Linear Discriminant Analysis
r_wrapper.sh $script_file
rm(list = objects() )
############# FORMAT X DATA #########################
format<-function(data) {
ind=NULL
for(i in 1 : ncol(data)){
if (is.na(data[nrow(data),i])) {
ind<-c(ind,i)
}
}
#print(is.null(ind))
if (!is.null(ind)) {
data<-data[,-c(ind)]
}
data
}
########GET RESPONSES ###############################
get_resp<- function(data) {
resp1<-as.vector(data[,ncol(data)])
resp=numeric(length(resp1))
for (i in 1:length(resp1)) {
if (resp1[i]=="Y ") {
resp[i] = 0
}
if (resp1[i]=="X ") {
resp[i] = 1
}
}
return(resp)
}
######## CHARS TO NUMBERS ###########################
f_to_numbers<- function(F) {
ind<-NULL
G<-matrix(0,nrow(F), ncol(F))
for (i in 1:nrow(F)) {
for (j in 1:ncol(F)) {
G[i,j]<-as.integer(F[i,j])
}
}
return(G)
}
###################NORMALIZING#########################
norm <- function(M, a=NULL, b=NULL) {
C<-NULL
ind<-NULL
for (i in 1: ncol(M)) {
if (sd(M[,i])!=0) {
M[,i]<-(M[,i]-mean(M[,i]))/sd(M[,i])
}
# else {print(mean(M[,i]))}
}
return(M)
}
##### LDA DIRECTIONS #################################
lda_dec <- function(data, k){
priors=numeric(k)
grandmean<-numeric(ncol(data)-1)
means=matrix(0,k,ncol(data)-1)
B = matrix(0, ncol(data)-1, ncol(data)-1)
N=nrow(data)
for (i in 1:k){
priors[i]=sum(data[,1]==i)/N
grp=subset(data,data\$group==i)
means[i,]=mean(grp[,2:ncol(data)])
#print(means[i,])
#print(priors[i])
#print(priors[i]*means[i,])
grandmean = priors[i]*means[i,] + grandmean
}
for (i in 1:k) {
B= B + priors[i]*((means[i,]-grandmean)%*%t(means[i,]-grandmean))
}
W = var(data[,2:ncol(data)])
svdW = svd(W)
inv_sqrtW =solve(svdW\$v %*% diag(sqrt(svdW\$d)) %*% t(svdW\$v))
B_star= t(inv_sqrtW)%*%B%*%inv_sqrtW
B_star_decomp = svd(B_star)
directions = inv_sqrtW%*%B_star_decomp\$v
return( list(directions, B_star_decomp\$d) )
}
################ NAIVE BAYES FOR 1D SIR OR LDA ##############
naive_bayes_classifier <- function(resp, tr_data, test_data, k=2, tau) {
tr_data=data.frame(resp=resp, dir=tr_data)
means=numeric(k)
#print(k)
cl=numeric(k)
predclass=numeric(length(test_data))
for (i in 1:k) {
grp = subset(tr_data, resp==i)
means[i] = mean(grp\$dir)
#print(i, means[i])
}
cutoff = tau*means[1]+(1-tau)*means[2]
#print(tau)
#print(means)
#print(cutoff)
if (cutoff>means[1]) {
cl[1]=1
cl[2]=2
}
else {
cl[1]=2
cl[2]=1
}
for (i in 1:length(test_data)) {
if (test_data[i] <= cutoff) {
predclass[i] = cl[1]
}
else {
predclass[i] = cl[2]
}
}
#print(means)
#print(mean(means))
#X11()
#plot(test_data,pch=predclass, col=resp)
predclass
}
################# EXTENDED ERROR RATES #################
ext_error_rate <- function(predclass, actualclass,msg=c("you forgot the message"), pr=1) {
er=sum(predclass != actualclass)/length(predclass)
matr<-data.frame(predclass=predclass,actualclass=actualclass)
escapes = subset(matr, actualclass==1)
subjects = subset(matr, actualclass==2)
er_esc=sum(escapes\$predclass != escapes\$actualclass)/length(escapes\$predclass)
er_subj=sum(subjects\$predclass != subjects\$actualclass)/length(subjects\$predclass)
if (pr==1) {
# print(paste(c(msg, 'overall : ', (1-er)*100, "%."),collapse=" "))
# print(paste(c(msg, 'within escapes : ', (1-er_esc)*100, "%."),collapse=" "))
# print(paste(c(msg, 'within subjects: ', (1-er_subj)*100, "%."),collapse=" "))
}
