#Market Segmentation
#identifying consumers with similar taste or habits ,
#and then grouping them.
#By doing so it becomes easier to target each group with different policies (in this example of mall segmentation , it would be discounts and other sale tactics),
#which would in turn maximise the profits and minimise the cost.
#As there are no pre imposed labels to classify the customers ,
#we use K-means, which is clustering technique used for unsupervised learning.
#K-means
#A clustering technique which groups similar data points by taking in account their airthmetic mean , in others forms gropus/clusters of data points with similar mean. It requires two arguments, the data and the number of centroids(k). The k tells the algorithm how many clusters it needs to make. The optimal number of clusters can be found using :-
#Elbow Method
#Silhouette Method.
#This study would employ the Silhouette Method(SM) to find the optimal number of centroids.
#Our Aim of the study is to form clusters based on the annual income,
#and the spending scores of the customers.
#This wpuld let us understand our customers better,
#and hence in the future help in better strategy planning.
#loading packages
pacman::p_load(pacman,tidyr,ggthemes,ggplot2,plotly,GGally,rio,
stringr,shiny,rmarkdown,lubridate,psych,ipred,caret,ROCR,pROC,
DT,dummies,rpart,rpart.plot,httr,randomForest,readr,doParallel,
xgboost,truncnorm,DMwR,tidyverse,cluster)
Mall_data<-read.csv('Mall_Customers.csv')
head(Mall_data)
## CustomerID Genre Age Annual.Income..k.. Spending.Score..1.100.
## 1 1 Male 19 15 39
## 2 2 Male 21 15 81
## 3 3 Female 20 16 6
## 4 4 Female 23 16 77
## 5 5 Female 31 17 40
## 6 6 Female 22 17 76
#check for any missing values
sum(is.na(Mall_data))
## [1] 0
colSums(is.na(Mall_data))
## CustomerID Genre Age
## 0 0 0
## Annual.Income..k.. Spending.Score..1.100.
## 0 0
#data contain no missing values
#Silhouette Analysis.
#The Silhouette Method allows you to calculate how similar each observations is within the cluster it is assigned relative to other clusters.
#The method uses average silhouette widths to explore what the "best" value of k should be.
#It provides a metric to analyse this , ranging from -1 to 1.
#while 1 being it is in the right cluster.
#Thus K with the average width closest to 1 is chosen as the optimal number of clusters.
#We create df1 having only two variables, Income and Spending scores, the variables for our study.As a thumb rules k Should not be more than the number of original variables, which in this case is 5.
# df1 with income and spending score as the only variables
df1<-Mall_data
df1 <- df1 %>%
select(-CustomerID,-Genre,-Age)
#silhouted annalysis for k ----
sil <- map_dbl(2:5,function(k){
model <- pam(df1 , k=k)
model$silinfo$avg.width
})
sil_df <- data.frame(k=2:5,sil_width=sil)
sil_df
## k sil_width
## 1 2 0.3960019
## 2 3 0.4649832
## 3 4 0.3544029
## 4 5 0.5535287
ggplot(sil_df, aes(x = k, y = sil_width)) +
geom_line(col = "red") +
scale_x_continuous(breaks = 2:5)+ ggtitle("Silhouette Method")
#From our analysis we can see that K with the value of 5,
#has the average width closest to 1.
#Thus we well be forming 5 clusters for our study.
#CLUSTER ANALYSIS
set.seed(1992)
clus <- kmeans(df1,5)
