R Notebook
Defining the Question
Segmentation of customers according to their spending habits on different products.
Understanding the Context
The wholesale customer segmentation problem is an issue of concern to most wholesale distributors in the business world. Classification of customers is fundamental since it enables marketing teams to have customized strategies meant for different groups of customers.Being able to understand customer behavior and patterns together with spending habits is key to strategizing. This influences better selling of products hence revenue to a business. Our case study is centered in Lisbon, porto and some parts of Portugal where our client supplies products.The data set includes the annual spending in monetary units on diverse product categories.
Business Objective.
The main objective of this project is; To be able to classify groups of customers hence customize marketing strategies for each group. To be able to identify spending habits of customers. Come up with insights that help with marketing strategies
Data provided
Dataset Url = https://www.kaggle.com/binovi/wholesale-customers-data-set
Data grossary
Model Behaviour will be using a dataset sourced from Kaggle. It contains 440 rows and 8 columns;
- FRESH: annual spending (m.u.) on fresh products (Continuous);
- MILK: annual spending (m.u.) on milk products (Continuous);
- GROCERY: annual spending (m.u.)on grocery products (Continuous);
- FROZEN: annual spending (m.u.)on frozen products (Continuous)
- DETERGENTS_PAPER: annual spending (m.u.) on detergents and paper products (Continuous)
- DELICATESSEN: annual spending (m.u.)on and delicatessen products (Continuous);
- CHANNEL: customers’ Channel - Horeca (Hotel/Restaurant/Café) or Retail channel (Nominal) 1: hotel/restaurant/cafe 2: retail
- REGION: customers’ Region – Lisnon, Oporto or Other (Nominal)
- 1: Lisbon / 2: Porto / 3: other region Dimensions are; 440*8 Region Frequency Lisbon 77 Oporto 47 Other Region 316 Total 440 Channel Frequency¶ Horeca 298 Retail 142 Total 440
Defining the metric for success
Being able to cluster customers based on spending habits.
1.4 Recording the Experimental
1.Data Loading
2.Data cleaning for missing values and outliers
3.Exploratory Data Analysis
- implementation using k-means and hierarchical clustering.
5.Recomendation and conclusion.
1.5 Assessing the Relevance of the Data
The dataset is genuine since it was got from kaggle which is trusted open source.
Importing and reading dataset
library(readr)
customers_data_2<-
read_csv("C:/Users/USER/Downloads/Wholesale customers data.csv")##
## -- Column specification --------------------------------------------------------
## cols(
## Channel = col_double(),
## Region = col_double(),
## Fresh = col_double(),
## Milk = col_double(),
## Grocery = col_double(),
## Frozen = col_double(),
## Detergents_Paper = col_double(),
## Delicassen = col_double()
## )# making dataframe copy
customers_data<-customers_data_2
#
#checking the fist 6 rows of the dataset.
head(customers_data)## # A tibble: 6 x 8
## Channel Region Fresh Milk Grocery Frozen Detergents_Paper Delicassen
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 2 3 12669 9656 7561 214 2674 1338
## 2 2 3 7057 9810 9568 1762 3293 1776
## 3 2 3 6353 8808 7684 2405 3516 7844
## 4 1 3 13265 1196 4221 6404 507 1788
## 5 2 3 22615 5410 7198 3915 1777 5185
## 6 2 3 9413 8259 5126 666 1795 1451checking the bottom rows of the dataset
tail(customers_data)## # A tibble: 6 x 8
## Channel Region Fresh Milk Grocery Frozen Detergents_Paper Delicassen
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 3 16731 3922 7994 688 2371 838
## 2 1 3 29703 12051 16027 13135 182 2204
## 3 1 3 39228 1431 764 4510 93 2346
## 4 2 3 14531 15488 30243 437 14841 1867
## 5 1 3 10290 1981 2232 1038 168 2125
## 6 1 3 2787 1698 2510 65 477 52getting the dataset summary
summary(customers_data)## Channel Region Fresh Milk
## Min. :1.000 Min. :1.000 Min. : 3 Min. : 55
## 1st Qu.:1.000 1st Qu.:2.000 1st Qu.: 3128 1st Qu.: 1533
## Median :1.000 Median :3.000 Median : 8504 Median : 3627
## Mean :1.323 Mean :2.543 Mean : 12000 Mean : 5796
## 3rd Qu.:2.000 3rd Qu.:3.000 3rd Qu.: 16934 3rd Qu.: 7190
## Max. :2.000 Max. :3.000 Max. :112151 Max. :73498
## Grocery Frozen Detergents_Paper Delicassen
## Min. : 3 Min. : 25.0 Min. : 3.0 Min. : 3.0
## 1st Qu.: 2153 1st Qu.: 742.2 1st Qu.: 256.8 1st Qu.: 408.2
## Median : 4756 Median : 1526.0 Median : 816.5 Median : 965.5
## Mean : 7951 Mean : 3071.9 Mean : 2881.5 Mean : 1524.9
## 3rd Qu.:10656 3rd Qu.: 3554.2 3rd Qu.: 3922.0 3rd Qu.: 1820.2
## Max. :92780 Max. :60869.0 Max. :40827.0 Max. :47943.0checking datatypes
str(customers_data)## spec_tbl_df [440 x 8] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
