R Code for Principal Component Analysis (PCA) and Factor Analysis (FA)
Data Set:- Bank Marketing https://www.blogger.com/blogger.g?blogID=4359514443959080595#editor/target=post;postID=5426750358330739357
Source of Data Set:- UCI Repository (http://archive.ics.uci.edu/ml/datasets/Bank+Marketing)
The Code includes the following:-
1. Data Exploration - Missing Values, Outliers
2. Data Visualisation
3. Correlation Matrix
4. Package "FactoMiner"
5. Topics Covered:- PCA, Correspondence analysis(CA), Dual Multiple Factor Analysis (DMFA), Factor Analysis for mixed data(FAMD), Generalised Procrustes Analysis (GPA), Hierarchical Tree
6. Detailed Plots
## The data has been imported using Import Dataset option in R Environment
## The data set can be obtained from http://archive.ics.uci.edu/ml/datasets/Bank+Marketing
## DATASET UNDERSTANDING
head(bank_full) ## Displays first 6 rows for each variable
str(bank_full) ## Describes each variables
summary(bank_full) ## Provides basic statistical information of each variable
## DATA EXPLORATION - Check for Missing Data
## Option 1
is.na(bank_full) ## Displays True for a missing value
## Since it is a large dataset, graphical display of missing values will prove to be easier
##Option 2
require(Amelia)
missmap(bank_full,main="Missing Data - Bank Subscription", col=c("red","grey"),legend=FALSE)
## No red colour stripes are visible. hence no missing values.
##Option 3
summary(bank_full) ## displays missing values if any under every variable
## DATA VISUALISATION
## Use Box plots (Only for continuous variables)- To Check Ouliers
boxplot(bank_full$age~bank_full$subscribed, main=" AGE",ylab="age of customers",xlab="Subscribed")
boxplot(bank_full$balance~bank_full$subscribed, main=" BALANCE",ylab="Balance of customers",xlab="Subscribed")
boxplot(bank_full$lastday~bank_full$subscribed, main=" LAST DAY",ylab="Last day of contact",xlab="Subscribed")
boxplot(bank_full$lastduration~bank_full$subscribed, main="LAST DURATION",ylab="Last duration of contact",xlab="Subscribed")
boxplot(bank_full$numcontacts~bank_full$subscribed, main="NUM CONTACTS",ylab="number of contacts",xlab="Subscribed")
boxplot(bank_full$pdays~bank_full$subscribed, main=" Previous DAYS",ylab="Previous days of contact",xlab="Subscribed")
boxplot(bank_full$pcontacts~bank_full$subscribed, main=" Previous Contacts",ylab="Previous Contacts with customers",xlab="Subscribed")
## Though some outliers are observed in Previous contacts, NumContacts and LastDuration, they have not bee removed keeping their significance into consideration
## Use Histograms (For both continuous and categorical variables)
## These histograms provide details abpout Skewness, Normal Distribution etc
## Function to create histograms for continuous variables with normal curve
bank_Conthist<-function(VarName,NumBreaks,xlab,main,lengthxfit) ## xlab and main should be mentioned under quotes as they are characters
{
hist(VarName,breaks=NumBreaks,col="yellow",xlab=xlab,main=main)
xfit<-seq(min(VarName),max(VarName),length=lengthxfit)
yfit<-dnorm(xfit,mean=mean(VarName),sd=sd(VarName))
yfit<-yfit*diff(h$mids[1:2])*length(VarName)
lines(xfit,yfit,col="red",lwd=3)
}
bank_Conthist(bank_full$age,10,"age of customers","AGE",30)
bank_Conthist(bank_full$balance,50,"Balance of customers","Balance",100)
## Balance is more skewed towards to Negative or Zero
bank_Conthist(bank_full$lastday,5,"Last Day of contact","LAst Day",10)
bank_Conthist(bank_full$lastduration,100,"LastDuration of COntact","Last Duration",10)
