如何针对具有多个组的数据集对每个组执行PCA？
我有一个来自四个人群,四个治疗和三个重复的个体数据集.每个人只有一个人群,治疗和复制组合.我从每个人那里做了四次测量.我想针对每个群体,底物和重复组合对这些测量进行PCA.
我知道如何对所有个体进行PCA,我可以将数据集分成多个数据集,用于每个群体,底物和复制的组合,然后在每个新数据集上执行PCA.
如何在完整的数据集上进行PCA,获得单独的PC1,PC2 ...每种组合的种群,底物和最高效的复制结果？我考虑过将数据集转换为列表,但不确定如何将princomp函数应用于列表.我是在正确的轨道上吗？
样本数据:
TestData<- structure(list(Location = c("A", "A", "A", "A", "A", "A", "A", "A", "A", "A", "A", "A",
"B", "B", "B", "B", "B", "B", "B", "B", "B", "B", "B", "B",
"C", "C", "C", "C", "C", "C", "C", "C", "C", "C", "C", "C",
"D", "D", "D", "D", "D", "D", "D", "D", "D", "D", "D", "D"),
Substrate = c("A", "B", "C", "D", "A", "B", "C", "D", "A", "B", "C", "D",
"A", "B", "C", "D", "A", "B", "C", "D", "A", "B", "C", "D",
"A", "B", "C", "D", "A", "B", "C", "D", "A", "B", "C", "D",
"A", "B", "C", "D", "A", "B", "C", "D", "A", "B", "C", "D"),
Replicate = c(1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L,
1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L,
1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L,
1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L),
Adult_Weight = c(0.0092, 0.0083, 0.0088, 0.0077, 0.0088, 0.01,
0.0099, 0.011, 0.0078, 0.0086, 0.0071, 0.0093,
0.0111, 0.01, 0.0097, 0.0091, 0.0083, 0.0098,
0.0093, 0.009, 0.0114, 0.0087, 0.0094, 0.0096,
0.0099, 0.0105, 0.0091, 0.0115, 0.0106, 0.0104,
0.0113, 0.0115, 0.0107, 0.0126, 0.0106, 0.0101,
0.0095, 0.0113, 0.0111, 0.0118, 0.0114, 0.0123,
0.0119, 0.0103, 0.0119, 0.0116, 0.0112, 0.0114),
Adult_Thorax_Width = c(1.31, 1.31, 1.43, 1.45, 1.52, 1.43, 1.57, 1.45, 1.43, 1.54, 1.32, 1.49,
1.58, 1.36, 1.42, 1.45, 1.48, 1.38, 1.55, 1.46, 1.52, 1.42, 1.6, 1.49,
1.48, 1.58, 1.51, 1.53, 1.54, 1.76, 1.63, 1.62, 1.44, 1.51, 1.53, 1.58,
1.46, 1.94, 1.54, 2.09, 1.5, 1.65, 1.86, 1.54, 1.8, 1.98, 1.82, 1.63),
Adult_Wing_Length = c(1359L, 1377L, 1555L, 1559L, 1562L, 1578L, 1580L, 1588L, 1597L, 1598L, 1603L, 1605L,
1612L, 1614L, 1616L, 1617L, 1623L, 1628L, 1639L, 1642L, 1643L, 1649L, 1651L, 1652L,
1653L, 1653L, 1654L, 1656L, 1656L, 1656L, 1662L, 1664L, 1665L, 1668L, 1670L, 1670L,
1671L, 1672L, 1674L, 1682L, 1685L, 1687L, 1688L, 1694L, 1698L, 1698L, 1707L, 1708L),
Adult_Leg_Length = c(414L, 390L, 627L, 541L, 430L, 450L, 451L, 462L, 443L, 582L, 435L, 579L,
499L, 418L, 444L, 646L, 589L, 466L, 435L, 477L, 450L, 606L, 660L, 450L,
446L, 480L, 462L, 438L, 483L, 454L, 492L, 457L, 463L, 499L, 470L, 474L,
627L, 478L, 473L, 496L, 666L, 499L, 480L, 461L, 450L, 483L, 460L, 584L)),
.Names = c("Location", "Substrate", "Replicate", "Weight", "Thorax_Width", "Wing_Length", "Leg_Length"),
row.names = c(NA, 48L),
class = "data.frame")
如果我正确理解您的数据组成,您应该将您的人口和治疗输入为因子变量,并将三个重复作为单独的行.列类型如下:
- 第一栏人口:因素
- 第二栏处理:因素
- 第3 - 第6列测量:数字(总共4列)
整个数据类应该优选为' data.frame ',因为在' data.frame '中,您的列可能具有不同的类类型(例如,与' matrix ' 不同).
