USL project - Customer Segmentation | Clustering & Dimension reduction

Introduction

Source: awkn.pro

The aim of the analysis is to segment customers using clustering methods. Correct customer segmentation can be extremely valuable for companies. It allows them to better understand their customers’ needs and preferences. In addition, correct customer clustering allows a company to carry out more effective and targeted marketing activities. This is due to the ability to tailor product and service offerings to a specific group of customers, which ultimately increases the likelihood of their interest and purchase. Ultimately, insightful customer segmentation also allows for a more efficient use of company resources and enables a better understanding of the market.

Both clustering and dimension reduction methods were used in the analysis. First, an analysis of the available data was carried out. Redundant variables were removed, some were also transformed and outliers were discarded. The data was then normalised and scaled for further dimension reduction and clustering analysis.

About Dataset

The data used in the analysis was taken from Kaggle: https://www.kaggle.com/datasets/imakash3011/customer-personality-analysis

Before cleaning, the data contains 29 variables and 2240 observations. The database contains information on the customers of a certain company. Among other things, a range of private customer information can be read out, such as year of birth, completed level of education, marital status and income. In addition, it includes information on the expenditure for each product group over the last two years, as well as the number of transactions and information on accepted marketing campaigns. All variables and their descriptions can be found in the tables below.

• People

Variable	Description
ID	Customer’s unique identifier
Year_Birth:	Customer’s birth year
Education	Customer’s education level
Marital_Status	Customer’s marital status
Income	Customer’s yearly household income
Kidhome	Number of children in customer’s household
Teenhome	Number of teenagers in customer’s household
Dt_Customer	Date of customer’s enrollment with the company
Recency	Number of days since customer’s last purchase
Complain	1 if the customer complained in the last 2 years, 0 otherwise

• Products

Variable	Description
MntWines	Amount spent on wine in last 2 years
MntFruits	Amount spent on fruits in last 2 years
MntMeatProducts	Amount spent on meat in last 2 years
MntFishProducts	Amount spent on fish in last 2 years
MntSweetProducts	Amount spent on sweets in last 2 years
MntGoldProds	Amount spent on gold in last 2 years

• Promotion

NumDealsPurchases	Number of purchases made with a discount
AcceptedCmp1	1 if customer accepted the offer in the 1st campaign, 0 otherwise
AcceptedCmp2	1 if customer accepted the offer in the 2nd campaign, 0 otherwise
AcceptedCmp3	1 if customer accepted the offer in the 3rd campaign, 0 otherwise
AcceptedCmp4	1 if customer accepted the offer in the 4th campaign, 0 otherwise
AcceptedCmp5	1 if customer accepted the offer in the 5th campaign, 0 otherwise
Response	1 if customer accepted the offer in the last campaign, 0 otherwise

• Place

Variable	Description
NumDealsPurchases	Number of purchases made on deals
NumWebPurchases	Number of purchases made through the company’s website
NumCatalogPurchases	Number of purchases made using a catalogue
NumStorePurchases	Number of purchases made directly in stores
NumWebVisitsMonth	Number of visits to company’s website in the last month

Loading data

data=read.table("USL_clustering_marketing_campaign.csv", sep = ",", header = T)
customers=data.frame(data)
head(customers)

Data cleaning and preprocessing

Searching for missing data

customers[!complete.cases(customers),]

customers<-na.omit(customers)

There aren’t many, so I decide to discard the missing data.

str(customers)

'data.frame':   2216 obs. of  29 variables:
 $ ID                 : int  5524 2174 4141 6182 5324 7446 965 6177 4855 5899 ...
 $ Year_Birth         : int  1957 1954 1965 1984 1981 1967 1971 1985 1974 1950 ...
 $ Education          : chr  "Graduation" "Graduation" "Graduation" "Graduation" ...
 $ Marital_Status     : chr  "Single" "Single" "Together" "Together" ...
 $ Income             : num  58138 46344 71613 26646 58293 ...
 $ Kidhome            : int  0 1 0 1 1 0 0 1 1 1 ...
 $ Teenhome           : int  0 1 0 0 0 1 1 0 0 1 ...
 $ Dt_Customer        : chr  "2012-04-09" "2014-08-03" "2013-08-21" "2014-10-02" ...
 $ Recency            : int  58 38 26 26 94 16 34 32 19 68 ...
 $ MntWines           : int  635 11 426 11 173 520 235 76 14 28 ...
 $ MntFruits          : int  88 1 49 4 43 42 65 10 0 0 ...
 $ MntMeatProducts    : int  546 6 127 20 118 98 164 56 24 6 ...
 $ MntFishProducts    : int  172 2 111 10 46 0 50 3 3 1 ...
 $ MntSweetProducts   : int  88 1 21 3 27 42 49 1 3 1 ...
 $ MntGoldProds       : int  88 6 42 5 15 14 27 23 2 13 ...
 $ NumDealsPurchases  : int  3 2 1 2 5 2 4 2 1 1 ...
 $ NumWebPurchases    : int  8 1 8 2 5 6 7 4 3 1 ...
 $ NumCatalogPurchases: int  10 1 2 0 3 4 3 0 0 0 ...
 $ NumStorePurchases  : int  4 2 10 4 6 10 7 4 2 0 ...
 $ NumWebVisitsMonth  : int  7 5 4 6 5 6 6 8 9 20 ...
 $ AcceptedCmp3       : int  0 0 0 0 0 0 0 0 0 1 ...
 $ AcceptedCmp4       : int  0 0 0 0 0 0 0 0 0 0 ...
 $ AcceptedCmp5       : int  0 0 0 0 0 0 0 0 0 0 ...
 $ AcceptedCmp1       : int  0 0 0 0 0 0 0 0 0 0 ...
 $ AcceptedCmp2       : int  0 0 0 0 0 0 0 0 0 0 ...
 $ Complain           : int  0 0 0 0 0 0 0 0 0 0 ...
 $ Z_CostContact      : int  3 3 3 3 3 3 3 3 3 3 ...
 $ Z_Revenue          : int  11 11 11 11 11 11 11 11 11 11 ...
 $ Response           : int  1 0 0 0 0 0 0 0 1 0 ...
 - attr(*, "na.action")= 'omit' Named int [1:24] 11 28 44 49 59 72 91 92 93 129 ...
  ..- attr(*, "names")= chr [1:24] "11" "28" "44" "49" ...

The ‘Dt_Customer’ variable, which indicates the date the customer was added to the database, should be in Date format. It is then worth creating a new variable ‘client_days’ stating how many days the customer has been in the system. (reference to the day of the last saved client)

customers$Dt_Customer <- as.Date(customers$Dt_Customer)
customers$client_days <- as.numeric(customers$Dt_Customer - min(customers$Dt_Customer))

Another variable to be improved is Education. Firstly, it is stored as a textual variable, but we would like it to be stored as a categorical variable (factor).

customers %>% group_by(Education) %>% tally()

Looking at the distribution of the Eductaion variable, it is worth reducing the number of its levels. In my opinion, only 3 levels are sufficient: Undergraduate, Graduate and Postgraduate

customers[customers$Education=='Basic',]$Education <- 'Undergraduate'
customers[(customers$Education=='Graduation' | customers$Education=='2n Cycle'),]$Education <- 'Graduate'
customers[(customers$Education=='Master' | customers$Education=='PhD'),]$Education <- 'Postgraduate'

customers$Education <- factor(customers$Education,
                                 levels = c('Undergraduate', 'Graduate', 'Postgraduate'),
                                 labels = c('Undergraduate', 'Graduate', 'Postgraduate'),
                                 ordered = T)

customers %>% group_by(Education) %>% tally()

Similarly, the Marital_Status variable should be corrected.

customers %>% group_by(Marital_Status) %>% tally()

filter(customers, Marital_Status=='YOLO' | Marital_Status=='Absurd')

The data for people with Marital_Status==‘YOLO’ seem to be repeated. As the data with marital status YOLO or Absurd is not much I decided to discard it. The remaining levels of the variable will be aggregated to two levels: Single and In_relationship.

customers<-customers[!(customers$Marital_Status=='YOLO' | customers$Marital_Status=='Absurd'),]
customers[(customers$Marital_Status=='Alone' | customers$Marital_Status=='Divorced' | customers$Marital_Status=='Widow'),]$Marital_Status <- 'Single'
customers[(customers$Marital_Status=='Married'| customers$Marital_Status=='Together'),]$Marital_Status <- 'In_relationship'
customers$Marital_Status <- factor(customers$Marital_Status)
customers %>% group_by(Marital_Status) %>% tally()

The other variables in the database appear to have the appropriate types. However, before proceeding with further analysis, it is worth supplementing the database with some useful new variables.

customers$Age <- 2014 - customers$Year_Birth
customers$Cmp_accepted <- customers$AcceptedCmp1 + customers$AcceptedCmp2 + customers$AcceptedCmp3 + customers$AcceptedCmp4 + customers$AcceptedCmp5
customers$Children <- customers$Teenhome + customers$Kidhome
customers$Money_spent <- customers$MntWines + customers$MntFruits + customers$MntMeatProducts + customers$MntFishProducts + customers$MntSweetProducts + customers$MntGoldProds
customers$Number_purchases <-  + customers$NumWebPurchases + customers$NumCatalogPurchases + customers$NumStorePurchases
customers$Number_deals_purchases <- customers$NumDealsPurchases
customers$Number_web_visits_month <- customers$NumWebVisitsMonth

The newly created variables are:

• Age - depicting the age of the customer

• Cmp_accepted - depicting the number of accepted marketing campaigns

• Children - depicting the number of children owned

• Money_spent - depicting the total spend on the listed products in the last 2 years