## Last Duration is more skewed towards 0 to 100 secs.
bank_Conthist(bank_full$numcontacts,30,"Number of Contacts","NUmContacts",20)
## NUmContacts are more skewed towards 1
bank_Conthist(bank_full$pdays,30,"Previous Days of contacts","PDays",20)
## Many were not contacted previously
bank_Conthist(bank_full$pcontacts,20,"Previous Contacts","PContacts",10)
## Since many were not contacted previously, therefore Pcontacts is 0
## Barplots for Categorical Variables
barplot(table(bank_full$job),col="red",main="JOB")
barplot(table(bank_full$marital),col="green",main="Marital")
barplot(table(bank_full$education),col="red",main="Education")
barplot(table(bank_full$creditdefault),col="red",main="Credit Default")
## Since Credit Default is highly skewed towards NO, this shall be removed from further analysis
bank_full[5]<-NULL
str(bank_full)
barplot(table(bank_full$housingloan),col="red",main="Housing Loan")
barplot(table(bank_full$personalloan),col="blue",main="Personal Loan")
barplot(table(bank_full$lastcommtype),col="red",main="Last communication type")
barplot(table(bank_full$lastmonth),col="violet",main="Last Month")
barplot(table(bank_full$poutcome),col="magenta",main="Previous Outcome")
## Correlation Matrix among input (or independent) continuous variables
bank_full.cont<-data.frame(bank_full$age,bank_full$balance,bank_full$lastday,bank_full$lastduration,bank_full$numcontacts,bank_full$pdays,bank_full$pcontacts)
str(bank_full.cont)
cor(bank_full.cont)
## It can be observed that No two variables are highly correlated
## First, Lets convert factors having character levels to numeric levels
str(bank_full)
bank_full_transform<-bank_full
bank_full_transform$marital=factor(bank_full_transform$marital,levels=c("single","married","divorced"),labels=c(1,2,3))
bank_full_transform$job=factor(bank_full_transform$job,levels=c("admin.","blue-collar","entrepreneur","housemaid","management","retired","self-employed","services","student","technician","unemployed","unknown"),labels=c(1,2,3,4,5,6,7,8,9,10,11,12))
bank_full_transform$education=factor(bank_full_transform$education,levels=c("primary","secondary","tertiary","unknown"),labels=c(1,2,3,4))
bank_full_transform$housingloan=factor(bank_full_transform$housingloan,levels=c("no","yes"),labels=c(1,2))
bank_full_transform$personalloan=factor(bank_full_transform$personalloan,levels=c("no","yes"),labels=c(1,2))
bank_full_transform$lastcommtype=factor(bank_full_transform$lastcommtype,levels=c("cellular","telephone","unknown"),labels=c(1,2,3))
bank_full_transform$poutcome=factor(bank_full_transform$poutcome,levels=c("failure","other","success","unknown"),labels=c(1,2,3,4))
bank_full_transform$lastmonth=factor(bank_full_transform$lastmonth,levels=c("apr","aug","dec","feb","jan","jul","jun","mar","may","nov","oct","sep"),labels=c(1,2,3,4,5,6,7,8,9,10,11,12))
str(bank_full_transform)
## Now convert these numerical factors into numeric
bank_full_transform$job<-as.numeric(as.character(bank_full_transform$job))
bank_full_transform$marital<-as.numeric(as.character(bank_full_transform$marital))
bank_full_transform$education<-as.numeric(as.character(bank_full_transform$education))
bank_full_transform$personalloan<-as.numeric(as.character(bank_full_transform$personalloan))
bank_full_transform$housingloan<-as.numeric(as.character(bank_full_transform$housingloan))
bank_full_transform$lastcommtype<-as.numeric(as.character(bank_full_transform$lastcommtype))
bank_full_transform$lastmonth<-as.numeric(as.character(bank_full_transform$lastmonth))
bank_full_transform$poutcome<-as.numeric(as.character(bank_full_transform$poutcome))
bank_full_transform$age<-as.numeric(as.character(bank_full_transform$age))
bank_full_transform$balance<-as.numeric(as.character(bank_full_transform$balance))
bank_full_transform$lastday<-as.numeric(as.character(bank_full_transform$lastday))
bank_full_transform$lastduration<-as.numeric(as.character(bank_full_transform$lastduration))
bank_full_transform$numcontacts<-as.numeric(as.character(bank_full_transform$numcontacts))
bank_full_transform$pdays<-as.numeric(as.character(bank_full_transform$pdays))
bank_full_transform$pcontacts<-as.numeric(as.character(bank_full_transform$pcontacts))
str(bank_full_transform)
##In bank_full_transform; the subscribed table is not quantitative
bank_full_transformfull<-bank_full_transform
bank_full_transformfull$subscribed<-factor(bank_full_transformfull$subscribed,levels=c("no","yes"),labels=c(1,2))
bank_full_transformfull$subscribed<-as.numeric(as.character(bank_full_transformfull$subscribed))
all(is.na(bank_full_transformfull))
write.table(bank_full_transformfull,"x1.csv",sep=",")
str(bank_full_transformfull)
## Now all the variables are either intergers or numeric except SUBSCRIBED (which is factor)
## Multivariate Exploratory Data Analysis using FACTOMINER Package
install.packages("FactoMineR")
library(FactoMineR)
## Two-Way Analysis of Variance with the contrasts sum (The sum of coefficients is Zero)
## T test and F test
AovSum(subscribed~.,data=bank_full)
## Two-Way Anova with interaction with Age
AovSum(subscribed~.:age,data=bank_full)
##RV Coefficient:- Squared Pearson Correlation Coefficient. It measures the closeness of 2 sets of points in a matrix.
