install.packages("FactoMineR")
install.packages("factoextra")
setwd("~/Bureau/Ana_donn/TP3")
library(knitr)
## Global options
options(max.print="75")
opts_chunk$set(echo=TRUE,
cache=FALSE,
prompt=FALSE,
tidy=TRUE,
comment=NA,
message=FALSE,
warning=FALSE,
class.source="badCode")
opts_knit$set(width=75)
library(corrplot)
library(ggplot2)
library(gridExtra)
library(FactoMineR)
library(factoextra)
library(reshape2)
library(knitr)
## Global options
options(max.print="75")
opts_chunk$set(echo=TRUE,
cache=FALSE,
prompt=FALSE,
tidy=TRUE,
comment=NA,
message=FALSE,
warning=FALSE,
class.source="badCode")
opts_knit$set(width=75)
library(knitr)
## Global options
options(max.print="75")
opts_chunk$set(echo=TRUE,
cache=FALSE,
prompt=FALSE,
tidy=TRUE,
comment=NA,
message=FALSE,
warning=FALSE,
class.source="badCode")
opts_knit$set(width=75)
library(corrplot)
library(ggplot2)
library(gridExtra)
library(FactoMineR)
library(factoextra)
library(reshape2)
Ozone<-read.table("Ozone.txt",header=T)
Ozone$pluie<-as.factor(Ozone$pluie)
Ozone$vent<-as.factor(Ozone$vent)
Ozone<-Ozone[,-11]
summary(Ozone)
dim(Ozone)
ggplot(melt(Ozone[,-c(11,12)]),aes(x=variable,y=value))+geom_boxplot()
g1<-ggplot(Ozone,aes(x=maxO3))+geom_density()
g2<-ggplot(melt(Ozone[,c(2:4)]),aes(x=value,color=variable))+geom_density()
g3<-ggplot(melt(Ozone[,c(5:7)]),aes(x=value,color=variable))+geom_density()
g4<-ggplot(melt(Ozone[,c(8:10)]),aes(x=value,color=variable))+geom_density()
grid.arrange(g1,g2,g3,g4,ncol=2)
ggplot(Ozone, aes(x = pluie)) +
geom_bar(aes(y = (..count..)/sum(..count..)))+ylab("")+ggtitle("Frequences")
quan <- as.vector(table(Ozone$vent))/nrow(Ozone)
df <- data.frame(group = levels(Ozone$vent),value = quan)
ggplot(df, aes(x="", y=value, fill=group))+
geom_bar(width = 1, stat = "identity")+ coord_polar("y", start=0)+ theme(legend.position="bottom")
corrplot(cor(Ozone[,-c(1,2)]),method = "ellipse")
corrplot(cor(Ozone[,-c(9,10)]),method = "ellipse")
corrplot(cor(Ozone[,-(9:10)]),method = "ellipse")
corrplot(cor(Ozone[,-(9,10)]),method = "ellipse")
corrplot(cor(Ozone[,-c(9,10)]),method = "ellipse")
corrplot(cor(Ozone[,-c(9,10)]),method = "ellipse")
dim(Ozone)
corrplot(cor(Ozone[,-c(11,12)]),method = "ellipse")
help("scale")
OzoneC<-scale(Ozone[,-c(11,12)],scale=FALSE) # A COMPLETER
apply(OzoneC,2,mean)
n=112
p=10
W<-diag(1/n,nrow=n,ncol=n)
M<- diag(1,nrow = p, ncol = p)
Gamma<- t(OzoneC)%*%W%*%OzoneC # A COMPLETER
A<-eigen(Gamma
Gamma<- t(OzoneC)%*%W%*%OzoneC # A COMPLETER
A<-eigen(Gamma)
Gamma<- t(OzoneC)%*%W%*%OzoneC # A COMPLETER
A<-eigen(Gamma)
A
n=112
p=10
W<- diag(1/n,nrow(OzoneC))
M<- diag(1,ncol(OzoneC))
n=nrow(OzoneC)
p=ncol(OzoneC)
W<- diag(1/n,n)
