主成分分析 - 如何获得每个参数对 Prin.Comp. 的贡献 (%)? [英] Principal Components Analysis - how to get the contribution (%) of each parameter to a Prin.Comp.?
问题描述
我想知道测量/参数对计算的主成分之一的贡献程度.
I want to know to what degree a measurement/parameter contributes to one of the calculated principal components.
真实世界的描述:
- 我有五个关于物种地理分布的气候参数
- 我使用这五个参数执行了 PCA
- PC1 与 PC2 的图显示了一个有趣的模式
问题:如何获得(每个参数)对每台 PC 的贡献百分比?
Question: How do I get the percentage of contribution (of each parameter) to each PC?
我期望的是:PC1 由参数 1 的 30%、参数 2 的 50%、参数 3 的 20%、参数 4 的 0% 和参数 5 的 0% 组成.PC2组成...
What I expect: PC1 is composed to 30% of parameter1, to 50% of parameter2, to 20% of parameter3, 0% of parameter4 and 0% of parameter5. PC2 is composed...
具有 5 个虚拟参数的示例:
An example with 5 dummy-parameters:
a <- rnorm(10, 50, 20)
b <- seq(10, 100, 10)
c <- seq(88, 10, -8)
d <- rep(seq(3, 16, 3), 2)
e <- rnorm(10, 61, 27)
my_table <- data.frame(a, b, c, d, e)
pca <- princomp(my_table, cor=T)
biplot(pca) # same: plot(pca$scores[,1], pca$scores[,2])
pca
summary(pca)
我的信息隐藏在哪里?
推荐答案
你想要返回对象的 $loadings 组件:
You want the $loadings component of the returned object:
R> class(pca$loadings)
[1] "loadings"
R> pca$loadings
Loadings:
Comp.1 Comp.2 Comp.3 Comp.4 Comp.5
a -0.198 0.713 -0.671
b 0.600 0.334 -0.170 0.707
c -0.600 -0.334 0.170 0.707
d 0.439 -0.880 -0.180
e 0.221 0.701 0.678
Comp.1 Comp.2 Comp.3 Comp.4 Comp.5
SS loadings 1.0 1.0 1.0 1.0 1.0
Proportion Var 0.2 0.2 0.2 0.2 0.2
Cumulative Var 0.2 0.4 0.6 0.8 1.0
请注意，它有一个特殊的 print() 方法，可以抑制打印小负载.
Note that this has a special print() method which suppresses printing of small loadings.
如果您希望将其作为相对贡献，则将每列的载荷相加，并将每个载荷表示为列(载荷)总和的比例，注意使用绝对值来说明负载荷.
If you want this as a relative contribution then sum up the loadings per column and express each loading as a proportion of the column (loading) sum, taking care to use the absolute values to account for negative loadings.
R> load <- with(pca, unclass(loadings))
R> load
Comp.1 Comp.2 Comp.3 Comp.4 Comp.5
a -0.1980087 0.712680378 0.04606100 -0.6713848 0.000000e+00
b 0.5997346 -0.014945831 0.33353047 -0.1698602 7.071068e-01
c -0.5997346 0.014945831 -0.33353047 0.1698602 7.071068e-01
d 0.4389388 0.009625746 -0.88032515 -0.1796321 5.273559e-16
e 0.2208215 0.701104321 -0.02051507 0.6776944 -1.110223e-16
这最后一步产生对每个主成分的比例贡献
This final step then yields the proportional contribution to the each principal component
R> aload <- abs(load) ## save absolute values
R> sweep(aload, 2, colSums(aload), "/")
Comp.1 Comp.2 Comp.3 Comp.4 Comp.5
a 0.09624979 0.490386943 0.02853908 0.35933068 0.000000e+00
b 0.29152414 0.010284050 0.20665322 0.09091055 5.000000e-01
c 0.29152414 0.010284050 0.20665322 0.09091055 5.000000e-01
d 0.21336314 0.006623362 0.54544349 0.09614059 3.728970e-16
e 0.10733880 0.482421595 0.01271100 0.36270762 7.850462e-17
R> colSums(sweep(aload, 2, colSums(aload), "/"))
Comp.1 Comp.2 Comp.3 Comp.4 Comp.5
1 1 1 1 1
<小时>
如果使用首选的 prcomp() 那么相关的加载在 $rotation 组件中:
If using the preferred prcomp() then the relevant loadings are in the $rotation component:
R> pca2 <- prcomp(my_table, scale = TRUE)
R> pca2$rotation
PC1 PC2 PC3 PC4 PC5
a -0.1980087 0.712680378 -0.04606100 -0.6713848 0.000000e+00
b 0.5997346 -0.014945831 -0.33353047 -0.1698602 -7.071068e-01
c -0.5997346 0.014945831 0.33353047 0.1698602 -7.071068e-01
d 0.4389388 0.009625746 0.88032515 -0.1796321 -3.386180e-15
e 0.2208215 0.701104321 0.02051507 0.6776944 5.551115e-17
现在相关的咒语是:
R> aload <- abs(pca2$rotation)
R> sweep(aload, 2, colSums(aload), "/")
PC1 PC2 PC3 PC4 PC5
a 0.09624979 0.490386943 0.02853908 0.35933068 0.000000e+00
b 0.29152414 0.010284050 0.20665322 0.09091055 5.000000e-01
c 0.29152414 0.010284050 0.20665322 0.09091055 5.000000e-01
d 0.21336314 0.006623362 0.54544349 0.09614059 2.394391e-15
e 0.10733880 0.482421595 0.01271100 0.36270762 3.925231e-17
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