Customer Segmentation
Uma Srinivas Majji
What is Customer Segmentation?
Customer Segmentation is the process of division of customer base into several groups of individuals that share a similarity in different ways that are relevant to marketing such as gender, age, interests, and miscellaneous spending habits.
Loading Packages
library(plotrix)
library(purrr)
library(cluster)
library(gridExtra)
library(grid)
library(NbClust)
library(factoextra)Data Exploration
customer_data <- read.csv("./data/Mall_Customers.csv")
str(customer_data)## 'data.frame': 200 obs. of 5 variables:
## $ CustomerID : int 1 2 3 4 5 6 7 8 9 10 ...
## $ Gender : chr "Male" "Male" "Female" "Female" ...
## $ Age : int 19 21 20 23 31 22 35 23 64 30 ...
## $ Annual.Income..k.. : int 15 15 16 16 17 17 18 18 19 19 ...
## $ Spending.Score..1.100.: int 39 81 6 77 40 76 6 94 3 72 ...names(customer_data)## [1] "CustomerID" "Gender" "Age"
## [4] "Annual.Income..k.." "Spending.Score..1.100."head(customer_data)## CustomerID Gender 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 76summary(customer_data$Age)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 18.00 28.75 36.00 38.85 49.00 70.00sd(customer_data$Age)## [1] 13.96901summary(customer_data$Annual.Income..k..)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 15.00 41.50 61.50 60.56 78.00 137.00sd(customer_data$Annual.Income..k..)## [1] 26.26472summary(customer_data$Spending.Score..1.100.)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.00 34.75 50.00 50.20 73.00 99.00sd(customer_data$Spending.Score..1.100.)## [1] 25.82352Visualization of Customer Gender
a <- table(customer_data$Gender)
barplot(a, main="Using BarPlot to display Gender Comparision",
ylab="Count",
xlab="Gender",
col = c("#05a399", "lightblue"),
legend = rownames(a))
percent <- round(a/sum(a)*100)
labels <- paste(c("Female","Male")," ",percent,"%",sep=" ")
#library(plotrix)
pie3D(a, labels = labels, main="Pie Chart Depicting Ratio of Female and Male",
col=c("#05a399", "lightblue"))
Visualization of age distribution
hist(customer_data$Age, col = "steelblue",
main="Histogram to Show Count of Age Class",
xlab="Age Class",
ylab="Frequency",
labels=TRUE)
boxplot(customer_data$Age, col="steelblue",
main="Boxplot for Descriptive Analysis of Age")
Analysis of the Annual Income of the Customers
summary(customer_data$Annual.Income..k..)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 15.00 41.50 61.50 60.56 78.00 137.00# Histogram of annual income
hist(customer_data$Annual.Income..k..,
main="Histogram for Annual Income",
xlab="Annual Income Class",
ylab="Frequency",
col="steelblue",
labels=TRUE)
# Density plot
plot(density(customer_data$Annual.Income..k..),
main="Density Plot for Annual Income",
xlab="Annual Income Class",
ylab="Density",
col="steelblue")
polygon(density(customer_data$Annual.Income..k..), col="steelblue")
Analyzing Spending Score of the Customers
summary(customer_data$Spending.Score..1.100.)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.00 34.75 50.00 50.20 73.00 99.00# boxplot
boxplot(customer_data$Spending.Score..1.100.,
horizontal=TRUE, col="steelblue",
main="BoxPlot for Descriptive Analysis of Spending Score")
# histogram
hist(customer_data$Spending.Score..1.100.,
main="HistoGram for Spending Score",
xlab="Spending Score Class",
ylab="Frequency",
col="steelblue",
labels=TRUE)
K-means Algorithm
While using the k-means clustering algorithm, the first step is to indicate the number of clusters (k) that we wish to produce in the final output. The algorithm starts by selecting k objects from dataset randomly that will serve as the initial centers for our clusters. These selected objects are the cluster means, also known as centroids. Then, the remaining objects have an assignment of the closest centroid. This centroid is defined by the Euclidean Distance present between the object and the cluster mean. We refer to this step as “cluster assignment”. When the assignment is complete, the algorithm proceeds to calculate new mean value of each cluster present in the data. After the recalculation of the centers, the observations are checked if they are closer to a different cluster. Using the updated cluster mean, the objects undergo reassignment. This goes on repeatedly through several iterations until the cluster assignments stop altering. The clusters that are present in the current iteration are the same as the ones obtained in the previous iteration.