X<-bank_full[,1:8]
Y<-bank_full[,9:14]
coeffRV(X,Y)
## Correlation of One Categorical or Continuous variable with other Categorical or quantitative variables
## Lets check with respect to Age variable (whose num.var=1, since it is first variable column)
condes(bank_full[1:14],num.var=1,proba=0.05)
## 1. Correspondence Analysis(CA) including supplementary row and (or)column points
## Applicable only on Categorical Data in Numeric or Integer format
bank_CA<-CA(bank_full_transform,ncp=5,col.sup=10:13,row.sup=1:100,quanti.sup=1:4,quali.sup=15,graph=TRUE)
summary(bank_CA)
## Dimension Description : It points out the variables and categories which are more characteristic according to each dimensionobtained by factor analysis
dimdesc(bank_CA,axes=1:3,proba=0.05)
## Visualise the active elements
plot(bank_CA,invisible=c("row.sup","col.sup"))
##2. PRINCIPAL COMPONENT ANALYSIS (PCA)
## Initially estimate the number of components in PCA
estim_ncp(bank_full_transform[,1:15],ncp.min=0,ncp.max=NULL,scale=TRUE, method="GCV")
## Using the above estmate, use the value as ncp. Here we get ncp=1
## PCA analysis for the above data
bank_pca<-PCA(bank_full_transformfull,ncp=5,quanti.sup=NULL,quali.sup=15)
summary(bank_pca)
##bar plot with the eigen values
barplot(bank_pca$eig[,1],main="Eigen Values",names.arg=paste("Dim",1:nrow(bank_pca$eig),sep=""))
##Print the results of PCA
print(bank_pca)
bank_pca$var$coord
## Lets observe the PCA interpretation using third and fourth dimension as your axes
plot(bank_pca,choix="var",axes=c(3,4),lim.cos2.var=0)
## Construction of Confidence Ellipses around the barycentres of all categorical variables
a<-cbind.data.frame(bank_full_transform[,16],bank_pca$ind$coord)
b<-coord.ellipse(a,bary=TRUE)
##habillage=15 indicates that the individuals are coloured according to 15th variable
plot(bank_pca,habillage=15,ellipse=b)
plotellipses(bank_pca)
## Dimension Description : It points out the variables and categories which are more characteristic according to each dimensionobtained by factor analysis
dimdesc(bank_pca,axes=1:3,proba=0.05)
## Graph of variable after factor analysis
graph.var(bank_pca,axes=c(1,2),xlim="Comp-1",ylim="Comp-2",title="Graph of Variables after PCA")
## Hierarchical clustering on Principal Components
HCPC(bank_pca,nb.clust=-1)
## 3. Dual Multiple Factor Analysis (DMFA) with supplementary individuals, supplementary quantitative variables and supplementary categorical variables
bank_dmfa<-DMFA(bank_full_transform,num.fact=16,scale.unit=TRUE,ncp=3,quanti.sup=NULL,quali.sup=16,graph=TRUE,axes=c(1,2))
summary(bank_dmfa)
## Construction of Confidence Ellipses around the barycentres of all categorical variables
a<-cbind.data.frame(bank_full_transform[,16],bank_dmfa$ind$coord)
b<-coord.ellipse(a,bary=TRUE)
plot.PCA(bank_dmfa,habillage=16,ellipse=b)
plotellipses(bank_dmfa)