• Number_purchases - depicting the total number of purchases of a given customer

• Number_deals_purchases - depicting the total number of purchases from a given customer’s promotions

• Number_web_visits_month - depicting the total number of visits to a given customer

Outliers

Checking whether the dataset contains any outlier observations.

describe(customers)

Warning: no non-missing arguments to min; returning InfWarning: no non-missing arguments to max; returning -Inf

Looking at the statistics, potential outliers are noticeable with the Age and Income variables. However, it is worthwhile using graphical analysis.

ggplot(customers, aes(Age)) +
  geom_histogram(aes(y = ..density..), color = "#000000", fill = "#0099F8") +
  geom_density(color = "#000000", fill = "#F85700", alpha = 0.6)

ggplot(customers, aes(y = Age))+
geom_boxplot(fill = '#0099F8',alpha = 0.5,color = 1,outlier.colour = 2)+
theme_bw()

boxplot.stats(customers$Age)$out

[1] 114 121 115

customers<-customers[customers$Age<114,]

ggplot(customers, aes(Income)) +
  geom_histogram(aes(y = ..density..), color = "#000000", fill = "#0099F8") +
  geom_density(color = "#000000", fill = "#F85700", alpha = 0.6)

ggplot(customers, aes(y = Income))+
geom_boxplot(fill = '#0099F8',alpha = 0.5,color = 1,outlier.colour = 2)+
theme_bw()

boxplot.stats(customers$Income)$out

[1] 157243 162397 153924 160803 157733 157146 156924 666666

customers<-customers[customers$Income<153924,]

It is also worth considering the suitability of some of the variables for further analysis.

hist(customers$Z_Revenue, col = "#0099F8")

hist(customers$Z_CostContact, col = "#0099F8")

hist(customers$Complain, col = "#0099F8")

The variables Z_Revenue and Z_CostContact have a fixed value for all observations. We can calmly remove them from the dataset. The variable Complain, on the other hand, takes the value 1 for too few observations to be retained in the database.

#Removing unnecessary variables from the dataset for further analysis
customers_df <- customers[c(-1,-2,-8,-26,-27,-28,-29)]

Dimension reduction

Correlation

corr_dim_red <- customers_df[c(-1,-2,-25,-26,-27,-28,-29,-30)]

ggcorr(corr_dim_red, method = c("everything", "pearson"), label = TRUE, label_size = 1.35, label_round = 3, hjust = 0.85, size = 1.75)

ggcorr(corr_dim_red, method = c("everything", "spearman"), label = TRUE, label_size = 1.35, label_round = 3, hjust = 0.85, size = 1.75)

As can be seen from the graphs, quite a few of the variables are correlated. Hence, reducing the dimensions will not only possibly provide some insight into the data, but will also help to get rid of the high correlation of the variables.

customers_dim_red$Edu_ug <- 0
customers_dim_red[customers$Education == 'Undergraduate',]$Edu_ug <- 1
customers_dim_red$Edu_g <- 0
customers_dim_red[customers$Education == 'Graduate',]$Edu_g <- 1
customers_dim_red$Edu_pg <- 0
customers_dim_red[customers$Education == 'Postgraduate',]$Edu_pg <- 1

customers_dim_red$Marital_status <- 0
customers_dim_red[customers$Marital_Status == 'In_relationship',]$Marital_status <- 1

customers_dim_red <- customers_dim_red[c(-1,-2)]

Normalizing and scaling

preproc2 <- preProcess(customers_dim_red, method=c("center", "scale"))
customers_dim_red.s <- predict(preproc2, customers_dim_red)
 
summary(customers_dim_red.s)

    Teenhome          Recency             MntWines         MntFruits       MntMeatProducts   MntFishProducts   MntSweetProducts   MntGoldProds     NumDealsPurchases NumWebPurchases  
 Min.   :-0.9304   Min.   :-1.695700   Min.   :-0.9062   Min.   :-0.6631   Min.   :-0.7587   Min.   :-0.6889   Min.   :-0.6597   Min.   :-0.8520   Min.   :-1.2282   Min.   :-1.4967  
 1st Qu.:-0.9304   1st Qu.:-0.865953   1st Qu.:-0.8352   1st Qu.:-0.6128   1st Qu.:-0.6853   1st Qu.:-0.6340   1st Qu.:-0.6354   1st Qu.:-0.6774   1st Qu.:-0.6980   1st Qu.:-0.7664  
 Median :-0.9304   Median :-0.001634   Median :-0.3852   Median :-0.4619   Median :-0.4466   Median :-0.4692   Median :-0.4653   Median :-0.3669   Median :-0.1677   Median :-0.0360  
 Mean   : 0.0000   Mean   : 0.000000   Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000  
 3rd Qu.: 0.9062   3rd Qu.: 0.862686   3rd Qu.: 0.5948   3rd Qu.: 0.1667   3rd Qu.: 0.3063   3rd Qu.: 0.2263   3rd Qu.: 0.1665   3rd Qu.: 0.2345   3rd Qu.: 0.3626   3rd Qu.: 0.6943  
 Max.   : 2.7429   Max.   : 1.727005   Max.   : 3.5138   Max.   : 4.3404   Max.   : 7.1600   Max.   : 4.0520   Max.   : 5.7071   Max.   : 5.3758   Max.   : 6.7259   Max.   : 8.3630  
 NumCatalogPurchases NumStorePurchases NumWebVisitsMonth  AcceptedCmp3      AcceptedCmp4      AcceptedCmp5      AcceptedCmp1      AcceptedCmp2      client_days             Age          
 Min.   :-0.9451     Min.   :-1.7946   Min.   :-2.2135   Min.   :-0.2827   Min.   :-0.2837   Min.   :-0.2799   Min.   :-0.2616   Min.   :-0.1175   Min.   :-2.371570   Min.   :-2.31631  
 1st Qu.:-0.9451     1st Qu.:-0.8700   1st Qu.:-0.9695   1st Qu.:-0.2827   1st Qu.:-0.2837   1st Qu.:-0.2799   1st Qu.:-0.2616   1st Qu.:-0.1175   1st Qu.:-0.749124   1st Qu.:-0.69263  
 Median :-0.2298     Median :-0.2536   Median : 0.2745   Median :-0.2827   Median :-0.2837   Median :-0.2799   Median :-0.2616   Median :-0.1175   Median :-0.004607   Median :-0.09443  
 Mean   : 0.0000     Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.000000   Mean   : 0.00000  
 3rd Qu.: 0.4856     3rd Qu.: 0.6710   3rd Qu.: 0.6892   3rd Qu.:-0.2827   3rd Qu.:-0.2837   3rd Qu.:-0.2799   3rd Qu.:-0.2616   3rd Qu.:-0.1175   3rd Qu.: 0.739911   3rd Qu.: 0.84560  
 Max.   : 9.0695     Max.   : 2.2120   Max.   : 6.0798   Max.   : 3.5352   Max.   : 3.5235   Max.   : 3.5708   Max.   : 3.8214   Max.   : 8.5049   Max.   : 2.203124   Max.   : 2.46929  
     Edu_ug            Edu_g             Edu_pg        Marital_status  
 Min.   :-0.1586   Min.   :-1.2123   Min.   :-0.7832   Min.   :-1.351  
 1st Qu.:-0.1586   1st Qu.:-1.2123   1st Qu.:-0.7832   1st Qu.:-1.351  
 Median :-0.1586   Median : 0.8245   Median :-0.7832   Median : 0.740  
 Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.000  
 3rd Qu.:-0.1586   3rd Qu.: 0.8245   3rd Qu.: 1.2763   3rd Qu.: 0.740  
 Max.   : 6.3041   Max.   : 0.8245   Max.   : 1.2763   Max.   : 0.740  

MDS

The Multidimensional Scaling (MDS) method is a way to simplify complex data by representing it in two dimensions. Despite the number of variables involved in the data, MDS can effectively present it in a more manageable form. This method has the added benefit of being able to easily identify outliers, making it an important step in the data analysis process. By using MDS, the data is transformed from multiple dimensions into a more comprehensible two-dimensional format.

dist.customers<-dist(customers_dim_red.s)
mds1<-cmdscale(dist.customers, k=2)
summary(mds1)

       V1                V2         
 Min.   :-4.7315   Min.   :-5.2298  
 1st Qu.:-2.1042   1st Qu.:-1.1029  
 Median :-0.7606   Median : 0.1407  
 Mean   : 0.0000   Mean   : 0.0000  
 3rd Qu.: 1.9036   3rd Qu.: 1.2791  
 Max.   : 7.5714   Max.   : 3.2274  

plot(mds1)
abline(v=-4)

abline(h=-4.5)
x.out<-which(mds1[,1]< -4)
y.out<-which(mds1[,2]< -4.5)
out.all<-c(x.out, y.out)
out.uni<-unique(out.all)
points(mds1[out.uni,], pch=4, col="red", cex=2)

customers_dim_red.s_2 <- customers_dim_red.s
full<-1:2201
limited<-as.numeric(out.all)
customers_dim_red.s_2$mark<-full %in% limited
customers_dim_red.s_2 <- subset(customers_dim_red.s_2, customers_dim_red.s_2$mark == FALSE, select = -c(mark))

PCA

PCA (Principal Component Analysis) like MDS is a statistical method used to reduce the dimensionality of large and complex data sets. The aim of PCA is to identify the underlying structure of the data and reduce it to a smaller set of uncorrelated variables, called principal components, which capture most of the information in the original data.

customers_pca.s <- customers_dim_red.s
customers_pca1<-prcomp(customers_pca.s, center=FALSE, scale.=FALSE) 
customers_pca1