M<- diag(1,p)
Gamma<- t(OzoneC)%*%W%*%OzoneC # A COMPLETER
A<-eigen(Gamma)
A$values
A$values
"La trace de gamma est l'inertie de Ozone"
sum(A$values)
dim(OzoneC)
dim(W)
dim(M)
A$values
"La trace de gamma est l'inertie de Ozone"
sum(A$values)
mean(OzoneC**2)
A$values
"La trace de gamma est l'inertie de Ozone"
sum(A$values)
sum(OzoneC**2)/n
A$values
"La trace de gamma est l'inertie de Ozone"
sum(A$values)
sum(OzoneC**2)/n
sum(A$values)==sum(OzoneC**2)/n
A$values
"La trace de gamma est l'inertie de Ozone"
sum(A$values)
sum(OzoneC**2)/n
sum(A$values)===sum(OzoneC**2)/n
A$values/sum(A$values)
A$values/sum(A$values)
cumsum(A$values)/sum(A$values)
A$values/sum(A$values)
B=cumsum(A$values)/sum(A$values)
hist(B)
B=A$values/sum(A$values)
C=cumsum(A$values)/sum(A$values)
hist(B)
hist(C)
A$values/sum(A$values)
cumsum(A$values)/sum(A$values)
C=OzoneC%*%A$vectors
C=OzoneC%*%A$vectors
C
dim(C)
C=OzoneC%*%A$vectors
C
dim(C)
boxplot(OzoneC)
respca<-PCA(Ozone,quali.sup=c(11,12),scale.unit = F,graph=F)
respca$eig
fviz_eig(respca)
respca$ind$coord$
2
respca<-PCA(Ozone,quali.sup=c(11,12),scale.unit = F,graph=F)
respca$eig
fviz_eig(respca)
fviz_pca_ind(respca,geom=c("point"))
fviz_pca_ind(respca,geom=c("point"))
fviz_pca_ind(respca,col.ind="contrib",geom=c("point"))
fviz_pca_ind(respca,geom=c("point"),select.ind = list(cos2=0.95))
fviz_pca_ind(respca,habillage=11,geom=c("point"))
fviz_pca_ind(respca,habillage=12,geom=c("point"))
plot(respca,choix="varcor")
corrplot(respca$var$cor,method="ellipse")
s<-sqrt((n-1)*apply(OzoneC,2,var)/n)
OzoneCR<-OzoneC%*%diag(1/s)
s<-sqrt((n-1)*apply(OzoneC,2,var)/n)
OzoneCR<-OzoneC%*%diag(1/s)
OzoneCR
scale(Ozone[,-c(11,12)])
Gamma2<- t(OzoneCR)%*%W%*%OzoneCR # A COMPLETER
B<-eigen(Gamma2)
Gamma2<- t(OzoneCR)%*%W%*%OzoneCR # A COMPLETER
B<-eigen(Gamma2)
B
sum(B$values)
Gamma2<- t(OzoneCR)%*%W%*%OzoneCR # A COMPLETER
B<-eigen(Gamma2)
B
n=nrow(OzoneC)
p=ncol(OzoneC)
W<- diag(1/n,n)
M<- diag(1,p)
M
n=nrow(OzoneC)
p=ncol(OzoneC)
W<- diag(1/n,n)
M<- diag(1,p)
sum(B$values)
Gamma2<- t(OzoneC)%*%W%*%OzoneC
B<-eigen(Gamma2)
B
Gamma2<- t(OzoneC)%*%W%*%OzoneC
B<-eigen(Gamma2)
B
Gamma2
Gamma2<- t(OzoneCR)%*%W%*%OzoneCR
B<-eigen(Gamma2)
B
Gamma2
M2<-diag(1/apply(OzoneC,2,var))
GammaM=Gamma%*%M2
eigen(Gamma2)
eigen(GammaM)
M2<-diag(1/apply(OzoneC,2,var))
GammaM=Gamma%*%M2
G=eigen(Gamma2)
GM=eigen(GammaM)
G$values
GM$values
M2<-diag(1/apply(OzoneC,2,var))
GammaM=Gamma%*%M2
G=eigen(Gamma2)
GM=eigen(GammaM)
sum(G$values)
sum(GM$values)
M2<-diag(1/apply(OzoneC,2,var))
GammaM=Gamma%*%M2
G=eigen(Gamma2)
GM=eigen(GammaM)
sum(G$values)
sum(GM$values)
G$vectors
GM$vectors
M2<-diag(1/(apply(OzoneC,2,var)*(n-1)/n))