## Dimension Description : It points out the variables and categories which are more characteristic according to each dimensionobtained by factor analysis
dimdesc(bank_dmfa,axes=1:3,proba=0.05)
## 4. FACTOR ANALYSIS FOR MIXED DATA (Continuous and Catgeorical Data)
bank_famd<-FAMD(bank_full_transform[,1:15],ncp=5,graph=TRUE,axes=c(1,2))
summary(bak_famd)
## Dimension Description : It points out the variables and categories which are more characteristic according to each dimensionobtained by factor analysis
dimdesc(bank_famd,axes=1:3,proba=0.05)
## 5. Generalised PROCRUSTES ANALYSIS(GPA)
## It take sinto account all the missing values and Applicable only for quantitative (continuous) data sets
bank_full_transform_cont<-data.frame(bank_full_transform$age,bank_full_transform$balance,bank_full_transform$lastday,bank_full_transform$lastduration,bank_full_transform$numcontacts,bank_full_transform$pdays,bank_full_transform$pcontacts)
bank_gpa<-GPA(bank_full_transform_cont,group=c(1,2,3))
## Construction of Partial Points only for some indivuals
plotGPApartial(bank_gpa)
## Dimension Description : It points out the variables and categories which are more characteristic according to each dimensionobtained by factor analysis
dimdesc(bank_famd,axes=1:3,proba=0.05)
## 6. HIERARCHICAL TREE FROM A DATA SET
## Usefull when all the variables play a significant role
## initially the data is partitioned using k means clustering (here kk=10 clusters made)
##If nb.clust= 0 (the tree is cut at the level the user clicks on); -1 (the tree is automatically cut at the suggested level)
HCPC(bank_full_transform[,1:15],kk=10,nb.clust=-1)
Data Set:- Bank Marketing https://www.blogger.com/blogger.g?blogID=4359514443959080595#editor/target=post;postID=5426750358330739357
Source of Data Set:- UCI Repository (http://archive.ics.uci.edu/ml/datasets/Bank+Marketing)
The Code includes the following:-
1. Data Exploration - Missing Values, Outliers
2. Data Visualisation
3. Correlation Matrix
4. Package "FactoMiner"
5. Topics Covered:- PCA, Correspondence analysis(CA), Dual Multiple Factor Analysis (DMFA), Factor Analysis for mixed data(FAMD), Generalised Procrustes Analysis (GPA), Hierarchical Tree
6. Detailed Plots
## The data has been imported using Import Dataset option in R Environment
## The data set can be obtained from http://archive.ics.uci.edu/ml/datasets/Bank+Marketing
## DATASET UNDERSTANDING
head(bank_full) ## Displays first 6 rows for each variable
str(bank_full) ## Describes each variables
summary(bank_full) ## Provides basic statistical information of each variable
## DATA EXPLORATION - Check for Missing Data
## Option 1
is.na(bank_full) ## Displays True for a missing value
## Since it is a large dataset, graphical display of missing values will prove to be easier
##Option 2
require(Amelia)
missmap(bank_full,main="Missing Data - Bank Subscription", col=c("red","grey"),legend=FALSE)