Standard deviations (1, .., p=24):
 [1] 2.385535e+00 1.524139e+00 1.409266e+00 1.282481e+00 1.165746e+00 1.047859e+00 1.004184e+00 9.943085e-01 9.664366e-01 8.981268e-01 8.901675e-01 8.196812e-01 7.813397e-01 7.721401e-01 7.385156e-01
[16] 7.302660e-01 7.116891e-01 6.510803e-01 6.206232e-01 6.080506e-01 5.368458e-01 4.983573e-01 4.350454e-01 2.656610e-15

Rotation (n x k) = (24 x 24):
                             PC1          PC2          PC3          PC4         PC5          PC6          PC7          PC8         PC9        PC10         PC11        PC12         PC13          PC14
Teenhome             0.073185952 -0.341133856  0.320645247 -0.032845418  0.31229689 -0.123272536  0.023820214 -0.047492341  0.24005215 -0.02986569  0.051765316 -0.05347785 -0.156577743 -0.1894530237
Recency             -0.007827026  0.006910237  0.039314118  0.005303605  0.04594928  0.348552473  0.480956802 -0.778170724 -0.09189307 -0.03384369  0.122481437 -0.08012419 -0.003891442  0.0396792246
MntWines            -0.325104699 -0.241264169 -0.010221154  0.157065224 -0.04611474  0.033097363  0.004020872  0.004656491 -0.04619117 -0.03119975  0.033880396  0.21942886 -0.030686751 -0.0465769893
MntFruits           -0.294236781  0.143093220  0.049030963 -0.180736660 -0.05489847  0.028552652 -0.018012615  0.053531498  0.02561488  0.08921164  0.003197363 -0.15418085 -0.197664325  0.1886904245
MntMeatProducts     -0.346283435  0.061446277 -0.083338395 -0.080423851 -0.04493856  0.044967260  0.012204253 -0.008085930 -0.08604396 -0.04834517 -0.059042219  0.04755970 -0.110398397 -0.1916050594
MntFishProducts     -0.306644806  0.150946826  0.044588192 -0.165157274 -0.04659368  0.038545067 -0.023676906  0.032078735  0.05424469  0.04164063 -0.088872033 -0.25703788 -0.038025137  0.1910952981
MntSweetProducts    -0.298423627  0.133633714  0.046946310 -0.129879520 -0.03865166  0.065852002 -0.018865292  0.011497341  0.03524294 -0.01114937 -0.010087239 -0.25277699 -0.287160417  0.0863810958
MntGoldProds        -0.243547875  0.015019708  0.221015331 -0.017678987 -0.13546042 -0.195567690  0.057934937 -0.080899611  0.09669337  0.12067843  0.072363347  0.09026913  0.779244867  0.0585350706
NumDealsPurchases    0.058003152 -0.271547632  0.438799616  0.062136375 -0.12257758 -0.004668105 -0.054033355  0.036207152 -0.05316077 -0.09503608  0.304162806 -0.25735820 -0.168362567 -0.3477078866
NumWebPurchases     -0.227955364 -0.242759089  0.287242311  0.031463994 -0.11124936 -0.046658590 -0.043710632  0.037930307 -0.04037265 -0.08643869  0.230723543  0.02470812  0.105509378  0.2947594593
NumCatalogPurchases -0.351624286 -0.050217157 -0.003873638 -0.043665266 -0.02846532 -0.073860403  0.038727780 -0.065144267  0.01816080  0.02720838 -0.030395052  0.08296407 -0.049395275 -0.1471509144
NumStorePurchases   -0.305783572 -0.146050314  0.125327302 -0.077776312  0.05584569  0.120011131 -0.050843125  0.085555959 -0.01677967  0.15618580  0.194918340  0.12784665 -0.084244819 -0.0803875666
NumWebVisitsMonth    0.258875376 -0.101551933  0.226265342  0.231979459 -0.31517978  0.004716936 -0.012576649  0.029317220 -0.12395842 -0.10989314 -0.081794161 -0.15678400  0.001475785  0.2348634696
AcceptedCmp3        -0.022182292  0.014948201 -0.040062015  0.114635358 -0.29393841 -0.750506890  0.113902405 -0.298816455  0.05931115  0.05101144 -0.006116423  0.17467647 -0.350800791  0.1570016805
AcceptedCmp4        -0.097130384 -0.193852028 -0.090585569  0.474794224  0.14375892  0.265464091  0.026389897  0.134733475  0.03550017 -0.03881517  0.120688082  0.23109850 -0.153852814  0.5268564386
AcceptedCmp5        -0.205040110 -0.011109829 -0.250472865  0.352272253  0.01852175 -0.010489983 -0.047182781 -0.053309987 -0.03492185 -0.26037839 -0.024536163  0.25969523  0.021961774 -0.4279174401
AcceptedCmp1        -0.185864798  0.010627459 -0.178009701  0.318181565  0.01673699 -0.125869794 -0.067972657 -0.032903794  0.04584277 -0.51499882 -0.074107621 -0.58205996  0.159998275  0.0003375772
AcceptedCmp2        -0.060493303 -0.089248476 -0.113873101  0.458999259  0.04871356 -0.021618725  0.088382709  0.016815675  0.12602370  0.73562547 -0.103651733 -0.35996883  0.022177841 -0.1448927932
client_days          0.039460236  0.069300733 -0.289438582 -0.092512057  0.46729932 -0.270418384 -0.006703345 -0.004358483  0.11657258 -0.01173306  0.637028410 -0.12482735  0.056837882  0.1188384631
Age                 -0.051983752 -0.288738153  0.097546358 -0.128135854  0.38777469 -0.086919371  0.096931260 -0.064688143  0.40935157 -0.13239242 -0.538848290  0.03498719  0.027311621  0.1307741243
Edu_ug               0.067315913  0.086927128 -0.103378021  0.001958897 -0.41200317  0.231644369 -0.018223978 -0.004207145  0.80005748 -0.06831803  0.204744354  0.06203049 -0.036203060 -0.0685189225
Edu_g               -0.035596849  0.458340262  0.381291969  0.246965133  0.26400760 -0.055115302  0.008869278  0.014488210 -0.04993636 -0.02750539 -0.038208473  0.09617673 -0.041128092 -0.0220934700
Edu_pg               0.014541191 -0.491140200 -0.352589998 -0.250336713 -0.13565093 -0.018089992 -0.003160484 -0.013308686 -0.20446350  0.04958237 -0.026612636 -0.11701398  0.053122494  0.0441742623
Marital_status       0.008282944 -0.019736489  0.017147116  0.027977229  0.06219102  0.073326393 -0.846219724 -0.500103315  0.01549563  0.11285110 -0.037292537  0.02107725  0.003797217  0.0699139223
                           PC15        PC16         PC17         PC18         PC19          PC20         PC21          PC22         PC23          PC24
Teenhome            -0.15837681  0.25638251 -0.505636400 -0.058804914  0.389016980 -2.186702e-02  0.106797438 -0.1147730629  0.089627260 -2.574958e-15
Recency             -0.01233471 -0.03411091 -0.005720900 -0.043256854 -0.023629420  3.750364e-02 -0.006565130  0.0021315031  0.003869343  5.848378e-17
MntWines             0.09419265 -0.16336709 -0.032200850 -0.094567073  0.113239937 -1.422494e-05  0.439326831  0.1685499318 -0.687581531  3.474832e-16
MntFruits           -0.31831007  0.18379038  0.032307697 -0.723390153 -0.106858428 -2.357716e-01 -0.064027558  0.1118870277 -0.026935728 -7.809101e-16
MntMeatProducts      0.18294654 -0.01947767  0.235925051 -0.044002680  0.276036969 -1.962685e-01  0.045650244 -0.7612013717  0.081111581 -4.385008e-16
MntFishProducts      0.05105992  0.18670926  0.100984974  0.075571254  0.327376733  7.527154e-01 -0.002797024  0.0638082420 -0.029231024  5.195270e-16
MntSweetProducts    -0.41680650  0.01075232 -0.084510711  0.625529280 -0.193303380 -2.559232e-01  0.182261676 -0.0002743741 -0.063659767  8.006048e-17
MntGoldProds        -0.11757191  0.33846372  0.006330666  0.075822973 -0.112140097 -8.820847e-02  0.100924311 -0.1100990561 -0.004537891  3.472787e-17
NumDealsPurchases    0.09419086  0.25062127  0.465152393  0.034004274 -0.213977935  4.160248e-02 -0.164389673  0.0313271583 -0.150440364 -2.085176e-17
NumWebPurchases     -0.16279114 -0.56257764 -0.038772735  0.041152227  0.229429129 -3.496007e-02 -0.474117603 -0.0147259887  0.041073044  1.112222e-16
NumCatalogPurchases  0.31918976  0.04628244  0.165835424  0.094387097  0.275765795 -2.939016e-01  0.082446157  0.5580791522  0.453683054  3.308902e-16
NumStorePurchases    0.20918533 -0.19940903 -0.283259288 -0.092820200 -0.552936686  2.946534e-01  0.209288942 -0.1125854103  0.349284564  3.358918e-18
NumWebVisitsMonth   -0.18938318 -0.15563178  0.193269157 -0.119495282  0.126641591  3.737228e-02  0.598936597 -0.0656474317  0.333491504  7.817682e-17
AcceptedCmp3         0.07239344  0.06653415 -0.047785467  0.021866276 -0.129418137  9.140870e-02 -0.060306421 -0.0820424115 -0.018200559  9.346817e-18
AcceptedCmp4         0.09698400  0.43106124  0.063716914  0.099607034 -0.031823466 -5.818113e-02 -0.103725203 -0.0801288716  0.081231753  1.284028e-17
AcceptedCmp5        -0.56498313  0.01856657  0.102680209 -0.047837601 -0.015742300  2.586764e-01 -0.089931342  0.0637440840  0.182019612  3.291880e-16
AcceptedCmp1         0.26558696 -0.02786658 -0.262603955 -0.092704721 -0.133598433 -7.312160e-02 -0.035279518 -0.0077800155 -0.002998012 -7.854050e-17
AcceptedCmp2        -0.04631960 -0.14981273  0.046269797 -0.007890175  0.044252711 -2.190371e-02 -0.066204959 -0.0361998805 -0.005939678  1.923083e-17
client_days         -0.07209616 -0.11899075  0.277044416 -0.022212308  0.058932686  1.659797e-02  0.235627309 -0.0145386344  0.034606570  1.069968e-17
Age                 -0.03155110 -0.16612330  0.374108016 -0.014506312 -0.227064846  2.721443e-02  0.008120800 -0.0289246150 -0.001520263 -2.093640e-18
Edu_ug               0.04517987 -0.06839611 -0.002787300 -0.020966576  0.034176812 -1.082798e-02  0.014338821 -0.0214677528 -0.001221529  2.186621e-01
Edu_g                0.05867348 -0.07918358  0.011959332 -0.013682832  0.003476073 -7.648098e-03  0.016963535  0.0157207076 -0.033274431  6.938013e-01
Edu_pg              -0.07372372  0.10186032 -0.011204140  0.020516492 -0.014405912  1.118375e-02 -0.021721615 -0.0090544336  0.034033855  6.861681e-01
Marital_status       0.02042953  0.02016865  0.035248256 -0.001334638  0.008255286 -2.831734e-02  0.012187251 -0.0146429687 -0.003913106  3.623449e-17

