sklearn降维

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PCA

from sklearn.datasets import load_iris
from sklearn.decomposition import PCA
import matplotlib.pyplot as mp, seaborn
from mpl_toolkits import mplot3d
import matplotlib.gridspec as mg  # 子图绘制

# 载入样本
iris = load_iris()
X = iris.data
y = iris.target

# 降维、设置参数
pca3 = PCA(n_components=3)  # 降到3d
X3 = pca3.fit_transform(X)
print(pca3.explained_variance_ratio_)

pca2 = PCA(n_components=0.93)  # 降到2d
X2 = pca2.fit_transform(X)

pca1 = PCA(n_components=1)  # 降到1d
X1 = pca1.fit_transform(X)

# 绘图
ax = mplot3d.Axes3D(mp.figure(figsize=(4, 3)))
ax.scatter(X3[:, 0], X3[:, 1], X3[:, 2], s=88, c=y, alpha=0.5)
mp.show()

c = ['purple', 'cyan', 'yellow']
gs = mg.GridSpec(1, 3)
mp.subplot(gs[0, :2])
mp.scatter(X2[:, 1], X2[:, 0], s=88, c=y, alpha=0.5)
mp.subplot(gs[0, 2])
for i in range(3):
    seaborn.boxplot(data=X1[y == i, 0], color=c[i])
mp.xticks(())
mp.yticks(())
mp.show()

LDA

from sklearn.datasets import load_iris
from sklearn.discriminant_analysis import LinearDiscriminantAnalysis
import matplotlib.pyplot as mp, seaborn
import matplotlib.gridspec as mg

# 载入样本
iris = load_iris()
X = iris.data
y = iris.target

# 降维、设置参数
lda2 = LinearDiscriminantAnalysis(n_components=2)  # 最多降到类别数k-1的维数
X2 = lda2.fit(X, y).transform(X)
print(lda2.explained_variance_ratio_)

lda1 = LinearDiscriminantAnalysis(n_components=1)  # 降到1维
X1 = lda1.fit(X, y).transform(X)

# 绘图
c = ['purple', 'cyan', 'yellow']
gs = mg.GridSpec(1, 3)
mp.subplot(gs[0, :2])
for i in range(3):
    mp.scatter(X2[y == i, 1], X2[y == i, 0], s=50, c=c[i], alpha=0.5)
mp.subplot(gs[0, 2])
for i in range(3):
    seaborn.boxplot(data=X1[y == i, 0], color=c[i])
mp.xticks(())
mp.yticks(())
mp.show()

附录

En	Cn
Dimensionality reduction	降维
Principal Components Analysis	主成分分析
Linear Discriminant Analysis	线性判别分析
decomposition	n. 分解
variance	变异；方差
ratio	比例
MLE	最大似然估计 Maximum Likelihood Estimate