return(c((1-er)*100, (1-er_esc)*100, (1-er_subj)*100))
}
## Main Function ##
files<-matrix("${input}", 1,1, byrow=T)
d<-"${cond}" # Number of PC
tau<-seq(0,1, by=0.005)
#tau<-seq(0,1, by=0.1)
for_curve=matrix(-10, 3,length(tau))
##############################################################
test_data_whole_X <-read.delim(files[1,1], row.names=1)
#### FORMAT TRAINING DATA ####################################
# get only necessary columns
test_data_whole_X<-format(test_data_whole_X)
oligo_labels<-test_data_whole_X[1:(nrow(test_data_whole_X)-1),ncol(test_data_whole_X)]
test_data_whole_X<-test_data_whole_X[,1:(ncol(test_data_whole_X)-1)]
X_names<-colnames(test_data_whole_X)[1:ncol(test_data_whole_X)]
test_data_whole_X<-t(test_data_whole_X)
resp<-get_resp(test_data_whole_X)
ldaqda_resp = resp + 1
a<-sum(resp) # Number of Subject
b<-length(resp) - a # Number of Escape
## FREQUENCIES #################################################
F<-test_data_whole_X[,1:(ncol(test_data_whole_X)-1)]
F<-f_to_numbers(F)
FN<-norm(F, a, b)
ss<-svd(FN)
eigvar<-NULL
eig<-ss\$d^2
for ( i in 1:length(ss\$d)) {
eigvar[i]<-sum(eig[1:i])/sum(eig)
}
#print(paste(c("Variance explained : ", eigvar[d]*100, "%"), collapse=""))
Z<-F%*%ss\$v
ldaqda_data <- data.frame(group=ldaqda_resp,Z[,1:d])
lda_dir<-lda_dec(ldaqda_data,2)
train_lda_pred <-Z[,1:d]%*%lda_dir[[1]]
############# NAIVE BAYES CROSS-VALIDATION #############
### LDA #####
y<-ldaqda_resp
X<-F
cv<-matrix(c(rep('NA',nrow(test_data_whole_X))), nrow(test_data_whole_X), length(tau))
for (i in 1:nrow(test_data_whole_X)) {
# print(i)
resp<-y[-i]
p<-matrix(X[-i,], dim(X)[1]-1, dim(X)[2])
testdata<-matrix(X[i,],1,dim(X)[2])
p1<-norm(p)
sss<-svd(p1)
pred<-(p%*%sss\$v)[,1:d]
test<- (testdata%*%sss\$v)[,1:d]
lda <- lda_dec(data.frame(group=resp,pred),2)
pred <- pred[,1:d]%*%lda[[1]][,1]
test <- test%*%lda[[1]][,1]
test<-matrix(test, 1, length(test))
for (t in 1:length(tau)) {
cv[i, t] <- naive_bayes_classifier (resp, pred, test,k=2, tau[t])
}
}
for (t in 1:length(tau)) {
tr_err<-ext_error_rate(cv[,t], ldaqda_resp , c("CV"), 1)
for_curve[1:3,t]<-tr_err
}
dput(for_curve, file="${output}")
.. class:: infomark
**TIP:** If you want to perform Principal Component Analysis (PCA) on the give numeric input data (which corresponds to the "Source file First in "Generate A Matrix" tool), please use *Multivariate Analysis/Principal Component Analysis*
-----
.. class:: infomark
**What it does**
This tool consists of the module to perform the Linear Discriminant Analysis as described in Carrel et al., 2006 (PMID: 17009873)
*Carrel L, Park C, Tyekucheva S, Dunn J, Chiaromonte F, et al. (2006) Genomic Environment Predicts Expression Patterns on the Human Inactive X Chromosome. PLoS Genet 2(9): e151. doi:10.1371/journal.pgen.0020151*
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.. class:: warningmark
**Note**
- Output from "Generate A Matrix" tool is used as input file for this tool
- Output of this tool contains LDA classification success rates for different values of the turning parameter tau (from 0 to 1 with 0.005 interval). This output file will be used to establish the ROC plot, and you can obtain more detail information from this plot.