选择主成分个数

R 中的多元概率分布

Surajit Ray

Professor, University of Glasgow

princomp 对象摘要

summary(cars.pca)

Importance of components:
                       Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8  Comp.9
Standard deviation      2.378  1.443  0.710 0.5148 0.4280 0.3518 0.3241 0.2419 0.14896
Proportion of Variance  0.628  0.231  0.056 0.0294 0.0204 0.0138 0.0117 0.0065 0.00247
Cumulative Proportion   0.628  0.860  0.916 0.9453 0.9656 0.9794 0.9910 0.9975 1.00000

使用碎石图

方法 1

方差解释占比

screeplot(cars.pca, type = "lines")

依据 {{2}} 选择：

曲线最陡处
随后进入平坦段

累计方差解释

方法 2

累计方差
解释预设阈值

summary(cars.pca)

Importance of components:
                      Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8  Comp.9
Standard deviation     2.378  1.443  0.710 0.5148 0.4280 0.3518 0.3241 0.2419 0.14896
Proportion of Variance 0.628  0.231  0.056 0.0294 0.0204 0.0138 0.0117 0.0065 0.00247
Cumulative Proportion  0.628  0.860  0.916 0.9453 0.9656 0.9794 0.9910 0.9975 1.00000

计算累计方差占比

累计占比

# Variance explained
pc.var <- cars.pca$sdev^2

# Proportion of variation
pc.pvar <- pc.var / sum(pc.var)

# Cumulative proportion
plot(cumsum(pc.pvar), type = 'b')

abline(h = 0.9, lty = 2)

计算累计方差占比

累计占比

# Variance explained
pc.var <- cars.pca$sdev^2

# Proportion of variation
pc.pvar <- pc.var / sum(pc.var)

# Cumulative proportion
plot(cumsum(pc.pvar), type = 'b')

abline(h = 0.9, lty = 2)

3 个主成分解释了 90% 的方差

让我们来练习！

R 中的多元概率分布