From f7a55d67c2a88e997eb6c43ee50727f076f11936 Mon Sep 17 00:00:00 2001 From: yumouqiu <32415965+yumouqiu@users.noreply.github.com> Date: Thu, 10 Oct 2019 22:56:24 -0500 Subject: [PATCH] Add files via upload --- Case-Study/EmpiricalStudy.txt | 375 ++++++ Case-Study/khan_train.csv | 2309 +++++++++++++++++++++++++++++++++ Case-Study/newdata.csv | 65 + 3 files changed, 2749 insertions(+) create mode 100644 Case-Study/EmpiricalStudy.txt create mode 100644 Case-Study/khan_train.csv create mode 100644 Case-Study/newdata.csv diff --git a/Case-Study/EmpiricalStudy.txt b/Case-Study/EmpiricalStudy.txt new file mode 100644 index 0000000..dba839e --- /dev/null +++ b/Case-Study/EmpiricalStudy.txt @@ -0,0 +1,375 @@ + + +######################################################################################################## +######################################################################################################## +# CODE FOR THE EMPIRICAL STUDY IN SECTION 6 # +######################################################################################################## +######################################################################################################## + +# Creating the new data set by drawing the top 100 and bottom 30 genes from the original data +####################################################################################################### +data=read.csv("khan_train.csv",header=TRUE, sep=",") # Reading the original dataset. +data$gene=NULL +data=as.matrix(data) +data=t(data) + +# Evaluating the F statistics in (6.14) +EWS=data[1:23,] +BL=data[24:31,] +NB=data[32:43,] +RMS=data[44:64,] +xbar=colMeans(data) +xbar1=colMeans(EWS) +xbar2=colMeans(BL) +xbar3=colMeans(NB) +xbar4=colMeans(RMS) + +n=dim(data)[1] +k=4 +difsq1=dim(EWS)[1]*(xbar1-xbar)^2 +difsq2=dim(BL)[1]*(xbar2-xbar)^2 +difsq3=dim(NB)[1]*(xbar3-xbar)^2 +difsq4=dim(RMS)[1]*(xbar4-xbar)^2 +num=(difsq1+difsq2+difsq3+difsq4)/(k-1)# Numerator of the F statistics +cowVar <- function(x,y) { + one=matrix(rep(1,dim(x)[1]),dim(x)[1]) + bar=one%*%y + S=colSums((x-bar)^2)/(dim(x)[1]-1) + +} +S1=cowVar(EWS,xbar1) +S2=cowVar(BL,xbar2) +S3=cowVar(NB,xbar3) +S4=cowVar(RMS,xbar4) + +dnr=(((dim(EWS)[1]-1)*S1)+((dim(BL)[1]-1)*S2)+((dim(NB)[1]-1)*S3)+((dim(RMS)[1]-1)*S4))/(n-k)# Denominator of F statistic + +Fstat=num/dnr # F statistics +jtop=order(Fstat)[1:100] +jbot=order(Fstat)[2279:2308] +topgene=data[,jtop] # Choosing the top 100 genes using the F statistics +botgene=data[,jbot] # Choosing the bottom 30 genes using the F statistics +newdata=cbind(topgene,botgene) # Combining top and bottom genes to create new data set +write.table(newdata,file="newdata.csv",sep=",",col.names=NA,qmethod="double") + +############The end of the code for creating the new data set of selected top and bottom genes ############### + + +# Case study using the proposed method +####################################### +newdata=data.matrix(read.csv("newdata.csv", header = TRUE, row.names = 1,sep = ",")) #Reading the created sub data set using top 100 and bottom 30 genes. +dimnames(newdata) <- NULL +newdata=as.matrix(newdata) +library(reshape2) +#library(gplots) +library(ggplot2) +covmat=cov(newdata) +p=dim(covmat)[1] +n=dim(newdata)[1] +thetahat = matrix(0, p, p) +mean.new = colMeans(newdata) +# Evaluating thetahat +t1=proc.time()[3] +for(i in 1 : p){ + for(j in 1 : p){ + s = c() + for(k in 1 : n){ + s[k] = (((newdata[k, i] - mean.new[i]) * (newdata[k, j] - mean.new[j])) - covmat[i, j])^2 + } + thetahat[i, j] = sum(s) / n + } +} +c1c2Est = function(n, Sn, thetahat, a1 , a2, c0 ){ + p = dim(Sn)[1] + ALamhat1 = c() + kk = 0 + for (i in 1 : (p-1 )){ + for (j in (i+1 ) : p){ + kk = kk + 1 + ALamhat1[kk] = abs(Sn[i, j] / sqrt(thetahat[i, j]) * sqrt(n / log(p))) + } + } + Mk = sum((ALamhat1 > a1) & (ALamhat1 < a2)) + nhat = Mk - 2 * (pnorm((a2) * sqrt(log(p))) - pnorm((a1)* sqrt(log(p)))) * ((p^2 - p) / 2) + if(nhat > c0) {on = (log(nhat / sqrt(log(p)))) / log(p); deltaStarhat = sqrt(2 * (2 - on))} + if(nhat <= c0) {deltaStarhat = 2} + list(deltaStarhat = deltaStarhat, nhat = nhat, ALamhat = ALamhat1, Mk = Mk) +} +#t1=proc.time()[3] + a = min(sqrt(2 + log(n) / log(p)),2) + b=sqrt(1/log(log(p))) + temp = c1c2Est(n, covmat, thetahat, a1 = 2 - a+b, a2 = 2 , c0 = sqrt(log(p))) +t2=proc.time()[3] +time.prop=t2-t1 + + +# Evaluating the adaptive thresholding covariance estimator using the proposed method +SigmaProp = matrix(0, p, p) +indexM = matrix(1, p, p) - diag(rep(1, p)) +thetahatDiag = thetahat * indexM +deltaProp = temp$deltaStarhat +SigmaProp[which(abs(covmat) > deltaProp * sqrt(thetahatDiag * log(p) / n), arr.ind = TRUE)] = covmat[which(abs(covmat) > deltaProp * sqrt(thetahatDiag * log(p) / n), arr.ind = TRUE)] +# Calculating the proportion of zeros produced by the proposed method +zeros.prop=sum(colSums(SigmaProp== 0))/(p^2) + + + +# Heatmap of absolute values of the covariance # +################################################# +library("lattice") +par(mar=c(3,4,2,2)) +SigmaProp[abs(SigmaProp) >1] =1 +ramp <- colorRamp(c( "white","black")) +c=rgb( ramp(seq(0, 1, length = 16)), max = 255) +xscale <- list(cex=1.3) +yscale <- list(cex=1.3) +levelplot(abs(SigmaProp),main=list(label="Heatmap (Proposed)",cex=1.5 ), col.regions = c , + scales=list(x=xscale, y=yscale),xlab="", ylab="" ,colorkey=list(labels=list(cex=1),space="bottom")) + + +# Gene co-expression networks on positive and negative correlations # +##################################################################### +library(igraph) +rprop=matrix(rep(0,p^2),p) +# Evaluating correlations using adaptive thresholding covariance estimator +for (i in 1 : (p - 1)){ + for (j in (i + 1) : p){ + + rprop[i,j]=SigmaProp[i,j]/sqrt(SigmaProp[i,i]*SigmaProp[j,j]) + + } +} + +trh=min(abs(rprop[which(abs(rprop)>0)])) # Choosing the smallest correlation as the cutoff value +edgesP=which(rprop>=trh,arr.ind = T) # Choosing edges with positive correlations +edgesN=which(-1*rprop>=trh,arr.ind = T) # Choosing edges with negative correlations +lp=as.vector(t(edgesP)) +gp<-graph(lp, directed=F) +ln=as.vector(t(edgesN)) +gn<-graph(ln, directed=F) + +# Function for wrapping strings +wrap <- function(strings,width){ + as.character(sapply(strings, FUN=function(x){ + paste(strwrap(x, width=width), collapse="\n") + })) +} + +# Wrapping the node labels +V(gp)$label = wrap(V(gp)$label, 12) +V(gn)$label = wrap(V(gn)$label, 12) + +#Change font size +V(gp)$label.cex = .8 +V(gn)$label.cex = .8 + +# Function for increasing node separation +layoutattr <- function(graph, wc, strength=1,layout=layout.auto) { + g <- graph.edgelist(get.edgelist(graph)) # create a lightweight copy of graph w/o the attributes. + E(g)$weight <- 1 + + attr <- cbind(id=1:vcount(g), val=wc) + g <- g + vertices(unique(attr[,2])) + igraph::edges(unlist(t(attr)), weight=strength) + + l <- layout(g, weights=E(g)$weight)[1:vcount(graph),] + return(l) +} +top=seq(1:100) +# Plotting positively correlated genes +plot(gp, vertex.shape="none", vertex.size=1,vertex.label.color =ifelse(V(gp) %in% top, "blue", "black"),layout=layoutattr(gp, wc=1)) +title("Co-expression network of positively correlated genes \n(Proposed)",cex.main=1.5) +legend("topleft",bty = "n", legend=c("Top genes", "Bottom genes"),col=c("blue", "black"), pch=c(15,15),cex=1) + +# Plotting negatively correlated genes +plot(gn, vertex.shape="none", vertex.size=1,vertex.label.color =ifelse(V(gn) %in% top, "blue", "black"), + layout=layoutattr(gn, wc=1)) +title("Co-expression network of negatively correlated genes \n(Proposed)",cex.main=1.5) +legend("topleft",bty = "n", legend=c("Top genes", "Bottom genes"),col=c("blue", "black"), pch=c(15,15),cex=1) +###################The end of codes for empirical study under the proposed method ################################# + + +# Case study using the CV method +################################# +newdata=data.matrix(read.csv("newdata.csv", header = TRUE, row.names = 1,sep = ",")) +dimnames(newdata) <- NULL +newdata=as.matrix(newdata) +library(reshape2) +#library(gplots) +library(ggplot2) +covmat=cov(newdata) + +p=dim(covmat)[1] +n=dim(newdata)[1] +thetahat = matrix(0, p, p) +mean.new = colMeans(newdata) + +# CV method to find delta +############################################ +find.del=function(n,p,H,N,X){ + nn1=floor(n*(1-(1/log(n)))) + sub=c() + Ra.ij=array(0,dim=c(H,2*N)) + for (l in 1:H){ + sub=sample(nrow(X),nn1,replace = FALSE, prob = NULL) + sam1=X[sub,] + sam2=X[-sub,] + n1=nrow(sam1) + n2=nrow(sam2) + Sig.hat1=((n1-1)/n1)*cov(sam1) + Sig.hat2=((n2-1)/n2)*cov(sam2) + one=matrix(1,nrow=n1,ncol=n1) + Xbar=one%*%sam1/n1 + t.hat=array(0,dim=c(p,p)) + that1=c() + for( i in 1:p){ + for(j in 1:p){ + s=c() + for(k in 1:n1){ + s[k]=((sam1[k,i]-Xbar[k,i])*(sam1[k,j]-Xbar[k,j])-Sig.hat1[i,j])^2 + } + that1[j]=sum(s)/n1 + } + t.hat[i,]=that1 + } + Raj.i=c() + to=2*N + for (m in 1:to){ + Sig.hat.star1=matrix(0,nrow=p,ncol=p) + am=m/N + Lam.am=am*sqrt(t.hat*log(p)/n1) + Sig.hat.star1[which(abs(Sig.hat1)>Lam.am)]=Sig.hat1[which(abs(Sig.hat1)>Lam.am)] + Raj.i[m]=sum((Sig.hat.star1-Sig.hat2)^2) + } + Ra.ij[l,]=Raj.i + } + aj=c() + Rhat.a=c() + for (j in 1:to){ + Rhat.a=c(Rhat.a,sum(Ra.ij[,j])/H) + aj[j]=j/N + } + j.hat=which(Rhat.a==min(Rhat.a)) + delta.hat=aj[min(j.hat)] + return(delta.hat) +} + + +thetahat = matrix(0, p, p) +mean.new = colMeans(newdata) +# Evaluating thetahat +for(i in 1 : p){ + for(j in 1 : p){ + s = c() + for(k in 1 : n){ + s[k] = (((newdata[k, i] - mean.new[i]) * (newdata[k, j] - mean.new[j])) - covmat[i, j])^2 + } + thetahat[i, j] = sum(s) / n + } +} + + + +# Evaluating the adaptive thresholding estimator using the CV method +indexM = matrix(1, p, p) - diag(rep(1, p)) +thetahatDiag = thetahat * indexM + +H = 50 +N=100 +tc1=proc.time()[3] +deltaCV = find.del(n,p,H,N,newdata) +tc2=proc.time()[3] +time.CV=tc2-tc1 +SigmaCV = matrix(0, p, p) +SigmaCV[which(abs(covmat) > deltaCV * sqrt(thetahatDiag * log(p) / n), arr.ind = TRUE)] = covmat[which(abs(covmat) > deltaCV *sqrt( thetahatDiag * log(p) / n), arr.ind = TRUE)] +zeros.CV=sum(colSums(SigmaCV== 0))/(p^2) # Calculating the proportion of zeros for the CV method + + + +# Creating co-expression networks +library(igraph) +rCV=matrix(rep(0,p^2),p) +for (i in 1 : (p - 1)){ + for (j in (i + 1) : p){ + rCV[i,j]=SigmaCV[i,j]/sqrt(SigmaCV[i,i]*SigmaCV[j,j]) + } +} +trh=min(abs(rCV[which(abs(rCV)>0)])) +edgesP=which(rCV>=trh,arr.ind = T) # Positively correlated edges +edgesN=which(-1*rCV>=trh,arr.ind = T) # Negatively correlated edges +lp=as.vector(t(edgesP)) +gp<-graph(lp, directed=F) +ln=as.vector(t(edgesN)) +gn<-graph(ln, directed=F) + +# Function for wrapping strings +wrap <- function(strings,width){ + as.character(sapply(strings, FUN=function(x){ + paste(strwrap(x, width=width), collapse="\n") + })) +} + + +V(gp)$label = wrap(V(gp)$label, 12) +V(gn)$label = wrap(V(gn)$label, 12) + + +V(gp)$label.cex = .8 +V(gn)$label.cex = .8 + +layoutattr <- function(graph, wc, strength=1,layout=layout.auto) { + g <- graph.edgelist(get.edgelist(graph)) + E(g)$weight <- 1 + attr <- cbind(id=1:vcount(g), val=wc) + g <- g + vertices(unique(attr[,2])) + igraph::edges(unlist(t(attr)), weight=strength) + l <- layout(g, weights=E(g)$weight)[1:vcount(graph),] + return(l) +} + +top=seq(1:100) +plot(gp, vertex.shape="none", vertex.size=1,vertex.label.color =ifelse(V(gp) %in% top, "blue", "black"), + layout=layoutattr(gp, wc=1)) +title("Co-expression network of positively correlated genes \n(CV)",cex.main=1.5) +legend("topleft",bty = "n", legend=c("Top genes", "Bottom genes"),col=c("blue", "black"), pch=c(15,15),cex=1) + + +plot(gn, vertex.shape="none", vertex.size=1,vertex.label.color =ifelse(V(gn) %in% top, "blue", "black"), + layout=layoutattr(gn, wc=1)) +title("Co-expression network of negatively correlated genes \n(CV)",cex.main=1.5) +legend("topleft",bty = "n", legend=c("Top genes", "Bottom genes"),col=c("blue", "black"), pch=c(15,15),cex=1) + + +# Creating heatmap +################### +library("lattice") +par(mar=c(3,4,2,2)) +SigmaCV[abs(SigmaCV) >1] =1 +ramp <- colorRamp(c( "white","black")) +c=rgb( ramp(seq(0, 1, length = 16)), max = 255) +xscale <- list(cex=1.3) +yscale <- list(cex=1.3) +levelplot(abs(SigmaCV),main=list(label="Heatmap (CV)",cex=1.5 ), col.regions = c , + scales=list(x=xscale, y=yscale),xlab="", ylab="" ,colorkey=list(labels=list(cex=1),space="bottom")) + +############################### The end of codes for empirical study under the CV method ################################# +cat("The estimators under the proposed method:",deltaProp,"\n" ) +cat("The estimators under the CV method:",deltaCV,"\n" ) + +cat("The percentage of zeros in the resulting covariance estimator under the proposed method:",zeros.prop,"\n") +cat("The percentage of zeros in the resulting covariance estimator under the CV method:",zeros.CV,"\n") + +cat("Time taken by the proposed method:",time.prop,"\n") +cat("Time taken by the CV method:",time.CV) + + + +################################################################################################################### +################################################################################################################### +# THE END OF CODES FOR EMPIRICAL STUDY # +################################################################################################################### +################################################################################################################### + + + + + + diff --git a/Case-Study/khan_train.csv b/Case-Study/khan_train.csv new file mode 100644 index 0000000..811ec8f --- /dev/null +++ b/Case-Study/khan_train.csv @@ -0,0 +1,2309 @@ 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