數據歸一化

除了·邊界比較明顯的數據集（像素），一般用均值方差歸一化。

測試數據集要用訓練集的平均數和標準差進行歸一化

import numpy as np import matplotlib.pyplot as plt

最值歸一化 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>

數據均值

np.mean(X[:,0]) 0.540204081632653 np.mean(X[:,1]) 0.5147916666666666

數據標準差

np.std(X[:,0]) 0.28443891736063087 np.std(X[:,1]) 0.28634346181639975

均值方差歸一化

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_表示標準差

stdScater.scale_ array([0.81019502, 0.44327067, 1.76401924, 0.75317107])

進行數據歸一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進行分類

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')

必須用歸一化處理后的測試數據集X_test_std進行預測

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.targetfrom 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

自己瞎寫

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])

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