05-05 主成分分析代碼(手寫數字識別)

時間 2019-11-10

標籤成分分析代碼手寫數字識別简体版

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主成分分析代碼(手寫數字識別)

1、導入模塊

import time
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.font_manager import FontProperties
from sklearn import datasets
from sklearn.model_selection import train_test_split
from sklearn.decomposition import PCA
from sklearn.neighbors import KNeighborsClassifier
%matplotlib inline
font = FontProperties(fname='/Library/Fonts/Heiti.ttc')

2、數據預處理

# 導入手寫識別數字數據集
digits = datasets.load_digits()
X = digits.data
y = digits.target

X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=1)

3、KNN訓練數據

knn = KNeighborsClassifier()
knn.fit(X_train, y_train)

KNeighborsClassifier(algorithm='auto', leaf_size=30, metric='minkowski',
           metric_params=None, n_jobs=None, n_neighbors=5, p=2,
           weights='uniform')

3.1 準確度

knn.score(X_train, y_train)

0.9866369710467706

4、降維(2維)

pca = PCA(n_components=2)

pca.fit(X_train)
X_train_reduction = pca.transform(X_train)
X_test_reduction = pca.transform(X_test)

4.1 KNN訓練數據

begin = time.time()
knn = KNeighborsClassifier()
knn.fit(X_train_reduction, y_train)
end = time.time()
print('訓練耗時:{}'.format(end-begin))

訓練耗時:0.0011568069458007812

4.2 準確度

knn.score(X_test_reduction, y_test)

0.6266666666666667

4.3 二維特徵方差比例

pca.explained_variance_ratio_

array([0.14566794, 0.13448185])

5、查看原始數據特徵方差比例

pca = PCA(n_components=X_train.shape[1])
pca.fit(X_train)
pca.explained_variance_ratio_

array([1.45667940e-01, 1.34481846e-01, 1.19590806e-01, 8.63833775e-02,
       5.90548655e-02, 4.89518409e-02, 4.31561171e-02, 3.63466115e-02,
       3.41098378e-02, 3.03787911e-02, 2.38923779e-02, 2.24613809e-02,
       1.81136494e-02, 1.81125785e-02, 1.51771863e-02, 1.39510696e-02,
       1.32079987e-02, 1.21938163e-02, 9.95264723e-03, 9.39755156e-03,
       9.02644073e-03, 7.96537048e-03, 7.64762648e-03, 7.10249621e-03,
       7.04448539e-03, 5.89513570e-03, 5.65827618e-03, 5.08671500e-03,
       4.97354466e-03, 4.32832415e-03, 3.72181436e-03, 3.42451450e-03,
       3.34729452e-03, 3.20924019e-03, 3.03301292e-03, 2.98738373e-03,
       2.61397965e-03, 2.28591480e-03, 2.21699566e-03, 2.14081498e-03,
       1.86018920e-03, 1.57568319e-03, 1.49171335e-03, 1.46157540e-03,
       1.17829304e-03, 1.06805854e-03, 9.41934676e-04, 7.76116004e-04,
       5.59378443e-04, 3.65463486e-04, 1.71625943e-04, 8.78242589e-05,
       5.20662123e-05, 5.19689192e-05, 4.16826522e-05, 1.50475650e-05,
       4.42917130e-06, 3.53610879e-06, 7.14554374e-07, 6.80092943e-07,
       3.48757835e-07, 8.17776361e-34, 8.17776361e-34, 7.97764241e-34])

5.1 主成分所佔方差比例

plt.plot([i for i in range(X_train.shape[1])],
         [np.sum(pca.explained_variance_ratio_[:i+1]) for i in range(X_train.shape[1])],c='r')
plt.xlabel('前n個主成分',fontproperties=font)
plt.ylabel('前n個主成分方差所佔比例',fontproperties=font)
plt.show()

經過上圖能夠肯定取多少比例的主成分能平衡模型的準確率和訓練速度。git

6、保留原始維度的80%的維度

# 0.95表示保留原始維度的80%的維度
pca = PCA(0.80)
pca.fit(X_train)

PCA(copy=True, iterated_power='auto', n_components=0.8, random_state=None,
  svd_solver='auto', tol=0.0, whiten=False)

6.1 查看主成分個數

pca.n_components_

6.2 降維(13維)

X_train_reduction = pca.transform(X_train)
X_test_reduction = pca.transform(X_test)

6.3 KNN訓練數據

begin = time.time()
knn = KNeighborsClassifier()
knn.fit(X_train_reduction, y_train)
end = time.time()
print('訓練耗時:{}'.format(end-begin))

訓練耗時:0.004214048385620117

6.4 準確度

knn.score(X_test_reduction, y_test)

0.9844444444444445

7、小結

主成分分析做爲降維的做用，可是若是過度降維，降維到2維的時候能夠看到模型的準確率很是低；若是降維到80%左右，準確度沒有什麼太大的影響。因爲數據量過少，因此降維的優勢即模型訓練速度加快的優點並無體現出來，可是在工業上PCA必定是經過丟失一部分信息+下降模型準確度換取模型訓練速度。算法

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