PCA和LDA降维的比较

PCA 主成分分析方法，LDA 线性判别分析方法，可以认为是有监督的数据降维。下面的代码分别实现了两种降维方式:

print(__doc__)

import matplotlib.pyplot as plt

from sklearn import datasets
from sklearn.decomposition import PCA
from sklearn.discriminant_analysis import LinearDiscriminantAnalysis

iris = datasets.load_iris()

X = iris.data
y = iris.target
target_names = iris.target_names

pca = PCA(n_components=2)
X_r = pca.fit(X).transform(X)

lda = LinearDiscriminantAnalysis(n_components=2)
X_r2 = lda.fit(X, y).transform(X)

# Percentage of variance explained for each components
print('explained variance ratio (first two components): %s'
      % str(pca.explained_variance_ratio_))

plt.figure()
for c, i, target_name in zip("rgb", [0, 1, 2], target_names):
    plt.scatter(X_r[y == i, 0], X_r[y == i, 1], c=c, label=target_name)
plt.legend()
plt.title('PCA of IRIS dataset')

plt.figure()
for c, i, target_name in zip("rgb", [0, 1, 2], target_names):
    plt.scatter(X_r2[y == i, 0], X_r2[y == i, 1], c=c, label=target_name)
plt.legend()
plt.title('LDA of IRIS dataset')

plt.show()

结果如下