## No red colour stripes are visible. hence no missing values.
##Option 3
summary(bank_full) ## displays missing values if any under every variable
## DATA VISUALISATION
## Use Box plots (Only for continuous variables)- To Check Ouliers
boxplot(bank_full$age~bank_full$subscribed, main=" AGE",ylab="age of customers",xlab="Subscribed")
boxplot(bank_full$balance~bank_full$subscribed, main=" BALANCE",ylab="Balance of customers",xlab="Subscribed")
boxplot(bank_full$lastday~bank_full$subscribed, main=" LAST DAY",ylab="Last day of contact",xlab="Subscribed")
boxplot(bank_full$lastduration~bank_full$subscribed, main="LAST DURATION",ylab="Last duration of contact",xlab="Subscribed")
boxplot(bank_full$numcontacts~bank_full$subscribed, main="NUM CONTACTS",ylab="number of contacts",xlab="Subscribed")
boxplot(bank_full$pdays~bank_full$subscribed, main=" Previous DAYS",ylab="Previous days of contact",xlab="Subscribed")
boxplot(bank_full$pcontacts~bank_full$subscribed, main=" Previous Contacts",ylab="Previous Contacts with customers",xlab="Subscribed")
## Though some outliers are observed in Previous contacts, NumContacts and LastDuration, they have not bee removed keeping their significance into consideration
## Use Histograms (For both continuous and categorical variables)
## These histograms provide details abpout Skewness, Normal Distribution etc
## Function to create histograms for continuous variables with normal curve
bank_Conthist<-function(VarName,NumBreaks,xlab,main,lengthxfit) ## xlab and main should be mentioned under quotes as they are characters
{
hist(VarName,breaks=NumBreaks,col="yellow",xlab=xlab,main=main)
xfit<-seq(min(VarName),max(VarName),length=lengthxfit)
yfit<-dnorm(xfit,mean=mean(VarName),sd=sd(VarName))
yfit<-yfit*diff(h$mids[1:2])*length(VarName)
lines(xfit,yfit,col="red",lwd=3)
}
bank_Conthist(bank_full$age,10,"age of customers","AGE",30)
bank_Conthist(bank_full$balance,50,"Balance of customers","Balance",100)
## Balance is more skewed towards to Negative or Zero
bank_Conthist(bank_full$lastday,5,"Last Day of contact","LAst Day",10)
bank_Conthist(bank_full$lastduration,100,"LastDuration of COntact","Last Duration",10)
## Last Duration is more skewed towards 0 to 100 secs.
bank_Conthist(bank_full$numcontacts,30,"Number of Contacts","NUmContacts",20)
## NUmContacts are more skewed towards 1
bank_Conthist(bank_full$pdays,30,"Previous Days of contacts","PDays",20)
## Many were not contacted previously
bank_Conthist(bank_full$pcontacts,20,"Previous Contacts","PContacts",10)
## Since many were not contacted previously, therefore Pcontacts is 0
## Barplots for Categorical Variables
barplot(table(bank_full$job),col="red",main="JOB")
barplot(table(bank_full$marital),col="green",main="Marital")
barplot(table(bank_full$education),col="red",main="Education")
barplot(table(bank_full$creditdefault),col="red",main="Credit Default")
## Since Credit Default is highly skewed towards NO, this shall be removed from further analysis
bank_full[5]<-NULL
str(bank_full)
barplot(table(bank_full$housingloan),col="red",main="Housing Loan")
barplot(table(bank_full$personalloan),col="blue",main="Personal Loan")
barplot(table(bank_full$lastcommtype),col="red",main="Last communication type")
barplot(table(bank_full$lastmonth),col="violet",main="Last Month")
barplot(table(bank_full$poutcome),col="magenta",main="Previous Outcome")
## Correlation Matrix among input (or independent) continuous variables
bank_full.cont<-data.frame(bank_full$age,bank_full$balance,bank_full$lastday,bank_full$lastduration,bank_full$numcontacts,bank_full$pdays,bank_full$pcontacts)
str(bank_full.cont)
cor(bank_full.cont)