clus
## K-means clustering with 5 clusters of sizes 22, 100, 38, 30, 10
##
## Cluster means:
## Annual.Income..k.. Spending.Score..1.100.
## 1 25.72727 79.36364
## 2 47.96000 43.25000
## 3 87.00000 18.63158
## 4 78.23333 81.36667
## 5 109.70000 82.00000
##
## Clustering vector:
## [1] 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
## [38] 1 2 1 2 1 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [75] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [112] 2 2 2 2 2 2 2 2 2 2 2 4 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4
## [149] 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 5 3 5 3
## [186] 5 3 5 3 5 3 5 3 5 3 5 3 5 3 5
##
## Within cluster sum of squares by cluster:
## [1] 3519.455 42058.590 14204.842 4370.333 2512.100
## (between_SS / total_SS = 75.3 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"
#Assig the variables into 5 clusters
Mall_data <- mutate(Mall_data,cluster = clus$cluster)
head(Mall_data)
## CustomerID Genre Age Annual.Income..k.. Spending.Score..1.100. cluster
## 1 1 Male 19 15 39 2
## 2 2 Male 21 15 81 1
## 3 3 Female 20 16 6 2
## 4 4 Female 23 16 77 1
## 5 5 Female 31 17 40 2
## 6 6 Female 22 17 76 1
#plot the Clusters
ggplot(Mall_data,aes(Annual.Income..k..,Spending.Score..1.100., col=factor(cluster)))+
geom_point()+
xlab("Annual Income")+
ylab("Spending Score")+
ggtitle("Cluster analysis")+
scale_color_discrete(name=" ",breaks=c("1", "2", "3", "4", "5"),
labels=c("Cluster 1", "Cluster 2", "Cluster 3", "Cluster 4", "Cluster 5"))
#From the graphical represenation we can make the following deduction about the clusters:
# Cluster 1 has individuals with low income and a high spending score.
# Cluster 2 has individuals with mid range annual income as well as mid spending score.
# Cluster 3 has individuals with mid range annual income as well as high spending score.
# Cluster 4 has individuals with high annual income as well as high spending score.
# Cluster 5 has individuals with mid to high annual incomes as well as low spending score.
#Now lets look at the gender and age diversion between these clusters:
ggplot(Mall_data,aes(Age,fill= factor(cluster)))+
geom_density(alpha=0.7)+
ggtitle("Cluster analysis by Age")+
scale_fill_discrete(name=" ",
breaks=c("1", "2", "3", "4", "5"),
labels=c("Cluster 1", "Cluster 2", "Cluster 3", "Cluster 4", "Cluster 5"))
#From the graphical representation we can see that the clusters are normally distributed.
#They have customers of all age groups in them , with peaks mostly seen in the late 30s or early 40s.
#Cluster 4, who are seen to have high spending score,as well as a high annual income,
#have customers that are mostly late 20s and early 50s or mid 40s,
#this is a good indication as to why the group has high spending score as,
#well as high annual income.this might be attributed to the fact that most peiple
#aged in 24 to 45 years of age have families,some with kids.
#Cluster 1 who have low income and high spending score is Right tailed,the customers in cluster1
#are mostly late teens or in their early 20s and some ealry 40s, this explains why they have high spending score with low income
#Cluster 2 and 3 has all the age groups included and with mid range income as well as mid range
#spending score.
#Cluster 5 has mid-high annual income with and are in their mid 20s to ealry 40s with a peak around the 30s
#Cluster 5 mostly in the 30s
ggplot(Mall_data,aes(Genre,fill= factor(cluster)))+
geom_bar(position = "fill")+
ggtitle("Cluster analysis by Gender")+
scale_fill_discrete(name=" ",
breaks=c("1", "2", "3", "4", "5"),
labels=c("Cluster 1", "Cluster 2", "Cluster 3", "Cluster 4", "Cluster 5")) +
ylab("Proportion")
#All the clusters have an equal representation of the genders.
#With the above clustering analysis,
#corporation can identify different groups of customers ,
#and thus target them more precisiely by bettering their strategies.
#The cluster analysis in the mall project has provided good insights into the customer data base.
#by income
ggplot(Mall_data,aes(Annual.Income..k..,fill= factor(cluster)))+
geom_bar(position = "fill")+
ggtitle("Cluster analysis by Income")+
scale_fill_discrete(name=" ",
breaks=c("1", "2", "3", "4", "5"),
labels=c("Cluster 1", "Cluster 2", "Cluster 3", "Cluster 4", "Cluster 5")) +
ylab("Proportion")
#it seems that all in Cluster 3 have an annual income range from around 60k and beyond 100k
#Cluster 5 have a range from 100k and above highest earners but lowest spenders
#cluster 1 have a range of less than 40K amking then the lowest earners
#cluster 4 has mid range income of >60k but less than 100k