fviz_eig(customers_pca1, addlabels = T) 

fviz_pca_var(customers_pca1, col.var = "contrib", repel = TRUE, labels = TRUE)

var<-get_pca_var(customers_pca1)
a<-fviz_contrib(customers_pca1, "var", axes=1, xtickslab.rt=90) 
b<-fviz_contrib(customers_pca1, "var", axes=2, xtickslab.rt=90)
grid.arrange(a,b,top='Contribution to the first two Principal Components')

fviz_eig(customers_pca1, choice='eigenvalue', addlabels = T) 

eig.val<-get_eigenvalue(customers_pca1)
eig.val

cumulative_variance_1<-summary(customers_pca1)
plot(cumulative_variance_1$importance[3,],type="l")

PCA - 12 principal components (80% var)

customers_pca2<-principal(customers_pca.s, nfactors=12, rotate="varimax")

Warning: Matrix was not positive definite, smoothing was doneWarning: The matrix is not positive semi-definite, scores found from Structure loadings

customers_pca2

Principal Components Analysis
Call: principal(r = customers_pca.s, nfactors = 12, rotate = "varimax")
Standardized loadings (pattern matrix) based upon correlation matrix

                       RC1  RC2  RC4  RC3  RC5 RC11  RC6  RC9  RC7  RC8 RC10 RC12
SS loadings           5.16 2.03 1.79 1.70 1.30 1.14 1.12 1.06 1.00 1.00 1.00 1.00
Proportion Var        0.21 0.08 0.07 0.07 0.05 0.05 0.05 0.04 0.04 0.04 0.04 0.04
Cumulative Var        0.21 0.30 0.37 0.44 0.50 0.55 0.59 0.64 0.68 0.72 0.76 0.80
Proportion Explained  0.27 0.10 0.09 0.09 0.07 0.06 0.06 0.06 0.05 0.05 0.05 0.05
Cumulative Proportion 0.27 0.37 0.46 0.55 0.62 0.68 0.74 0.79 0.84 0.90 0.95 1.00

Mean item complexity =  1.5
Test of the hypothesis that 12 components are sufficient.

The root mean square of the residuals (RMSR) is  0.04 
 with the empirical chi square  1834.91  with prob <  0 

Fit based upon off diagonal values = 0.97

print(loadings(customers_pca2), digits=3, cutoff=0.35, sort=TRUE)

Loadings:
                    RC1    RC2    RC4    RC3    RC5    RC11   RC6    RC9    RC7    RC8    RC10   RC12  
MntWines             0.617         0.582                                                               
MntFruits            0.775                                                                             
MntMeatProducts      0.790                                                                             
MntFishProducts      0.796                                                                             
MntSweetProducts     0.758                                                                             
MntGoldProds         0.599                                                                             
NumCatalogPurchases  0.788                                                                             
NumStorePurchases    0.720                                                                             
NumWebVisitsMonth   -0.631                0.394        -0.414                                          
Edu_g                      -0.977                                                                      
Edu_pg                      0.979                                                                      
AcceptedCmp4                       0.774                                                               
AcceptedCmp5                       0.667                                                               
NumDealsPurchases                         0.835                                                        
NumWebPurchases      0.504                0.565                                                        
Teenhome                                  0.534  0.603                                                 
Age                                              0.926                                                 
client_days                                             0.945                                          
AcceptedCmp3                                                   0.938                                   
Edu_ug                                                                0.987                            
Marital_status                                                               0.997                     
Recency                                                                             0.998              
AcceptedCmp2                                                                               0.958       
AcceptedCmp1                                                                                      0.868

                 RC1   RC2   RC4   RC3   RC5  RC11   RC6   RC9   RC7   RC8  RC10  RC12
SS loadings    5.157 2.026 1.790 1.704 1.302 1.141 1.116 1.064 1.004 1.003 1.000 0.998
Proportion Var 0.215 0.084 0.075 0.071 0.054 0.048 0.047 0.044 0.042 0.042 0.042 0.042
Cumulative Var 0.215 0.299 0.374 0.445 0.499 0.547 0.593 0.637 0.679 0.721 0.763 0.804

fviz_eig(customers_pca1, addlabels = T)

Twelve principal components account for almost 80% of the variance in the data. We can see how well the algorithm has dealt with correlated variables by assigning them to a single principal component. One can also try to interpret the principal components to better understand the data. Thus, high PC1 values will be held by customers who generally spend a lot and do a lot of transactions. PC2, on the other hand, can distinguish between customers with a master’s or doctorate degree and those with a bachelor’s degree. In a similar way, further principal components can be interpreted and relationships in the data highlighted by the PCA can be explored.

Hierarchical Clustering

m <- c( "average", "single", "complete", "ward")
names(m) <- c( "average", "single", "complete", "ward")

ac <- function(x) {
  agnes(customers_dim_red.s, method = x)$ac
}

map_dbl(m, ac)

  average    single  complete      ward 
0.8747472 0.8509067 0.9051705 0.9854785 

# dendrogram
hc <- agnes(customers_dim_red.s, method = "ward")
pltree(hc, cex = 0.6, hang = -1, main = "dendrogram - agnes")

# dissimilarity matrix
d <- dist(customers_dim_red.s)
hc1 <- hclust(d, method = "ward.D" )
plot(hc1, cex = 0.6)
rect.hclust(hc1, k = 3
            
            , border = 2:5)

Hierarchical clustering on principal components

res.pca <- PCA(customers_dim_red.s, graph=FALSE)
dendr <- HCPC(res.pca, nb.clust= -1, graph = F)

fviz_dend(dendr, 
          palette = "rickandmorty", 
          rect = TRUE, rect_fill = TRUE, 
          rect_border = "rickandmorty",          
)

Hierarchical clustering is a method of grouping data into clusters based on their similarity. The algorithm creates a hierarchy of clusters by dividing and combining smaller clusters into larger ones. The result is a tree-like diagram that shows the relationships between the clusters. The advantage of using hierarchical clustering is that it can help identify meaningful patterns in large datasets and is useful for exploratory data analysis. The suggested partition appears to be the best, so it will be used in further analysis.

Clustering on continuous data - K-means

#Dropping Education and Marital_Status for corr plot preparation. Also dropping variables which are represented by new variables.
customers_correlation <- customers_df[c(-1,-2,-4,-5,-7,-8,-9,-10,-11,-12,-13,-14,-15,-16,-17,-18,-19,-20,-21,-22)]

ggcorr(customers_correlation, method = c("everything", "pearson"), label = TRUE, label_size = 3, label_round = 2, hjust = 0.85, size = 3)

ggcorr(customers_correlation, method = c("everything", "spearman"), label = TRUE, label_size = 3, label_round = 2, hjust = 0.85, size = 3)

As can be seen from the graph, the variables Income, Money_spent and Number_purchases are highly correlated. For further analysis on continuous variables, therefore, only the Money_spent variable will be used and the other two will be temporarily discarded.

customers_data_con <- customers_correlation[c(-1,-8)]
skim(customers_data_con)

── Data Summary ────────────────────────
                           Values            
Name                       customers_data_con
Number of rows             2201              
Number of columns          8                 
_______________________                      
Column type frequency:                       
  numeric                  8                 
________________________                     
Group variables            None              

get_clust_tendency(customers_data_con, n=ceiling(nrow(customers_data_con)/10), graph=TRUE, gradient=list(low="red", mid="white", high="blue"), seed = 123)

$hopkins_stat
[1] 0.6487238

$plot

Before proceeding with further analysis, it is useful to check the clustering tendency of the data. This can be done using the Hopkins statistic. Near zero values of the statistic indicate that the data is clustered. In this case, the value of the Hopkins statistic is not very low, so clustering obtained using only continuous variables is unlikely to be of high quality.