Determining Optimal Clusters
Elbow Method
library("purrr")
set.seed(321)
# function to calculate total intra-cluster sum of square
iss <- function(k){
kmeans(customer_data[,3:5], k,iter.max = 100, nstart = 100,
algorithm = "Lloyd")$tot.withinss
}
k.values <- 1:10
iss_values <- map_dbl(k.values,iss)
plot(k.values, iss_values,
type="b", pch = 19, frame = FALSE,
xlab="Number of clusters K",
ylab="Total intra-clusters sum of squares")
Average Silhouette Method
#library(cluster)
#library(gridExtra)
#library(grid)
k2<-kmeans(customer_data[,3:5],2,iter.max=100,nstart=50,algorithm="Lloyd")
s2<-plot(silhouette(k2$cluster,dist(customer_data[,3:5],"euclidean")))
k3<-kmeans(customer_data[,3:5],3,iter.max=100,nstart=50,algorithm="Lloyd")
s3<-plot(silhouette(k3$cluster,dist(customer_data[,3:5],"euclidean")))
k4<-kmeans(customer_data[,3:5],4,iter.max=100,nstart=50,algorithm="Lloyd")
s4<-plot(silhouette(k4$cluster,dist(customer_data[,3:5],"euclidean")))
k5<-kmeans(customer_data[,3:5],5,iter.max=100,nstart=50,algorithm="Lloyd")
s5<-plot(silhouette(k5$cluster,dist(customer_data[,3:5],"euclidean")))
k6<-kmeans(customer_data[,3:5],6,iter.max=100,nstart=50,algorithm="Lloyd")
s6<-plot(silhouette(k6$cluster,dist(customer_data[,3:5],"euclidean")))
k7<-kmeans(customer_data[,3:5],7,iter.max=100,nstart=50,algorithm="Lloyd")
s7<-plot(silhouette(k7$cluster,dist(customer_data[,3:5],"euclidean")))
k8<-kmeans(customer_data[,3:5],8,iter.max=100,nstart=50,algorithm="Lloyd")
s8<-plot(silhouette(k8$cluster,dist(customer_data[,3:5],"euclidean")))
k9<-kmeans(customer_data[,3:5],9,iter.max=100,nstart=50,algorithm="Lloyd")
s9<-plot(silhouette(k9$cluster,dist(customer_data[,3:5],"euclidean")))
k10<-kmeans(customer_data[,3:5],10,iter.max=100,nstart=50,algorithm="Lloyd")
s10<-plot(silhouette(k10$cluster,dist(customer_data[,3:5],"euclidean")))
# we make use of the fviz_nbclust() function to determine
# and visualize the optimal number of clusters
#library(NbClust)
#library(factoextra)
fviz_nbclust(customer_data[,3:5], kmeans, method = "silhouette")
Gap Statistic Method
set.seed(125)
stat_gap <- clusGap(customer_data[,3:5], FUN = kmeans, nstart = 25,
K.max = 10, B = 50)
fviz_gap_stat(stat_gap)
# let us take k = 6 as our optimal cluster
k6<-kmeans(customer_data[,3:5],6,iter.max=100,nstart=50,algorithm="Lloyd")
k6## K-means clustering with 6 clusters of sizes 45, 22, 21, 38, 35, 39
##
## Cluster means:
## Age Annual.Income..k.. Spending.Score..1.100.
## 1 56.15556 53.37778 49.08889
## 2 25.27273 25.72727 79.36364
## 3 44.14286 25.14286 19.52381
## 4 27.00000 56.65789 49.13158
## 5 41.68571 88.22857 17.28571
## 6 32.69231 86.53846 82.12821
##
## Clustering vector:
## [1] 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3
## [38] 2 3 2 1 2 1 4 3 2 1 4 4 4 1 4 4 1 1 1 1 1 4 1 1 4 1 1 1 4 1 1 4 4 1 1 1 1
## [75] 1 4 1 4 4 1 1 4 1 1 4 1 1 4 4 1 1 4 1 4 4 4 1 4 1 4 4 1 1 4 1 4 1 1 1 1 1
## [112] 4 4 4 4 4 1 1 1 1 4 4 4 6 4 6 5 6 5 6 5 6 4 6 5 6 5 6 5 6 5 6 4 6 5 6 5 6
## [149] 5 6 5 6 5 6 5 6 5 6 5 6 5 6 5 6 5 6 5 6 5 6 5 6 5 6 5 6 5 6 5 6 5 6 5 6 5
## [186] 6 5 6 5 6 5 6 5 6 5 6 5 6 5 6
##
## Within cluster sum of squares by cluster:
## [1] 8062.133 4099.818 7732.381 7742.895 16690.857 13972.359
## (between_SS / total_SS = 81.1 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"# cluster - This is a vector of several integers that denote the cluster which has an allocation of each point.
# totss - This represents the total sum of squares.
# centers - Matrix comprising of several cluster centers
# withinss - This is a vector representing the intra-cluster sum of squares having one component per cluster.
# tot.withinss - This denotes the total intra-cluster sum of squares.
# betweenss - This is the sum of between-cluster squares.
# size - The total number of points that each cluster holds.
## Visualizing the Clustering Results using the First Two Principle Components
pcclust=prcomp(customer_data[,3:5],scale=FALSE) #principal component analysis
summary(pcclust)## Importance of components:
## PC1 PC2 PC3
## Standard deviation 26.4625 26.1597 12.9317
## Proportion of Variance 0.4512 0.4410 0.1078
## Cumulative Proportion 0.4512 0.8922 1.0000pcclust$rotation[,1:2] ## PC1 PC2
## Age 0.1889742 -0.1309652
## Annual.Income..k.. -0.5886410 -0.8083757
## Spending.Score..1.100. -0.7859965 0.5739136# visualize the clusters
set.seed(147)
ggplot(customer_data, aes(x =Annual.Income..k.., y = Spending.Score..1.100.)) +
geom_point(stat = "identity", aes(color = as.factor(k6$cluster))) +
scale_color_discrete(name=" ",
breaks=c("1", "2", "3", "4", "5", "6"),
labels=c("Cluster 1", "Cluster 2", "Cluster 3",
"Cluster 4", "Cluster 5","Cluster 6")) +
ggtitle("Segments of Mall Customers", subtitle = "Using K-means Clustering")
kCols=function(vec){cols=rainbow (length (unique (vec)))
return (cols[as.numeric(as.factor(vec))])}
digCluster<-k6$cluster
dignm<-as.character(digCluster) # K-means clusters
plot(pcclust$x[,1:2], col =kCols(digCluster),pch =19,xlab ="K-means",ylab="classes")
legend("bottomleft",unique(dignm),fill=unique(kCols(digCluster)))