PCA（主成分分析）

import numpy as np
import pandas as pd

# 读取数据集
df=pd.read_csv('iris.data')
#原始数据没有给定别名，自己加上
df.columns=['sepal_len', 'sepal_wid', 'petal_len', 'petal_wid', 'class']
print(df.head())

# 把数据分成特征和标签
X=df.iloc[:,0:4].values
y=df.iloc[:,4].values

from matplotlib import pyplot as plt
# 展示我们标签用的
label_dict={
    1:'Iris-Setosa',
    2:'Iris-Versicolor',
    3:'Iris-Virgnica'
}

# 展示特征用的
feature_dict={
    0:'speal length [cm]',
    1:'sepal width [cm]',
    2:'petal length [cm]',
    3:'petal width [cm]'
}

# 指定绘图区域大小
plt.figure(figsize=(8,6))
for cnt in range(4):
#     这里用子图来呈现4个特征
    plt.subplot(2,2,cnt+1)
    for lab in ('Iris-setosa','Iris-versicolor','Iris-virginica'):
        plt.hist(X[y == lab, cnt],
                 label=lab,
                 bins=10,
                 alpha=0.3, )
        plt.xlabel(feature_dict[cnt])
        plt.legend(loc='upper right', fancybox=True, fontsize=8)

plt.tight_layout()
plt.show()

# 一般情况都是先对数据进行标准化处理
from sklearn.preprocessing import StandardScaler
X_std=StandardScaler().fit_transform(X)

# 计算协方差矩阵
mean_vec=np.mean(X_std,axis=0)
cov_mat=(X_std-mean_vec).T.dot((X_std-mean_vec))/(X_std.shape[0]-1)
print('协方差矩阵\n%s'%cov_mat)

# numpy计算协方差矩阵
print('Numpy 计算协方差矩阵：\n%s'%np.cov(X_std.T))

# 计算特征向量与特征值
cov_mat=np.cov(X_std.T)

eig_vals,eig_vecs=np.linalg.eig(cov_mat)

print('特征向量\n%s'%eig_vecs)
print('\n特征值\n%s'%eig_vals)

# 把特征值和特征向量对应起来
eig_pairs = [(np.abs(eig_vals[i]), eig_vecs[:,i]) for i in range(len(eig_vals))]
print (eig_pairs)
print ('----------')
# 把它们按照特征值大小进行排序
eig_pairs.sort(key=lambda x: x[0], reverse=True)

# 打印排序结果
print('特征值由大到小排序结果:')
for i in eig_pairs:
    print(i[0])

# 计算累加结果
tot = sum(eig_vals)
var_exp = [(i / tot)*100 for i in sorted(eig_vals, reverse=True)]
print (var_exp)
cum_var_exp = np.cumsum(var_exp)
print(cum_var_exp)


plt.figure(figsize=(6, 4))

plt.bar(range(4), var_exp, alpha=0.5, align='center',
            label='individual explained variance')
plt.step(range(4), cum_var_exp, where='mid',
             label='cumulative explained variance')
plt.ylabel('Explained variance ratio')
plt.xlabel('Principal components')
plt.legend(loc='best')
plt.tight_layout()
plt.show()

matrix_w = np.hstack((eig_pairs[0][1].reshape(4,1),
                      eig_pairs[1][1].reshape(4,1)))

print('Matrix W:\n', matrix_w)

Y = X_std.dot(matrix_w)
print(Y)

plt.figure(figsize=(6, 4))
for lab, col in zip(('Iris-setosa', 'Iris-versicolor', 'Iris-virginica'),
                        ('blue', 'red', 'green')):
     plt.scatter(X[y==lab, 0],
                X[y==lab, 1],
                label=lab,
                c=col)
plt.xlabel('sepal_len')
plt.ylabel('sepal_wid')
plt.legend(loc='best')
plt.tight_layout()
plt.show()

plt.figure(figsize=(6, 4))
for lab, col in zip(('Iris-setosa', 'Iris-versicolor', 'Iris-virginica'),
                        ('blue', 'red', 'green')):
     plt.scatter(Y[y==lab, 0],
                Y[y==lab, 1],
                label=lab,
                c=col)
plt.xlabel('Principal Component 1')
plt.ylabel('Principal Component 2')
plt.legend(loc='lower center')
plt.tight_layout()
plt.show()