1.03620816e-16, 3.70074342e-16])
X_train_std
array([1.04213681, 1.18109687, 1.02159309, 0.97603196])