preproc <- preProcess(customers_data_con, method=c("center", "scale"))
customers_data_con.s <- predict(preproc, customers_data_con)
 
summary(customers_data_con.s)

    Recency           client_days             Age            Cmp_accepted        Children      
 Min.   :-1.695700   Min.   :-2.371570   Min.   :-2.31631   Min.   :-0.4396   Min.   :-1.2672  
 1st Qu.:-0.865953   1st Qu.:-0.749124   1st Qu.:-0.69263   1st Qu.:-0.4396   1st Qu.:-1.2672  
 Median :-0.001634   Median :-0.004607   Median :-0.09443   Median :-0.4396   Median : 0.0673  
 Mean   : 0.000000   Mean   : 0.000000   Mean   : 0.00000   Mean   : 0.0000   Mean   : 0.0000  
 3rd Qu.: 0.862686   3rd Qu.: 0.739911   3rd Qu.: 0.84560   3rd Qu.:-0.4396   3rd Qu.: 0.0673  
 Max.   : 1.727005   Max.   : 2.203124   Max.   : 2.46929   Max.   : 5.4427   Max.   : 2.7362  
  Money_spent      Number_deals_purchases Number_web_visits_month
 Min.   :-0.9992   Min.   :-1.2282        Min.   :-2.2135        
 1st Qu.:-0.8929   1st Qu.:-0.6980        1st Qu.:-0.9695        
 Median :-0.3496   Median :-0.1677        Median : 0.2745        
 Mean   : 0.0000   Mean   : 0.0000        Mean   : 0.0000        
 3rd Qu.: 0.7286   3rd Qu.: 0.3626        3rd Qu.: 0.6892        
 Max.   : 3.1873   Max.   : 6.7259        Max.   : 6.0798        

K-means is a widely used and well-known clustering algorithm. It segments a dataset into k clusters. The algorithm operates by assigning each data point to the cluster with the closest centroid (average), and then adjusting the centroids based on the new cluster assignments. This continues until the centroids stop changing or a stopping criterion is met. One drawback of K-means is that the number of clusters must be specified in advance by the user. To address this limitation, there are various techniques available to determine the optimal number of clusters. These techniques include for example the Elbow method, where the number of clusters is selected based on where the explained variance stops increasing, and the Silhouette score, which measures a data point’s similarity to its own cluster compared to other clusters.

opt_elbow_grpd<-Optimal_Clusters_KMeans(customers_data_con.s, max_clusters=20, plot_clusters = TRUE)

opt_silhouette_grpd<-Optimal_Clusters_KMeans(customers_data_con.s, max_clusters=20, plot_clusters=TRUE, criterion="silhouette")

opt_grpd<-NbClust(customers_data_con.s, distance="euclidean", min.nc=2, max.nc=12, method="complete", index="ch")
opt_grpd$Best.nc

Number_clusters     Value_Index 
        11.0000        162.4258 

agr_km2<-eclust(customers_data_con.s, "kmeans", k = 2) 

fviz_silhouette(agr_km2)

agr_km3<-eclust(customers_data_con.s, "kmeans", k = 3) 

fviz_silhouette(agr_km3)

agr_km6<-eclust(customers_data_con.s, "kmeans", k = 6) 

fviz_silhouette(agr_km6)

agr_km11<-eclust(customers_data_con.s, "kmeans", k = 11) 

fviz_silhouette(agr_km11)

score_agr_km2<-kmeans(customers_data_con.s, 2) 
round(calinhara(customers_data_con.s, score_agr_km2$cluster),digits=2)

[1] 580.37

score_agr_km3<-kmeans(customers_data_con.s, 3) 
round(calinhara(customers_data_con.s, score_agr_km3$cluster),digits=2)

[1] 471.86

score_agr_km6<-kmeans(customers_data_con.s, 6) 
round(calinhara(customers_data_con.s, score_agr_km6$cluster),digits=2)

[1] 363.26

score_agr_km11<-kmeans(customers_data_con.s, 11) 
round(calinhara(customers_data_con.s, score_agr_km11$cluster),digits=2)

[1] 276.6

dudahart2(customers_data_con.s, score_agr_km2$cluster)

$p.value
[1] 0

$dh
[1] 0.7911873

$compare
[1] 0.8892011

$cluster1
[1] FALSE

$alpha
[1] 0.001

$z
[1] 3.090232

dudahart2(customers_data_con.s, score_agr_km3$cluster)

$p.value
[1] 0

$dh
[1] 0.5080522

$compare
[1] 0.8892011

$cluster1
[1] FALSE

$alpha
[1] 0.001

$z
[1] 3.090232

dudahart2(customers_data_con.s, score_agr_km6$cluster)

$p.value
[1] 0

$dh
[1] 0.1511493

$compare
[1] 0.8892011

$cluster1
[1] FALSE

$alpha
[1] 0.001

$z
[1] 3.090232

dudahart2(customers_data_con.s, score_agr_km11$cluster)

$p.value
[1] 0

$dh
[1] 0.07948125

$compare
[1] 0.8892011

$cluster1
[1] FALSE

$alpha
[1] 0.001

$z
[1] 3.090232

Clustering using K-means achieved the best results for the number of clusters of 2 followed by 3. This was confirmed by all statistics including Calinski-Harabasz and Duda-Hart indices. The highest average silhouette width achieved was only 0.24, which shows that the clustering results are poor.

Clustering on PCA data

data_pca<-customers_pca1$x[,1:12]

get_clust_tendency(data_pca, n=ceiling(nrow(data_pca)/10), seed = 123)$hopkins_stat

[1] 0.8377595

opt_elbow<-Optimal_Clusters_KMeans(data_pca, max_clusters=20, plot_clusters = TRUE)

opt_silhouette<-Optimal_Clusters_KMeans(data_pca, max_clusters=20, plot_clusters=TRUE, criterion="silhouette")

opt1<-NbClust(data_pca, distance="euclidean", min.nc=2, max.nc=12, method="complete", index="ch")

opt1$All.index

       2        3        4        5        6        7        8        9       10       11       12 
550.4834 385.3125 377.4499 356.5730 290.3140 267.5355 248.6706 220.3645 207.1051 188.0100 184.8578 

opt1$Best.nc

Number_clusters     Value_Index 
         2.0000        550.4834 

pca12_km2 <- eclust(data_pca, "kmeans", k = 2) 

fviz_silhouette(pca12_km2)

pca12_km3<-eclust(data_pca, "kmeans", k = 3) 

fviz_silhouette(pca12_km3)

pca12_km6<-eclust(data_pca, "kmeans", k = 6) 

fviz_silhouette(pca12_km6)

score_pca12_km2<-kmeans(data_pca, 2) 
round(calinhara(data_pca, score_pca12_km2$cluster),digits=2)

[1] 261.79

score_pca12_km3<-kmeans(data_pca, 3) 
round(calinhara(data_pca, score_pca12_km3$cluster),digits=2)

[1] 459.97

score_pca12_km6<-kmeans(data_pca, 6) 
round(calinhara(data_pca, score_pca12_km6$cluster),digits=2)

[1] 378.71

dudahart2(data_pca, score_pca12_km2$cluster)

$p.value
[1] 1.097645e-10

$dh
[1] 0.8936152

$compare
[1] 0.9209815

$cluster1
[1] FALSE

$alpha
[1] 0.001

$z
[1] 3.090232

dudahart2(data_pca, score_pca12_km3$cluster)

$p.value
[1] 0

$dh
[1] 0.5575084

$compare
[1] 0.9209815

$cluster1
[1] FALSE

$alpha
[1] 0.001

$z
[1] 3.090232

dudahart2(data_pca, score_pca12_km6$cluster)

$p.value
[1] 0

$dh
[1] 0.126912

$compare
[1] 0.9209815

$cluster1
[1] FALSE

$alpha
[1] 0.001

$z
[1] 3.090232

The k-means clustering results obtained on the PCA data are again very poor. The high Hopkins statistic and low average silhouette width show that this is a bad method for clustering these data.

Clustering on mixed data

Another idea is to use more variables, not just continuous ones, and see if clustering on them will be better. There are many methods for clustering mixed data. Some of the most popular include clustering using Factorial Analysis of Mixed Data (FAMD), clustering data using Grower distance and K-prototypes. All of these methods were tested on this dataset.

