目录
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主成分分析代码(手写数字识别)
一、导入模块
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')
二、数据预处理
# 导入手写识别数字数据集
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)
三、KNN训练数据
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 准确度
knn.score(X_train, y_train)
0.9866369710467706
四、降维(2维)
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训练数据
begin = time.time()
knn = KNeighborsClassifier()
knn.fit(X_train_reduction, y_train)
end = time.time()
print('训练耗时:{}'.format(end-begin))
训练耗时:0.0011568069458007812
4.2 准确度
knn.score(X_test_reduction, y_test)
0.6266666666666667
4.3 二维特征方差比例
pca.explained_variance_ratio_
array([0.14566794, 0.13448185])
五、查看原始数据特征方差比例
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 主成分所占方差比例
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个主成分',fontproperties=font)
plt.ylabel('前n个主成分方差所占比例',fontproperties=font)
plt.show()
通过上图可以确定取多少比例的主成分能平衡模型的准确率和训练速度。
六、保留原始维度的80%的维度
# 0.95表示保留原始维度的80%的维度
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 查看主成分个数
pca.n_components_
13
6.2 降维(13维)
X_train_reduction = pca.transform(X_train)
X_test_reduction = pca.transform(X_test)
6.3 KNN训练数据
begin = time.time()
knn = KNeighborsClassifier()
knn.fit(X_train_reduction, y_train)
end = time.time()
print('训练耗时:{}'.format(end-begin))
训练耗时:0.004214048385620117
6.4 准确度
knn.score(X_test_reduction, y_test)
0.9844444444444445
七、小结
主成分分析作为降维的作用，但是如果过分降维，降维到2维的时候可以看到模型的准确率非常低；如果降维到80%左右，准确度没有什么太大的影响。由于数据量过少，所以降维的优点即模型训练速度加快的优势并没有体现出来，但是在工业上PCA一定是通过丢失一部分信息+降低模型准确度换取模型训练速度。