選擇主成分數量

R 的多變量機率分配

Surajit Ray

Professor, University of Glasgow

princomp 物件摘要

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 scree plot

方法 1

解釋變異比例

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

依 {{2}} 決定：

曲線前段越陡越好
之後進入平坦段

累積變異解釋

方法 2

累積變異
達到預設門檻

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

計算累積解釋變異比例

累積比例

# 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)

計算累積解釋變異比例

累積比例

# 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 個主成分可解釋 90% 的變異

一起來練習吧！

R 的多變量機率分配