Factorial Analysis of Mixed Data (FAMD)

Factorial Analysis of Mixed Data (FAMD) is a method for examining data that includes both numerical and categorical variables. It takes advantage of two statistical techniques, PCA and MCA, to condense the data and highlight the connections between variables. In this case, the results obtained with FAMD will be used to perform clustering with k-means.

customers_data_con <- customers_correlation[c(-1,-8)]
skim(customers_data_con)

── Data Summary ────────────────────────
                           Values            
Name                       customers_data_con
Number of rows             2201              
Number of columns          8                 
_______________________                      
Column type frequency:                       
  numeric                  8                 
________________________                     
Group variables            None              

summary(famd)

Call:
FAMD(base = customers_mixed, ncp = 20, graph = FALSE) 


Eigenvalues
                       Dim.1   Dim.2   Dim.3   Dim.4   Dim.5   Dim.6   Dim.7   Dim.8   Dim.9  Dim.10  Dim.11  Dim.12
Variance               2.870   1.556   1.281   1.028   1.006   0.987   0.865   0.799   0.739   0.429   0.297   0.143
% of var.             23.918  12.969  10.671   8.570   8.383   8.223   7.206   6.662   6.157   3.579   2.472   1.190
Cumulative % of var.  23.918  36.887  47.558  56.128  64.511  72.734  79.940  86.602  92.759  96.338  98.810 100.000

Individuals (the 10 first)
                            Dist    Dim.1    ctr   cos2    Dim.2    ctr   cos2    Dim.3    ctr   cos2  
1                       |  3.807 |  1.646  0.043  0.187 |  1.845  0.099  0.235 | -1.514  0.081  0.158 |
2                       |  3.406 | -1.558  0.038  0.209 | -0.828  0.020  0.059 |  1.810  0.116  0.282 |
3                       |  2.398 |  1.398  0.031  0.340 | -0.554  0.009  0.053 | -0.096  0.000  0.002 |
4                       |  3.035 | -1.294  0.027  0.182 | -1.787  0.093  0.347 |  0.277  0.003  0.008 |
5                       |  2.953 | -0.501  0.004  0.029 |  0.486  0.007  0.027 |  0.499  0.009  0.029 |
6                       |  2.232 |  0.370  0.002  0.027 |  0.445  0.006  0.040 |  0.814  0.023  0.133 |
7                       |  2.311 | -0.169  0.000  0.005 |  1.071  0.034  0.215 | -0.998  0.035  0.187 |
8                       |  2.609 | -1.378  0.030  0.279 | -0.489  0.007  0.035 | -0.155  0.001  0.004 |
9                       |  2.905 | -1.676  0.044  0.333 | -0.548  0.009  0.036 |  0.161  0.001  0.003 |
10                      |  7.090 | -3.743  0.222  0.279 |  0.931  0.025  0.017 |  0.814  0.024  0.013 |

Continuous variables
                           Dim.1    ctr   cos2    Dim.2    ctr   cos2    Dim.3    ctr   cos2  
Recency                 |  0.010  0.003  0.000 |  0.061  0.242  0.004 | -0.051  0.202  0.003 |
client_days             |  0.003  0.000  0.000 | -0.522 17.523  0.273 |  0.601 28.241  0.362 |
Age                     |  0.148  0.768  0.022 |  0.363  8.490  0.132 |  0.586 26.796  0.343 |
Cmp_accepted            |  0.532  9.864  0.283 |  0.043  0.120  0.002 | -0.128  1.278  0.016 |
Children                | -0.697 16.907  0.485 |  0.353  8.022  0.125 |  0.282  6.204  0.079 |
Money_spent             |  0.895 27.914  0.801 |  0.263  4.459  0.069 | -0.102  0.816  0.010 |
Number_purchases        |  0.800 22.271  0.639 |  0.431 11.931  0.186 | -0.041  0.134  0.002 |
Number_deals_purchases  | -0.324  3.650  0.105 |  0.772 38.265  0.595 | -0.040  0.123  0.002 |
Number_web_visits_month | -0.710 17.545  0.504 |  0.291  5.444  0.085 | -0.288  6.460  0.083 |

Categories
                            Dim.1     ctr    cos2  v.test     Dim.2     ctr    cos2  v.test     Dim.3     ctr    cos2  v.test  
Undergraduate           |  -1.815   0.981   0.077  -7.970 |  -2.007   4.082   0.094 -11.969 |  -2.987  13.352   0.208 -19.637 |
Graduate                |   0.001   0.000   0.000   0.044 |  -0.083   0.171   0.010  -3.799 |  -0.338   4.140   0.165 -16.974 |
Postgraduate            |   0.115   0.061   0.008   2.495 |   0.260   1.061   0.040   7.655 |   0.721  12.066   0.307  23.420 |
In_relationship         |  -0.040   0.013   0.003  -1.497 |   0.051   0.068   0.005   2.571 |   0.041   0.067   0.003   2.304 |
Single                  |   0.073   0.023   0.003   1.497 |  -0.092   0.125   0.005  -2.571 |  -0.075   0.122   0.003  -2.304 |

fviz_eig(famd, ncp=20, addlabels=TRUE)

fviz_pca_var(famd, col.var = "contrib", repel = TRUE, labels = TRUE)

fviz_contrib(famd, "var", axes=1, xtickslab.rt=90) 

fviz_contrib(famd, "var", axes=2, xtickslab.rt=90)

opt_silhouette<-Optimal_Clusters_KMeans(customers_famd, max_clusters=20, plot_clusters=TRUE, criterion="silhouette")

famd_kmeans <- eclust(customers_famd, "kmeans", k = 3) 

fviz_silhouette(famd_kmeans)

score_famd_kmeans<-kmeans(customers_famd, 3) 
round(calinhara(customers_famd, score_famd_kmeans$cluster),digits=2)

[1] 370.08

dudahart2(customers_famd, score_famd_kmeans$cluster)

$p.value
[1] 0

$dh
[1] 0.4123133

$compare
[1] 0.9209815

$cluster1
[1] FALSE

$alpha
[1] 0.001

$z
[1] 3.090232

Again, the clustering results obtained by this method are not satisfactory. Average silhouette width is only 0.15, which shows how poor this clustering is.

PAM (Partitioning Around Medoids) with Grower distance

The combination of Grower distance and PAM is a clustering technique that aims to tackle the challenges posed by high-dimensional and complex data. The Grower distance measure is used as a way to assess the similarity between data points, while PAM uses medoids to represent the clusters instead of centroids. This approach aims to provide improved results in clustering complex data compared to traditional techniques such as the K-means algorithm and Euclidean distance.

gower_dist <- daisy(customers_mixed, metric = "gower",
              stand = FALSE, warnType = TRUE)

summary(gower_dist)

2421100 dissimilarities, summarized :
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.0000  0.1859  0.2427  0.2455  0.3015  0.6837 
Metric :  mixed ;  Types = O, N, I, I, I, I, I, I, I, I, I 
Number of objects : 2201

sil_width <- c(NA)
for(i in 2:10){
  
  pam_fit <- pam(gower_dist,
                 diss = TRUE,
                 k = i)
  
  sil_width[i] <- pam_fit$silinfo$avg.width
  
}

plot(1:10, sil_width,
     xlab = "Number of clusters",
     ylab = "Silhouette Width",
    main = "Optimal number of clusters PAM")
lines(1:10, sil_width)

c1<-eclust(gower_dist, "pam", k = 2) 
fviz_silhouette(c1)

fviz_cluster(c1)

c2<-eclust(gower_dist, "pam", k = 3) 
fviz_silhouette(c2)

fviz_cluster(c2)

score_pam2<-pam(gower_dist, 2) 
round(calinhara(gower_dist, score_pam2$cluster),digits=2)

[1] 1058.05

score_pam3<-pam(gower_dist, 3) 
round(calinhara(gower_dist, score_pam3$cluster),digits=2)

[1] 856.1

dudahart2(gower_dist, score_pam2$cluster)

$p.value
[1] 0

$dh
[1] 0.6751517

$compare
[1] 0.9977256

$cluster1
[1] FALSE

$alpha
[1] 0.001

$z
[1] 3.090232

dudahart2(gower_dist, score_pam3$cluster)

$p.value
[1] 0

$dh
[1] 0.388104

$compare
[1] 0.9977256

$cluster1
[1] FALSE

$alpha
[1] 0.001

$z
[1] 3.090232

As can be seen, clustering with this method improved previous results. This is indicated by quality measures including average silhouette width = 0.28, or Calinsk-Harabasz = 856.1 (for k=3), among others.

K-prototypes

K-Prototypes is a clustering method specifically designed for datasets that have a combination of both categorical and numerical variables. It combines the principles of K-means (for numerical data) and K-modes (for categorical data) to create a more comprehensive approach to clustering mixed data. The algorithm operates by assigning each data point to a cluster based on both its categorical and numerical values, and then continuously refining the cluster prototypes (centroids) until they reach a stable state.

kproto_twsos <- numeric(12)
for(i in 1:12){
  kpres <- kproto(customers_mixed, k = i)
  kproto_twsos[i] <- kpres$tot.withinss
}

# NAs in variables:
              Education          Marital_Status                 Recency             client_days                     Age            Cmp_accepted                Children             Money_spent        Number_purchases 
                      0                       0                       0                       0                       0                       0                       0                       0                       0 
 Number_deals_purchases Number_web_visits_month 
                      0                       0 
0 observation(s) with NAs.

Estimated lambda: 96825.71 

0 observation(s) with NAs.

# NAs in variables:
              Education          Marital_Status                 Recency             client_days                     Age            Cmp_accepted                Children             Money_spent        Number_purchases 
                      0                       0                       0                       0                       0                       0                       0                       0                       0 
 Number_deals_purchases Number_web_visits_month 
                      0                       0 
0 observation(s) with NAs.

Estimated lambda: 96825.71 

0 observation(s) with NAs.

# NAs in variables:
              Education          Marital_Status                 Recency             client_days                     Age            Cmp_accepted                Children             Money_spent        Number_purchases 
                      0                       0                       0                       0                       0                       0                       0                       0                       0 
 Number_deals_purchases Number_web_visits_month 
                      0                       0 
0 observation(s) with NAs.

Estimated lambda: 96825.71 

0 observation(s) with NAs.

# NAs in variables:
              Education          Marital_Status                 Recency             client_days                     Age            Cmp_accepted                Children             Money_spent        Number_purchases 
                      0                       0                       0                       0                       0                       0                       0                       0                       0 
 Number_deals_purchases Number_web_visits_month 
                      0                       0 
0 observation(s) with NAs.

Estimated lambda: 96825.71 

0 observation(s) with NAs.

# NAs in variables:
              Education          Marital_Status                 Recency             client_days                     Age            Cmp_accepted                Children             Money_spent        Number_purchases 
                      0                       0                       0                       0                       0                       0                       0                       0                       0 
 Number_deals_purchases Number_web_visits_month 
                      0                       0 
0 observation(s) with NAs.