## It can be observed that No two variables are highly correlated
## First, Lets convert factors having character levels to numeric levels
str(bank_full)
bank_full_transform<-bank_full
bank_full_transform$marital=factor(bank_full_transform$marital,levels=c("single","married","divorced"),labels=c(1,2,3))
bank_full_transform$job=factor(bank_full_transform$job,levels=c("admin.","blue-collar","entrepreneur","housemaid","management","retired","self-employed","services","student","technician","unemployed","unknown"),labels=c(1,2,3,4,5,6,7,8,9,10,11,12))
bank_full_transform$education=factor(bank_full_transform$education,levels=c("primary","secondary","tertiary","unknown"),labels=c(1,2,3,4))
bank_full_transform$housingloan=factor(bank_full_transform$housingloan,levels=c("no","yes"),labels=c(1,2))
bank_full_transform$personalloan=factor(bank_full_transform$personalloan,levels=c("no","yes"),labels=c(1,2))
bank_full_transform$lastcommtype=factor(bank_full_transform$lastcommtype,levels=c("cellular","telephone","unknown"),labels=c(1,2,3))
bank_full_transform$poutcome=factor(bank_full_transform$poutcome,levels=c("failure","other","success","unknown"),labels=c(1,2,3,4))
bank_full_transform$lastmonth=factor(bank_full_transform$lastmonth,levels=c("apr","aug","dec","feb","jan","jul","jun","mar","may","nov","oct","sep"),labels=c(1,2,3,4,5,6,7,8,9,10,11,12))
str(bank_full_transform)
## Now convert these numerical factors into numeric
bank_full_transform$job<-as.numeric(as.character(bank_full_transform$job))
bank_full_transform$marital<-as.numeric(as.character(bank_full_transform$marital))
bank_full_transform$education<-as.numeric(as.character(bank_full_transform$education))
bank_full_transform$personalloan<-as.numeric(as.character(bank_full_transform$personalloan))
bank_full_transform$housingloan<-as.numeric(as.character(bank_full_transform$housingloan))
bank_full_transform$lastcommtype<-as.numeric(as.character(bank_full_transform$lastcommtype))
bank_full_transform$lastmonth<-as.numeric(as.character(bank_full_transform$lastmonth))
bank_full_transform$poutcome<-as.numeric(as.character(bank_full_transform$poutcome))
bank_full_transform$age<-as.numeric(as.character(bank_full_transform$age))
bank_full_transform$balance<-as.numeric(as.character(bank_full_transform$balance))
bank_full_transform$lastday<-as.numeric(as.character(bank_full_transform$lastday))
bank_full_transform$lastduration<-as.numeric(as.character(bank_full_transform$lastduration))
bank_full_transform$numcontacts<-as.numeric(as.character(bank_full_transform$numcontacts))
bank_full_transform$pdays<-as.numeric(as.character(bank_full_transform$pdays))
bank_full_transform$pcontacts<-as.numeric(as.character(bank_full_transform$pcontacts))
str(bank_full_transform)
##In bank_full_transform; the subscribed table is not quantitative
bank_full_transformfull<-bank_full_transform
bank_full_transformfull$subscribed<-factor(bank_full_transformfull$subscribed,levels=c("no","yes"),labels=c(1,2))
bank_full_transformfull$subscribed<-as.numeric(as.character(bank_full_transformfull$subscribed))
all(is.na(bank_full_transformfull))
write.table(bank_full_transformfull,"x1.csv",sep=",")
str(bank_full_transformfull)
## Now all the variables are either intergers or numeric except SUBSCRIBED (which is factor)
## Multivariate Exploratory Data Analysis using FACTOMINER Package
install.packages("FactoMineR")
library(FactoMineR)
## Two-Way Analysis of Variance with the contrasts sum (The sum of coefficients is Zero)
## T test and F test
AovSum(subscribed~.,data=bank_full)
## Two-Way Anova with interaction with Age
AovSum(subscribed~.:age,data=bank_full)
##RV Coefficient:- Squared Pearson Correlation Coefficient. It measures the closeness of 2 sets of points in a matrix.
