PCA 降维



import numpy as np
import pandas as pda
from sklearn.datasets import load_iris
import matplotlib.pyplot as plt
#加载数据
iris=load_iris()
# print(iris)
data=iris["data"]
labels=iris["target"]
# print(data,labels)
df=pda.DataFrame(data,columns=["sepal_len","sepal_width","petal_len","petal_width"])
df["Irsa-setosa"]=labels
#处理数据
df.ix[df["Irsa-setosa"]==0,"Irsa-setosa"]="Iris-Setosa"
df.ix[df["Irsa-setosa"]==1,"Irsa-setosa"]="Iris-Versicolor"
df.ix[df["Irsa-setosa"]==2,"Irsa-setosa"]="Iris-Virgnica"

# print(df)
# print(df.shape)
X=data
# print(X)
y=df["Irsa-setosa"].values

label_dict={1:"Iris-Setosa",
            2: "Iris-Versicolor",
            3: "Iris-Virgnica"}
feature_dict={0:"sepal  length(cm)",
              1:"sepal width(cm)",
              2:"petal length(cm)",
              3:"petal width(cm)"}

plt.figure(figsize=(14,8))
for i in range(4):
    plt.subplot(2,2,i+1)
    for lab in ("Iris-Setosa","Iris-Versicolor","Iris-Virgnica"):
        plt.hist(X[y==lab,i],bins=20,alpha=0.8,label=lab)
    plt.xlabel(feature_dict[i])
    plt.legend(loc="upper right",fancybox=True,fontsize=8)
plt.show()

#标准化，消除量纲
from sklearn.preprocessing import StandardScaler

X_std=StandardScaler().fit_transform(X)
# print(X_std)
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("Covarinance matrix :\n",cov_mat)

eig_vals,eig_vecs=np.linalg.eig(cov_mat)
# print("Eigenvectors \n %s" %eig_vecs)  #特征向量
# print("\nEigenvalues \n %s" %eig_vals)   #特征值

eig_pairs=[(np.abs(eig_vals[i]),eig_vecs[:,i]) for i in range(len(eig_vals))]
print()
print(eig_pairs)

eig_pairs.sort(key= lambda x:x[0],reverse=True)  #按照键值进行排序

print("Eigenvalues in descending order:")
for i in eig_pairs:
    print(i[0])
print("==========================================")
tot=sum(eig_vals)
vars_exp=[(i/tot)*100 for i in sorted(eig_vals,reverse=True)]
print(vars_exp)
# [72.77045209380134, 23.030523267680636, 3.683831957627396, 0.5151926808906299]
#cumsum n等于(0,n-1)的和
cum_var_exp=np.cumsum(vars_exp)
print(cum_var_exp)
# [ 72.77045209  95.80097536  99.48480732 100.        ]

plt.figure(figsize=(10,8))
plt.bar(range(4),vars_exp,alpha=0.5,align="center",label="individual explained variance ")
plt.step(range(4),cum_var_exp,where="mid",label="cumulative explained variance ")
plt.xlabel("Principal components")
plt.ylabel("Explained variance ratio")
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",matrix_w)

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

plt.figure(figsize=(6, 4))
for lab, col in zip(('Iris-Setosa', 'Iris-Versicolor', 'Iris-Virgnica'),('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-Virgnica'),('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()