Estimated lambda: 96825.71 

0 observation(s) with NAs.

# NAs in variables:
              Education          Marital_Status                 Recency             client_days                     Age            Cmp_accepted                Children             Money_spent        Number_purchases 
                      0                       0                       0                       0                       0                       0                       0                       0                       0 
 Number_deals_purchases Number_web_visits_month 
                      0                       0 
0 observation(s) with NAs.

Estimated lambda: 96825.71 

0 observation(s) with NAs.

# NAs in variables:
              Education          Marital_Status                 Recency             client_days                     Age            Cmp_accepted                Children             Money_spent        Number_purchases 
                      0                       0                       0                       0                       0                       0                       0                       0                       0 
 Number_deals_purchases Number_web_visits_month 
                      0                       0 
0 observation(s) with NAs.

Estimated lambda: 96825.71 

0 observation(s) with NAs.

# NAs in variables:
              Education          Marital_Status                 Recency             client_days                     Age            Cmp_accepted                Children             Money_spent        Number_purchases 
                      0                       0                       0                       0                       0                       0                       0                       0                       0 
 Number_deals_purchases Number_web_visits_month 
                      0                       0 
0 observation(s) with NAs.

Estimated lambda: 96825.71 

0 observation(s) with NAs.

# NAs in variables:
              Education          Marital_Status                 Recency             client_days                     Age            Cmp_accepted                Children             Money_spent        Number_purchases 
                      0                       0                       0                       0                       0                       0                       0                       0                       0 
 Number_deals_purchases Number_web_visits_month 
                      0                       0 
0 observation(s) with NAs.

Estimated lambda: 96825.71 

0 observation(s) with NAs.

# NAs in variables:
              Education          Marital_Status                 Recency             client_days                     Age            Cmp_accepted                Children             Money_spent        Number_purchases 
                      0                       0                       0                       0                       0                       0                       0                       0                       0 
 Number_deals_purchases Number_web_visits_month 
                      0                       0 
0 observation(s) with NAs.

Estimated lambda: 96825.71 

0 observation(s) with NAs.

# NAs in variables:
              Education          Marital_Status                 Recency             client_days                     Age            Cmp_accepted                Children             Money_spent        Number_purchases 
                      0                       0                       0                       0                       0                       0                       0                       0                       0 
 Number_deals_purchases Number_web_visits_month 
                      0                       0 
0 observation(s) with NAs.

Estimated lambda: 96825.71 

0 observation(s) with NAs.

# NAs in variables:
              Education          Marital_Status                 Recency             client_days                     Age            Cmp_accepted                Children             Money_spent        Number_purchases 
                      0                       0                       0                       0                       0                       0                       0                       0                       0 
 Number_deals_purchases Number_web_visits_month 
                      0                       0 
0 observation(s) with NAs.

Estimated lambda: 96825.71 

0 observation(s) with NAs.

plot(1:12, kproto_twsos,
     xlab = "Number of clusters",
     ylab = "Total Within Sum Of Squares",
    main = "Optimal number of clusters K-prototypes")
lines(1:12, kproto_twsos)

kproto_ss <- numeric(12)
for(i in 2:12){
  kpres <- kproto(customers_mixed, k = i)
  kproto_ss[i] <- validation_kproto(object = kpres, method = "silhouette")
}

# NAs in variables:
              Education          Marital_Status                 Recency             client_days                     Age            Cmp_accepted                Children             Money_spent        Number_purchases 
                      0                       0                       0                       0                       0                       0                       0                       0                       0 
 Number_deals_purchases Number_web_visits_month 
                      0                       0 
0 observation(s) with NAs.

Estimated lambda: 96825.71 

0 observation(s) with NAs.

# NAs in variables:
              Education          Marital_Status                 Recency             client_days                     Age            Cmp_accepted                Children             Money_spent        Number_purchases 
                      0                       0                       0                       0                       0                       0                       0                       0                       0 
 Number_deals_purchases Number_web_visits_month 
                      0                       0 
0 observation(s) with NAs.

Estimated lambda: 96825.71 

0 observation(s) with NAs.

# NAs in variables:
              Education          Marital_Status                 Recency             client_days                     Age            Cmp_accepted                Children             Money_spent        Number_purchases 
                      0                       0                       0                       0                       0                       0                       0                       0                       0 
 Number_deals_purchases Number_web_visits_month 
                      0                       0 
0 observation(s) with NAs.

Estimated lambda: 96825.71 

0 observation(s) with NAs.

# NAs in variables:
              Education          Marital_Status                 Recency             client_days                     Age            Cmp_accepted                Children             Money_spent        Number_purchases 
                      0                       0                       0                       0                       0                       0                       0                       0                       0 
 Number_deals_purchases Number_web_visits_month 
                      0                       0 
0 observation(s) with NAs.

Estimated lambda: 96825.71 

0 observation(s) with NAs.

# NAs in variables:
              Education          Marital_Status                 Recency             client_days                     Age            Cmp_accepted                Children             Money_spent        Number_purchases 
                      0                       0                       0                       0                       0                       0                       0                       0                       0 
 Number_deals_purchases Number_web_visits_month 
                      0                       0 
0 observation(s) with NAs.

Estimated lambda: 96825.71 

0 observation(s) with NAs.

# NAs in variables:
              Education          Marital_Status                 Recency             client_days                     Age            Cmp_accepted                Children             Money_spent        Number_purchases 
                      0                       0                       0                       0                       0                       0                       0                       0                       0 
 Number_deals_purchases Number_web_visits_month 
                      0                       0 
0 observation(s) with NAs.

Estimated lambda: 96825.71 

0 observation(s) with NAs.

# NAs in variables:
              Education          Marital_Status                 Recency             client_days                     Age            Cmp_accepted                Children             Money_spent        Number_purchases 
                      0                       0                       0                       0                       0                       0                       0                       0                       0 
 Number_deals_purchases Number_web_visits_month 
                      0                       0 
0 observation(s) with NAs.

Estimated lambda: 96825.71 

0 observation(s) with NAs.

# NAs in variables:
              Education          Marital_Status                 Recency             client_days                     Age            Cmp_accepted                Children             Money_spent        Number_purchases 
                      0                       0                       0                       0                       0                       0                       0                       0                       0 
 Number_deals_purchases Number_web_visits_month 
                      0                       0 
0 observation(s) with NAs.

Estimated lambda: 96825.71 

0 observation(s) with NAs.

# NAs in variables:
              Education          Marital_Status                 Recency             client_days                     Age            Cmp_accepted                Children             Money_spent        Number_purchases 
                      0                       0                       0                       0                       0                       0                       0                       0                       0 
 Number_deals_purchases Number_web_visits_month 
                      0                       0 
0 observation(s) with NAs.

Estimated lambda: 96825.71 

0 observation(s) with NAs.

# NAs in variables:
              Education          Marital_Status                 Recency             client_days                     Age            Cmp_accepted                Children             Money_spent        Number_purchases 
                      0                       0                       0                       0                       0                       0                       0                       0                       0 
 Number_deals_purchases Number_web_visits_month 
                      0                       0 
0 observation(s) with NAs.

Estimated lambda: 96825.71 

0 observation(s) with NAs.

# NAs in variables:
              Education          Marital_Status                 Recency             client_days                     Age            Cmp_accepted                Children             Money_spent        Number_purchases 
                      0                       0                       0                       0                       0                       0                       0                       0                       0 
 Number_deals_purchases Number_web_visits_month 
                      0                       0 
0 observation(s) with NAs.

Estimated lambda: 96825.71 

0 observation(s) with NAs.

# Plot sihouette width (higher is better)
plot(1:12, kproto_ss,
     xlab = "Number of clusters",
     ylab = "Silhouette Width",
    main = "Optimal number of clusters K-prototypes")
lines(1:12, kproto_ss)

customers_k_prototypes <- kproto(customers_mixed, 3)

# NAs in variables:
              Education          Marital_Status                 Recency             client_days                     Age            Cmp_accepted                Children             Money_spent        Number_purchases 
                      0                       0                       0                       0                       0                       0                       0                       0                       0 
 Number_deals_purchases Number_web_visits_month 
                      0                       0 
0 observation(s) with NAs.

Estimated lambda: 96825.71 

0 observation(s) with NAs.

customers_k_prototypes$centers

validation_kproto(object = customers_k_prototypes, method = "silhouette")

[1] 0.398714

c_assignment_kproto <- customers_k_prototypes$cluster
customers_kproto <- cbind(customers_mixed, c_assignment_kproto)
customers_kproto$c_assignment_kproto <- as.factor(customers_kproto$c_assignment_kproto)

ggplot(customers_kproto, aes(x = Money_spent, y = Number_purchases, color = c_assignment_kproto)) +
  geom_point() +
  labs(title = "Money spent ~ Number of purchases",
       x = "Money_spent", y = "Number_purchases")   + guides(color = guide_legend(title = "Cluster"))

Definitely performing K-prototypes on mixed data gives the best clustering results. Average silhouette width is highest for 2 clusters and is more than 0.7, but for further analysis a split into 3 clusters was chosen with the second highest average silhouette width = 0.398 guided by indications from hierachical clustering and wanting to see potential differences between more clusters.

