import pandas as pd
import  numpy as np
import matplotlib.pyplot as pltdf = pd.read_csv('iris.data')
print(df.head())df.columns=['sepal_len', 'sepal_wid', 'petal_len', 'petal_wid', 'class']
print(df.head())# 用来储存变量
X = df.ix[:, 0:4].values
#用来储存标签
y = df.ix[:, 4].values   msg ={'Iris-setosa':0, 'Iris-versicolor':1, 'Iris-virginica':2}
df['class'] = df['class'].map(msg)  #把字母换成数字#进行标准化
from sklearn.preprocessing import StandardScaler
Scaler = StandardScaler()
X_Scaler = Scaler.fit_transform(X)# 求每一行的均值
mean_vec = np.mean(X_Scaler, axis=0)
#去均值后求协方差矩阵
cov_mat = (X_Scaler-mean_vec).T.dot(X_Scaler-mean_vec)/(X_Scaler.shape[0]-1)
print(cov_mat)
#使用np求协方差矩阵,结果是一样的
cov_mat = np.cov(X_Scaler.T)
print(cov_mat)

# 求特征值和特征向量
eig_vals, eig_vecs = np.linalg.eig(cov_mat)
print(eig_vals, eig_vecs)#将特征值与特征向量合并
eig_pairs = [(np.abs(eig_vals[i]), eig_vecs[:, i]) for i in range(len(eig_vals))] #组合对应
eig_pairs.sort(key=lambda x:x[0], reverse=True)tot = sum(eig_vals)var_exp = [(i/tot)*100 for i in sorted(eig_vals, reverse=True)]
#cumsum表示每前两个数相加
cum_var_exp = np.cumsum(var_exp)
#画图
plt.figure(figsize=(6, 4))
#画柱状图
plt.bar(range(4), var_exp, alpha=0.5, align='center',label='individual explained variance')
#画步阶图
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()

#把4维矩阵降低到两维，取前两个特征向量组合转置点乘即可#np.hstack合并两个向量,reshape让一行变成一列,相当于转置
matrix_w = np.hstack((eig_pairs[0][1].reshape(4,1),eig_pairs[1][1].reshape(4,1)))#变换以后的矩阵149*4 .dot 4*2 = 149*2
become_X_Scaler = X_Scaler.dot(matrix_w)
print(become_X_Scaler)
plt.figure(figsize=(6, 4))color = np.array(['red', 'green', 'blue']) #构成行列式
plt.scatter(become_X_Scaler[:,0], become_X_Scaler[:,1], c=color[df['class']])  #画出种类对应颜色的散点图
plt.show()