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标准化
归一化
- scale
- limma标准化
标准化 VS 归一化
DESeq2 Vst

标准化

 log2(18*1000000/sum(dat[,3])+1)
  ## 18 -- > 6.459884  ## SS2_15_0048_A5
  dat=log2(edgeR::cpm(dat)+1) 
  ##归一化的一种选择，这里是CPM(count-per-million，每百万碱基中每个转录本的count值)
  ###CPM只对read count相对总reads数做了数量的均一化，去除文库大小差异。
  apply(mRNA_count,2,function(x)x/sum(x)*1000000)

归一化

以下三者等价

pheatmap(expr_sig,col=col,show_colnames=F,show_rownames=F,scale="row")
pheatmap(t(scale(t(expr_sig))),col=col,show_colnames=F,show_rownames=F)
pheatmap(t(apply(expr_sig,1,function(x){ ( x-mean(x))/sd(x) })),col=col,show_colnames=F,show_rownames=F)

过滤表达量为0的行

dat=a[apply(a,1, function(x) sum(x>1) > floor(ncol(a)/50)),]

scale

scale: 对列进行操作

mat <- matrix(1:12, ncol = 3)

     [,1] [,2] [,3]
[1,]    1    5    9
[2,]    2    6   10
[3,]    3    7   11
[4,]    4    8   12

scale(mat,center = T, scale = T)
apply(mat,2,function(x){ ( x-mean(x)) /sd(x) })

           [,1]       [,2]       [,3]
[1,] -1.1618950 -1.1618950 -1.1618950
[2,] -0.3872983 -0.3872983 -0.3872983
[3,]  0.3872983  0.3872983  0.3872983
[4,]  1.1618950  1.1618950  1.1618950

scale默认对行进行归一化（减去均值，除以标准差）

gene_count <- apply(gene_count,1,function(x){ (x-mean(x)) / sd(x)})%>%t()

图片alt

limma标准化

 dge <- DGEList(counts=expr)
 dge <- calcNormFactors(dge)   
 v <- voom(dge,design,plot=TRUE, normalize="quantile") 
  par(mfrow=c(1,1),mar=c(7,3,2,2))
 boxplot(log2(v[['E']]), boxwex=0.6, notch=T, main=GEO, outline=FALSE, las=2, col=group[ord])

 expr <- expr[complete.cases(expr), ]
 v <- vooma(log2(expr), design, plot=T)
 expr <- normalizeBetweenArrays(expr) # normalize data
 par(mfrow=c(1,1),mar=c(7,3,2,2))
 boxplot(log2(v[['E']]), boxwex=0.6, notch=T, main=GEO, outline=FALSE, las=2, col=group[ord])

      qx <- as.numeric(quantile(expr, c(0., 0.25, 0.5, 0.75, 0.99, 1.0), na.rm=T))
      LogC <- (qx[5] > 100) ||
        (qx[6]-qx[1] > 50 && qx[2] > 0)
      if (LogC) {
        message("##############",GEO,"log2 转换")
        expr[which(expr <= 0)] <- NaN
        expr <- log2(expr) 
      }
      expr<- normalizeBetweenArrays(expr)
      par(mfrow=c(1,1),mar=c(7,3,2,2))
      boxplot(expr, boxwex=0.6, notch=T, main=GEO, outline=FALSE, las=2, col=group[ord])

标准化 VS 归一化

       GSM1062765 GSM1062766 GSM1062767 GSM1062768 GSM1062769
ABCA8    6.782756   7.128726   4.571173   5.631289   7.457750
ABCC3   10.612708  10.651995   9.720073   9.887744   6.458206
ABI3BP  10.810602   9.640165   8.725722   7.912306   8.213121
ACADL    5.396239   7.040040   4.790250   7.120997   5.107281
ADGRF1   5.463918   9.036063   9.297348  10.522882   5.316363

标准化是对测序深度进标准化，使所有样本的reads数目相等
- 对列进行标准化
- 样本之间可以相互比较
- CPM=106*Cij/∑iCij
- data=log((CPM/10) + 1)
归一化
- 对行进行归一化
- 基因归一化是指一个基因减去其在所有样品表达的均值然后除以其在所有样品表达值的标准差
- 有的基因表达量很高，有的转录因子表达量很低，不让高表达基因占主导地位，进行scaling
- 使得该基因在所有样本中的平均表达量为0
- 缩放每个基因的表达，使细胞间的方差为1

rowSums(t(apply(expr_sig,1,function(x){ ( x-mean(x))/sd(x)  })))[1:5]
#        ABCA8         ABCC3        ABI3BP         ACADL        ADGRF1 
#-2.681882e-15  2.740169e-14 -1.838980e-14 -1.357768e-14  2.004646e-14 
rowSums(t(apply(expr_sig,1,function(x){ ( x/sum(x))*1000 })))[1:5]
# ABCA8  ABCC3 ABI3BP  ACADL ADGRF1 
#  1000   1000   1000   1000   1000

DESeq2 Vst

vsd <- varianceStabilizingTransformation(dds_filt,blind=FALSE) 
vsd@assays@data@listData[[1]]
assay(vsd)