Clustering visualization using T-SNE

set.seed(123)
features <- subset(customers_dim_red.s) 
tsne <- tsne(features, initial_dims = 26, k = 3, max_iter = 300, epoch = 50)

sigma summary: Min. : 0.33590247385282 |1st Qu. : 0.50268605673983 |Median : 0.555157820787002 |Mean : 0.593604554549779 |3rd Qu. : 0.653023509629496 |Max. : 1.15235770954057 |
Epoch: Iteration #50 error is: 18.2826308570591
Epoch: Iteration #100 error is: 18.0346360515252
Epoch: Iteration #150 error is: 1.31086852227389
Epoch: Iteration #200 error is: 1.08051232062025
Epoch: Iteration #250 error is: 0.98146496383044
Epoch: Iteration #300 error is: 0.870987572159646

tsne <- data.frame(tsne)

fig <-  plot_ly(data = tsne ,x =  ~X1, y = ~X2, z = ~X3, colors = c('#636EFA','#EF553B','#00CC96') ) %>% 
  add_markers(size = 8) %>%
  layout( 
    xaxis = list(
      zerolinecolor = "#ffff",
      zerolinewidth = 2,
      gridcolor='#ffff'), 
    yaxis = list(
      zerolinecolor = "#ffff",
      zerolinewidth = 2,
      gridcolor='#ffff'),
    scene =list(bgcolor = "#e5ecf6"))
fig

fig2 <-  plot_ly(data = tsne ,x =  ~X1, y = ~X2, z = ~X3, color = ~customers_kproto$c_assignment_kproto, colors = c('#636EFA','#EF553B','#00CC96') ) %>% 
  add_markers(size = 8) %>%
  layout( 
    xaxis = list(
      zerolinecolor = "#ffff",
      zerolinewidth = 2,
      gridcolor='#ffff'), 
    yaxis = list(
      zerolinecolor = "#ffff",
      zerolinewidth = 2,
      gridcolor='#ffff'),
    scene =list(bgcolor = "#e5ecf6"))
fig2

c_assignment_pam <- c2$cluster
customers_pam <- cbind(customers_mixed, c_assignment_pam)
customers_pam$c_assignment_pam <- as.factor(customers_pam$c_assignment_pam)

fig3 <-  plot_ly(data = tsne ,x =  ~X1, y = ~X2, z = ~X3, color = ~customers_pam$c_assignment_pam, colors = c('#636EFA','#EF553B','#00CC96') ) %>% 
  add_markers(size = 8) %>%
  layout( 
    xaxis = list(
      zerolinecolor = "#ffff",
      zerolinewidth = 2,
      gridcolor='#ffff'), 
    yaxis = list(
      zerolinecolor = "#ffff",
      zerolinewidth = 2,
      gridcolor='#ffff'),
    scene =list(bgcolor = "#e5ecf6"))
fig3

features2 <- subset(customers_dim_red.s) 

set.seed(123)
tsne2 <- tsne(features2, initial_dims = 26, k = 2, max_iter = 300, epoch = 50)

sigma summary: Min. : 0.33590247385282 |1st Qu. : 0.50268605673983 |Median : 0.555157820787002 |Mean : 0.593604554549779 |3rd Qu. : 0.653023509629496 |Max. : 1.15235770954057 |
Epoch: Iteration #50 error is: 18.6989606457907
Epoch: Iteration #100 error is: 18.3985917244678
Epoch: Iteration #150 error is: 1.59540704101302
Epoch: Iteration #200 error is: 1.34819514926882
Epoch: Iteration #250 error is: 1.23263486520246
Epoch: Iteration #300 error is: 1.09182863987721

tsne2 <- data.frame(tsne2)

options(warn = -1)
fig4 <-  plot_ly(data = tsne2 ,x =  ~X1, y = ~X2, type = 'scatter', mode = 'markers', split = ~customers_kproto$c_assignment_kproto)

fig4 <- fig4 %>%
  layout(
    plot_bgcolor = "#e5ecf6"
  )

fig4

options(warn = -1)
fig5 <-  plot_ly(data = tsne2 ,x =  ~X1, y = ~X2, type = 'scatter', mode = 'markers', split = ~customers_pam$c_assignment_pam)

fig5 <- fig5 %>%
  layout(
    plot_bgcolor = "#e5ecf6"
  )

fig5

Clusters analysis

customers_kproto <- customers_kproto %>% mutate(Income = customers_df[, "Income"])
customers_kproto_grpd <- customers_kproto %>% group_by(c_assignment_kproto)

skim(customers_kproto_grpd)

── Data Summary ────────────────────────
                           Values               
Name                       customers_kproto_grpd
Number of rows             2201                 
Number of columns          13                   
_______________________                         
Column type frequency:                          
  factor                   2                    
  numeric                  10                   
________________________                        
Group variables            c_assignment_kproto  

customers_kproto_grpd %>%  
  summarize(Count = n()) %>% 
  ggplot(aes(x=c_assignment_kproto, y=Count, fill=c_assignment_kproto)) + 
  theme_solarized() +
  scale_fill_solarized() +
  labs(title="Number of observations in each cluster",
        x ="Cluster", y = "Number of observations", fill = "Clusters") +
  geom_bar(stat='identity', position= "dodge")

target_variables <- c("Money_spent","Income","Age","client_days","Number_purchases","Number_deals_purchases","Number_web_visits_month","Cmp_accepted","Children","Recency")


for (each_variable in target_variables) {
  plot_var_name <- str_c(c("ggplot", each_variable), collapse = "_")

  temp_plot <- ggplot(customers_kproto, aes_string(x="c_assignment_kproto", y=each_variable, fill = "c_assignment_kproto")) +
  theme_solarized() +
  scale_fill_solarized() +
  ggtitle(str_c("Cluster ~ ",each_variable)) +
  labs(fill = "Clusters") +
  geom_boxplot()

  assign(plot_var_name, temp_plot)
}

gridExtra::grid.arrange(ggplot_Money_spent, ggplot_Income, ggplot_Age, ggplot_client_days, ggplot_Number_purchases, ggplot_Number_deals_purchases, ggplot_Number_web_visits_month, ggplot_Cmp_accepted, ggplot_Children, ggplot_Recency, ncol = 2)

customers_kproto_grpd %>%  
  summarize(Mean_money_spent = mean(Money_spent))  %>% 
  ggplot(aes(x=c_assignment_kproto, y=Mean_money_spent, fill = c_assignment_kproto)) +
  theme_solarized() +
  scale_fill_solarized() +
  labs(title="Mean money spent in each cluster",
        x ="Cluster", y = "Mean money spent", fill = "Clusters") +
  geom_bar(stat='identity', position= "dodge")

customers_kproto_grpd %>%  
  summarize(Mean_income = mean(Income))  %>% 
  ggplot(aes(x=c_assignment_kproto, y=Mean_income, fill = c_assignment_kproto)) +
  theme_solarized() +
  scale_fill_solarized() +
  labs(title="Mean income in each cluster",
        x ="Cluster", y = "Mean income", fill = "Clusters") +
  geom_bar(stat='identity', position= "dodge")

ggplot(customers_kproto, aes(x = Money_spent, y = Income, color = c_assignment_kproto)) +
  geom_point() +
  theme_solarized() +
  scale_fill_solarized() +
  labs(title = "Money spent ~ Income",
       x = "Money spent", y = "Income")   + guides(color = guide_legend(title = "Cluster"))

customers_kproto_grpd %>%  
  summarize(Mean_client_days = mean(client_days))  %>% 
  ggplot(aes(x=c_assignment_kproto, y=Mean_client_days, fill = c_assignment_kproto)) +
  theme_solarized() +
  scale_fill_solarized() +
  labs(title="Mean client days in each cluster",
        x ="Cluster", y = "Mean client days", fill = "Clusters") +
  geom_bar(stat='identity', position= "dodge")

customers_kproto_summ <- customers_kproto_grpd[,-c(1,2)]
customers_kproto_summ %>% summarize(across(everything(), mean)) 

customers_kproto_summ %>% summarize(across(everything(), median))

customers_kproto_summ %>% summarize(across(everything(), min)) 

customers_kproto_summ %>% summarize(across(everything(), max)) 

Cluster 1

• Customers with the highest average income
• They make the most transactions
• Customers with the highest spendings
• Mostly childless
• They do not often make purchases on deals
• Average length of being a customer neither the highest nor the lowest
• Highest average of accepted marketing campaigns

Cluster 2

• Customers with the lowest average income (however, a value close to cluster 3)
• Customers with the lowest spendings
• Mostly parents (The highest average Childrens: 1.27)
• Average length of being a customer the highest
• They make the least transactions
• Low average of accepted marketing campaigns

Cluster 3

• Customers with average income neither the highest nor the lowest (however, a value close to cluster 2)
• Customers with spendings neither the highest nor the lowest
• Mostly parents (Average Childrens: 1.15)
• Average length of being a customer the lowest
• They do not make a lot of transactions, however most on deals
• Low average of accepted marketing campaigns

Summary

The purpose of the analysis was to segment customers by applying clustering methods. The best approach turned out to be the use of the K-prototypes method on both continuous and categorical variables. Accurate customer segmentation is of great value to companies because it allows them to better understand customer needs and preferences. Thanks to the performed clustering, it was possible to divide customers into those spending the most, with the highest earnings, while not being mostly parents (Cluster 1), and those with less spending, but making purchases on promotions and being mostly parents (Cluster 2 or 3). It is now also possible to carry out targeted marketing activities, thereby increasing the likelihood of customer interest and purchase.

Given the high similarity of clusters 2 and 3 and the highest value of average silhouette width for clustering using the K-prototypes method, it would be worthwhile in further work on the project to conduct the analysis by two clusters and compare the results.

References

https://plotly.com/r/t-sne-and-umap-projections/
https://medium.com/analytics-vidhya/the-ultimate-guide-for-clustering-mixed-data-1eefa0b4743b
https://www.kaggle.com/datasets/imakash3011/customer-personality-analysis