X<-bank_full[,1:8]
Y<-bank_full[,9:14]
coeffRV(X,Y)
## Correlation of One Categorical or Continuous variable with other Categorical or quantitative variables
## Lets check with respect to Age variable (whose num.var=1, since it is first variable column)
condes(bank_full[1:14],num.var=1,proba=0.05)
## 1. Correspondence Analysis(CA) including supplementary row and (or)column points
## Applicable only on Categorical Data in Numeric or Integer format
bank_CA<-CA(bank_full_transform,ncp=5,col.sup=10:13,row.sup=1:100,quanti.sup=1:4,quali.sup=15,graph=TRUE)
summary(bank_CA)
## Dimension Description : It points out the variables and categories which are more characteristic according to each dimensionobtained by factor analysis
dimdesc(bank_CA,axes=1:3,proba=0.05)
## Visualise the active elements
plot(bank_CA,invisible=c("row.sup","col.sup"))
##2. PRINCIPAL COMPONENT ANALYSIS (PCA)
## Initially estimate the number of components in PCA
estim_ncp(bank_full_transform[,1:15],ncp.min=0,ncp.max=NULL,scale=TRUE, method="GCV")
## Using the above estmate, use the value as ncp. Here we get ncp=1
## PCA analysis for the above data
bank_pca<-PCA(bank_full_transformfull,ncp=5,quanti.sup=NULL,quali.sup=15)
summary(bank_pca)
##bar plot with the eigen values
barplot(bank_pca$eig[,1],main="Eigen Values",names.arg=paste("Dim",1:nrow(bank_pca$eig),sep=""))
##Print the results of PCA
print(bank_pca)
bank_pca$var$coord
## Lets observe the PCA interpretation using third and fourth dimension as your axes
plot(bank_pca,choix="var",axes=c(3,4),lim.cos2.var=0)
## Construction of Confidence Ellipses around the barycentres of all categorical variables
a<-cbind.data.frame(bank_full_transform[,16],bank_pca$ind$coord)
b<-coord.ellipse(a,bary=TRUE)
##habillage=15 indicates that the individuals are coloured according to 15th variable
plot(bank_pca,habillage=15,ellipse=b)
plotellipses(bank_pca)
## Dimension Description : It points out the variables and categories which are more characteristic according to each dimensionobtained by factor analysis
dimdesc(bank_pca,axes=1:3,proba=0.05)
## Graph of variable after factor analysis
graph.var(bank_pca,axes=c(1,2),xlim="Comp-1",ylim="Comp-2",title="Graph of Variables after PCA")
## Hierarchical clustering on Principal Components
HCPC(bank_pca,nb.clust=-1)
## 3. Dual Multiple Factor Analysis (DMFA) with supplementary individuals, supplementary quantitative variables and supplementary categorical variables
bank_dmfa<-DMFA(bank_full_transform,num.fact=16,scale.unit=TRUE,ncp=3,quanti.sup=NULL,quali.sup=16,graph=TRUE,axes=c(1,2))
summary(bank_dmfa)
## Construction of Confidence Ellipses around the barycentres of all categorical variables
a<-cbind.data.frame(bank_full_transform[,16],bank_dmfa$ind$coord)
b<-coord.ellipse(a,bary=TRUE)
plot.PCA(bank_dmfa,habillage=16,ellipse=b)
plotellipses(bank_dmfa)
## Dimension Description : It points out the variables and categories which are more characteristic according to each dimensionobtained by factor analysis
dimdesc(bank_dmfa,axes=1:3,proba=0.05)
## 4. FACTOR ANALYSIS FOR MIXED DATA (Continuous and Catgeorical Data)
bank_famd<-FAMD(bank_full_transform[,1:15],ncp=5,graph=TRUE,axes=c(1,2))
summary(bak_famd)
## Dimension Description : It points out the variables and categories which are more characteristic according to each dimensionobtained by factor analysis
dimdesc(bank_famd,axes=1:3,proba=0.05)
## 5. Generalised PROCRUSTES ANALYSIS(GPA)
## It take sinto account all the missing values and Applicable only for quantitative (continuous) data sets
bank_full_transform_cont<-data.frame(bank_full_transform$age,bank_full_transform$balance,bank_full_transform$lastday,bank_full_transform$lastduration,bank_full_transform$numcontacts,bank_full_transform$pdays,bank_full_transform$pcontacts)
bank_gpa<-GPA(bank_full_transform_cont,group=c(1,2,3))
## Construction of Partial Points only for some indivuals
plotGPApartial(bank_gpa)
## Dimension Description : It points out the variables and categories which are more characteristic according to each dimensionobtained by factor analysis
dimdesc(bank_famd,axes=1:3,proba=0.05)
## 6. HIERARCHICAL TREE FROM A DATA SET
## Usefull when all the variables play a significant role
## initially the data is partitioned using k means clustering (here kk=10 clusters made)
##If nb.clust= 0 (the tree is cut at the level the user clicks on); -1 (the tree is automatically cut at the suggested level)
HCPC(bank_full_transform[,1:15],kk=10,nb.clust=-1)
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