分类（PCA）

1. PCA

• PCA（Principal Components Analysis）即主成分分析，也称主分量分析或主成分回归分析法，首先利用线性变换，将数据变换到一个新的坐标系统中；然后再利用降维的思想，使得任何数据投影的第一大方差在第一个坐标(称为第一主成分)上，第二大方差在第二个坐标(第二主成分)上。这种降维的思想首先减少数据集的维数，同时还保持数据集的对方差贡献最大的特征，最终使数据直观呈现在二维坐标系。

##7.4.1 Principal Component Analysis (PCA)
abund_table=read.csv("VdrFecalGenusCounts.csv",row.names=1,check.names=FALSE)
abund_table<-t(abund_table)
head(abund_table)

meta_table <- data.frame(row.names=rownames(abund_table),t(as.data.frame(strsplit(rownames(abund_table),"_"))))
meta_table$Group <- with(meta_table,ifelse(as.factor(X2)%in% c(11,12,13,14,15),c("Vdr-/-"), c("WT")))

# 标准化PCA 
stand_abund_table <- decostand(abund_table, method = "total")
PCA <-rda(stand_abund_table)
PCA

sum (apply (stand_abund_table, 2, var))

biplot(PCA, display = 'species')
ordiplot(PCA, display = "sites", type = "text")


"cleanplot.pca" <- function(res.pca, ax1=1, ax2=2, point=FALSE, 
                            ahead=0.07, cex=0.5) 
{
  # A function to draw two biplots (scaling 1 and scaling 2) from an object 
  # of class "rda" (PCA or RDA result from vegan's rda() function)
  #
  # License: GPL-2 
  # Authors: Francois Gillet & Daniel Borcard, 24 August 2012
  
  require("vegan")
  
  par(mfrow=c(1,2))
  p <- length(res.pca$CA$eig)
  
  # Scaling 1: "species" scores scaled to relative eigenvalues
  sit.sc1 <- scores(res.pca, display="wa", scaling=1, choices=c(1:p))
  spe.sc1 <- scores(res.pca, display="sp", scaling=1, choices=c(1:p))
  plot(res.pca, choices=c(ax1, ax2), display=c("wa", "sp"), type="n", 
       main="PCA - scaling 1", scaling=1)
  if (point)
  {
    points(sit.sc1[,ax1], sit.sc1[,ax2], pch=20)
    text(res.pca, display="wa", choices=c(ax1, ax2), cex=cex, pos=1, scaling=1)
  }
  else
  {
    text(res.pca, display="wa", choices=c(ax1, ax2), cex=cex, scaling=1)
  }
  text(res.pca, display="sp", choices=c(ax1, ax2), cex=cex, pos=1, col="blue", scaling=1)
  arrows(0, 0, spe.sc1[,ax1], spe.sc1[,ax2], length=ahead, angle=20, col="red")
  pcacircle(res.pca)
  
  # Scaling 2: site scores scaled to relative eigenvalues
  sit.sc2 <- scores(res.pca, display="wa", choices=c(1:p))
  spe.sc2 <- scores(res.pca, display="sp", choices=c(1:p))
  plot(res.pca, choices=c(ax1,ax2), display=c("wa","sp"), type="n", 
       main="PCA - scaling 2")
  if (point) {
    points(sit.sc2[,ax1], sit.sc2[,ax2], pch=20)
    text(res.pca, display="wa", choices=c(ax1 ,ax2), cex=cex, pos=1)
  }
  else
  {
    text(res.pca, display="wa", choices=c(ax1, ax2), cex=cex)
  }
  text(res.pca, display="sp", choices=c(ax1, ax2), cex=cex, pos=1, col="blue")
  arrows(0, 0, spe.sc2[,ax1], spe.sc2[,ax2], length=ahead, angle=20, col="red")
}


"pcacircle" <- function (pca) 
{
  # Draws a circle of equilibrium contribution on a PCA plot 
  # generated from a vegan analysis.
  # vegan uses special constants for its outputs, hence 
  # the 'const' value below.
  
  eigenv <- pca$CA$eig
  p <- length(eigenv)
  n <- nrow(pca$CA$u)
  tot <- sum(eigenv)
  const <- ((n - 1) * tot)^0.25
  radius <- (2/p)^0.5
  radius <- radius * const
  symbols(0, 0, circles=radius, inches=FALSE, add=TRUE, fg=2)
}

cleanplot.pca(PCA)

image.png