下面是根据因子变量对示例Iris数据集进行分层的示例,此处为' iris $ Species '.如果您要对多个因子进行分层,则可以使用两个(或更多)柱状矩阵作为INDICES参数的输入.你确定你真的不是指一个带注释的PCA吗？这可以通过将因子类型变量更改为数字并在散点图中注释它们来轻松完成,例如通过' col '(= color)和' pch '(= symbol)参数.
data(iris) # Load the example Iris-dataset
class(iris)
lapply(iris, FUN=class)
#> class(iris)
#[1] "data.frame"
#>
#> lapply(iris, FUN=class)
#$Sepal.Length
#[1] "numeric"
#
#$Sepal.Width
#[1] "numeric"
#
#$Petal.Length
#[1] "numeric"
#
#$Petal.Width
#[1] "numeric"
#
#$Species
#[1] "factor"
par(mfrow=c(2,2), mar=c(4,4,2,1))
# Separate PCA plot for each Species
# Apply our defined PCA-function where each unique INDICES are handled as a separate function call
by(iris, INDICES=iris$Species, FUN=function(z){
# Use numeric fields for the PCA
pca <- prcomp(z[,unlist(lapply(z, FUN=class))=="numeric"])
plot(pca$x[,1:2], pch=16, main=z[1,"Species"]) # 2 first principal components
z
})
# Color annotation
# Use numeric fields for the PCA
pca <- prcomp(iris[,unlist(lapply(iris, FUN=class))=="numeric"])
plot(pca$x[,1:2], pch=16, col=as.numeric(iris[,"Species"]), main="Color annotation") # 2 first principal components
legend("bottom", pch=16, col=unique(as.numeric(iris[,"Species"])), legend=unique(iris[,"Species"]))
请注意,从左上角开始计算的前三个面板中的PCA轴不相同.这是因为当仅计算分组PCA时,PCA计算中的协方差矩阵不相同.
或者,如果您想要一个PCA,但只是在自己的窗口中绘制属于不同类别的观察结果,您可以尝试以下方面的内容:
par(mfrow=c(1,3))
# Compute the PCA
pca <- prcomp(iris[,unlist(lapply(iris, FUN=class))=="numeric"])
# Apply a plotting function over unique values of iris$Species, notice we always plot the same 'pca' object in all categories
lapply(unique(iris$Species), FUN=function(z) {
plot(pca$x[which(z==iris$Species),1:2], xlim=extendrange(pca$x[,1]), ylim=extendrange(pca$x[,2]),pch=16, main=z)
})
编辑:
出"的帮助文件的由 " -function:'指数:一个因素或因素的列表,每个长度nrow(数据)的’.
因此,我们可以分层的数据对于多个因子变量,如果我们提供了一个列表中内指数由 -function.这是一个人为的例子,其中"第一"和"第二"是两个同时分解数据的因素.这应该是微不足道的扩展到三个(或更多)变量:
ex <- cbind(matrix(rnorm(400), ncol=4), first = c("A", "B"), second = c("foo", "bar", "asd", "fgh", "jkl"))
by(ex, INDICES=list(ex[,"first"], ex[,"second"]), FUN=function(z) z)
# Modify the above function provided in FUN to suit your needs