python 实现主成份分析

from sklearn.datasets import load_iris
import numpy as np
from numpy import linalg

def pca(X,k):
    #去中心化
    X = X-X.mean(axis = 0)
    #每一行代表特征，每一列代表样本
    X_cov = np.cov(X.T,ddof = 0)
    #特征值，和特征向量
    eigenvalues,eigenvectors = linalg.eig(X_cov)
    #前k个最大的特征向量
    klarge_index = eigenvalues.argsort()[-k:][::-1]
    k_eigenvectors = eigenvectors[klarge_index]
    return np.dot(X,k_eigenvectors.T)
iris = load_iris()
X = iris.data
k =2
X_pca = pca(X,k)

#查看各特征值的贡献率

from sklearn.datasets import load_iris
import numpy as np
from numpy import linalg
import matplotlib.pyplot as plt

iris = load_iris()
X = iris.data
X = X-X.mean(axis = 0)
#每一行代表特征，每一列代表样本
X_cov = np.cov(X.T,ddof = 0)
#特征值，和特征向量
 eigenvalues,eigenvectors = linalg.eig(X_cov)
total =sum(eigenvalues)
var_exp = [ (i/total) for i in sorted(eigenvalues,reverse = True)]
cum_var_exp =np.cumsum(var_exp)
plt.bar(range(1,5),var_exp,alpha=0.5,align = ‘center‘,label = ‘individual var‘)
plt.step(range(1,5),cum_var_exp,where = ‘mid‘,label = ‘cumulative var‘)
plt.ylabel(‘variance rtion‘)
plt.xlabel(‘principal conponents‘)
plt.legend(loc = ‘best‘)
plt.show()