GammaM=Gamma%*%M2
G=eigen(Gamma2)
GM=eigen(GammaM)
sum(G$values)
sum(GM$values)
G$vectors
GM$vectors
respca2<-PCA(Ozone,quali.sup=c(11,12),scale.unit=T,graph=F)
respca2$eig
fviz_eig(respca2)
fviz_pca_ind(respca2,geom=c("point"))
fviz_pca_ind(respca2,geom=c("point"))
fviz_pca_var(respca2)
corrplot(OzoneCR)
corrplot(OzoneCR([,-c(11,12)]))
corrplot(respca2$var$cor,method="ellipse")
fviz_pca_ind(respca2,col.ind="contrib",geom=c("point"))
fviz_pca_ind(respca2,geom=c("point"),select.ind = list(cos2=0.95))
fviz_pca_ind(respca2,habillage=11,geom=c("point"))
fviz_pca_ind(respca2,habillage=12,geom=c("point"))
fviz_pca_ind(respca2,geom=c("point"))
fviz_pca(respca2)
fviz_pca_ind(respca2,geom=c("point"))
fviz_pca(respca2,geom=c("point"))
g1<-fviz_pca_ind(respca2,geom=c("point"))
g2<-fviz_pca_var(respca2)
library(gridExtra)
grid.arrange(g1,g2,ncol=2)
fviz_pca_ind(respca2,col.ind="contrib",geom=c("point"))
fviz_pca_ind(respca2,geom=c("point"),select.ind = list(cos2=0.95))
fviz_pca_ind(respca2,habillage=11,geom=c("point"))
fviz_pca_ind(respca2,habillage=11,geom=c("point"))
fviz_pca_ind(respca2,col.ind="contrib",geom=c("point"))
fviz_pca_ind(respca2,geom=c("point"),select.ind = list(cos2=0.95))
fviz_pca_ind(respca2,habillage=11,geom=c("point"))
fviz_pca_ind(respca2,habillage=12,geom=c("point"))
g1<-fviz_pca_ind(respca2,geom=c("point"),habillage = 11)
g2<-fviz_pca_var(respca2)
library(gridExtra)
grid.arrange(g1,g2,ncol=2)
g1<-fviz_pca_ind(respca2,geom=c("point"))
g2<-fviz_pca_var(respca2,habillage = 11)
library(gridExtra)
grid.arrange(g1,g2,ncol=2)
g1<-fviz_pca_ind(respca2,geom=c("point"))
g2<-fviz_pca_var(respca2)
library(gridExtra)
grid.arrange(g1,g2,ncol=2)
fviz_pca_ind(respca2,col.ind="contrib",geom=c("point"))
fviz_pca_ind(respca2,geom=c("point"),select.ind = list(cos2=0.95))
fviz_pca_ind(respca2,habillage=11,geom=c("point"))
fviz_pca(respca2,habillage=12,geom=c("point"))
fviz_pca_ind(respca2,col.ind="contrib",geom=c("point"))
fviz_pca_ind(respca2,geom=c("point"),select.ind = list(cos2=0.95))
g3=fviz_pca_ind(respca2,habillage=11,geom=c("point"))
g4=fviz_pca(respca2,habillage=12,geom=c("point"))
grid.arrange(g3,g4,newpage=FALSE)
fviz_pca_ind(respca2,col.ind="contrib",geom=c("point"))
fviz_pca_ind(respca2,geom=c("point"),select.ind = list(cos2=0.95))
g3=fviz_pca_ind(respca2,habillage=11,geom=c("point"))
g4=fviz_pca_ind(respca2,habillage=12,geom=c("point"))
grid.arrange(g3,g4,newpage=FALSE)
fviz_pca_ind(respca2,col.ind="contrib",geom=c("point"))
fviz_pca_ind(respca2,geom=c("point"),select.ind = list(cos2=0.95))
g3=fviz_pca_ind(respca2,habillage=11,geom=c("point"))
g4=fviz_pca_ind(respca2,habillage=12,geom=c("point"))
grid.arrange(g3,g4)