【sklearn】PCA

sklearn.decomposition.PCA

import matplotlib.pyplot as plt
from sklearn.datasets import load_iris
from sklearn.decomposition import PCA

iris = load_iris()
X = iris.data
Y = iris.target
#  Two dimensional array , Four dimensional characteristic matrix 
X.shape 
(150, 4)

PCA() Use

#  Default dimension reduction to min(X.shape)
pca = PCA(n_components=2) #  drop to 2 dimension 
pca = pca.fit(X)
X_dr = pca.transform(X)
# X_dr = PCA(2).fit_transform(X)
X_dr.shape
 (150, 2)

#  Dimensionality reduction 2 Weihou , It is convenient to draw pictures to view the sample distribution 
plt.figure()
plt.scatter(X_dr[Y==0, 0], X_dr[Y==0, 1], c='red', label=iris.target_names[0])
plt.scatter(X_dr[Y==1, 0], X_dr[Y==1, 1], c='black', label=iris.target_names[1])
plt.scatter(X_dr[Y==2, 0], X_dr[Y==2, 1], c='orange', label=iris.target_names[2])
plt.title('PCA of IRIS dataset')
plt.legend()
plt.show()
#  Closer, more similar , It's perfect for KNN Equal clustering model 

#  Check the amount of information of the new eigenvector ( Interpretable variance )
print(pca.explained_variance_)
#  View the percentage of the information of the new feature vector in the information of the original data ( Explanatory variance contribution rate )
print(pca.explained_variance_ratio_)
#  The amount of information retained after dimensionality reduction 
print(pca.explained_variance_ratio_.sum())
''' [4.22824171 0.24267075] [0.92461872 0.05306648] 0.9776852063187949 '''

Cumulative interpretable variance contribution rate curve

pca_line = PCA().fit(X)
print(pca_line.explained_variance_ratio_)
 [0.92461872 0.05306648 0.01710261 0.00521218]
'''  drop to 1 Dimension retention 0.92461872,  drop to 2 Dimension retention 0.92461872+0.05306648  drop to 4 Dimension retention 1 array([0.92461872, 0.05306648, 0.01710261, 0.00521218]) '''
import numpy as np
# np.cumsum(pca_line.explained_variance_ratio_) #  Add up 
plt.plot([1,2,3,4], np.cumsum(pca_line.explained_variance_ratio_))
plt.xticks([1,2,3,4]) #  Limit the axis to display integers 
plt.xlabel('number of components after dimention reduction')
plt.ylabel('cumulative explained variance ratio')
plt.show()

n_components=‘mle’ Optional

#  Maximum likelihood estimation (mle) Optional super parameter 
#  Large amount of computation 
pca_mle = PCA(n_components='mle')
pca_mle = pca_mle.fit(X)
X_mle = pca_mle.transform(X)
print(pca_mle.explained_variance_ratio_)
 [0.92461872 0.05306648 0.01710261]
#  Visible drop 3 Best dimension 

Select the super parameter according to the proportion of information SVD

'''  Try , Select the dimension to drop   It is stipulated that the information will be retained after dimensionality reduction 0.97, add to svd_solver='full' svd Singular value decomposition (solver solver ) auto  Automatically select according to the amount of data full or randomized full  Suitable for small amount of data  randomized  Fit feature matrix  arpack ( commonly auto, It doesn't work out randomized) '''
pca_f = PCA(n_components=0.97, svd_solver='full')
pca_f = pca_f.fit(X)
X_f = pca_f.transform(X)
print(pca_f.explained_variance_ratio_)
 [0.92461872 0.05306648]