## $ Channel : num [1:440] 2 2 2 1 2 2 2 2 1 2 ...
## $ Region : num [1:440] 3 3 3 3 3 3 3 3 3 3 ...
## $ Fresh : num [1:440] 12669 7057 6353 13265 22615 ...
## $ Milk : num [1:440] 9656 9810 8808 1196 5410 ...
## $ Grocery : num [1:440] 7561 9568 7684 4221 7198 ...
## $ Frozen : num [1:440] 214 1762 2405 6404 3915 ...
## $ Detergents_Paper: num [1:440] 2674 3293 3516 507 1777 ...
## $ Delicassen : num [1:440] 1338 1776 7844 1788 5185 ...
## - attr(*, "spec")=
## .. cols(
## .. Channel = col_double(),
## .. Region = col_double(),
## .. Fresh = col_double(),
## .. Milk = col_double(),
## .. Grocery = col_double(),
## .. Frozen = col_double(),
## .. Detergents_Paper = col_double(),
## .. Delicassen = col_double()
## .. )converting the data into a tibble for easy manupulation
library(caret)## Loading required package: lattice## Loading required package: ggplot2library(tibble)
#For ease in analysis,we convert the data into a tibble
customers_data<-as_tibble(customers_data) # there is suggestion to use as_tibble instead of as.tibble.
head(customers_data)## # A tibble: 6 x 8
## Channel Region Fresh Milk Grocery Frozen Detergents_Paper Delicassen
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 2 3 12669 9656 7561 214 2674 1338
## 2 2 3 7057 9810 9568 1762 3293 1776
## 3 2 3 6353 8808 7684 2405 3516 7844
## 4 1 3 13265 1196 4221 6404 507 1788
## 5 2 3 22615 5410 7198 3915 1777 5185
## 6 2 3 9413 8259 5126 666 1795 1451##. Data cleaning
#checking the missing values
is.null(customers_data)## [1] FALSE# checking for duplicates
anyDuplicated(customers_data)## [1] 0checking for outliers
installing the packages.
# install.packages("magrittr") # package installations are only needed the first time you use it
# install.packages("dplyr") # alternative installation of the %>%
library(magrittr) # needs to be run every time you start R and want to use %>%
library(dplyr) # alternatively, this also loads %>%##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionconverting some colunms to categorical datatypes.
channel and Region are categorical in nature and not numerical, they have already been encoded to make them easier to work with. We will convert them to their appropriate data type.
##converting colunms to categorical datatypes
#
customers_df <-customers_data
customers_df$Channel <- as.factor(customers_df$Channel)
customers_df$Region <- as.factor(customers_df$Region)##confirming the datatype changes
# confirming the data types changes
str(customers_df)## tibble [440 x 8] (S3: tbl_df/tbl/data.frame)
## $ Channel : Factor w/ 2 levels "1","2": 2 2 2 1 2 2 2 2 1 2 ...
## $ Region : Factor w/ 3 levels "1","2","3": 3 3 3 3 3 3 3 3 3 3 ...
## $ Fresh : num [1:440] 12669 7057 6353 13265 22615 ...
## $ Milk : num [1:440] 9656 9810 8808 1196 5410 ...
## $ Grocery : num [1:440] 7561 9568 7684 4221 7198 ...
## $ Frozen : num [1:440] 214 1762 2405 6404 3915 ...
## $ Detergents_Paper: num [1:440] 2674 3293 3516 507 1777 ...
## $ Delicassen : num [1:440] 1338 1776 7844 1788 5185 ...
## - attr(*, "spec")=
## .. cols(
## .. Channel = col_double(),
## .. Region = col_double(),
## .. Fresh = col_double(),
## .. Milk = col_double(),
## .. Grocery = col_double(),
## .. Frozen = col_double(),
## .. Detergents_Paper = col_double(),
## .. Delicassen = col_double()
## .. )the two variables has been transformed to categorical datatype.
###3.2a Identifying the numeric class in the data and evaluating if there are any outliers
#
#Checking the data types of the columns
#
data.num<- customers_df %>% select_if(is.numeric)
data.num## # A tibble: 440 x 6
## Fresh Milk Grocery Frozen Detergents_Paper Delicassen
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 12669 9656 7561 214 2674 1338
## 2 7057 9810 9568 1762 3293 1776
## 3 6353 8808 7684 2405 3516 7844
## 4 13265 1196 4221 6404 507 1788
## 5 22615 5410 7198 3915 1777 5185
## 6 9413 8259 5126 666 1795 1451
## 7 12126 3199 6975 480 3140 545
## 8 7579 4956 9426 1669 3321 2566
## 9 5963 3648 6192 425 1716 750
## 10 6006 11093 18881 1159 7425 2098
## # ... with 430 more rowschecking for outliers
for (i in 1:ncol(data.num)) {
boxplot(data.num[, i], main=names(data.num[, i]))
}
observation: all variables has outliers. However we will not drop them as they look genuine.
renaming the rows of the channel, and region for analysis purpose.
#Renaming colunms for analysis purpose
#
library(caret)
library(lattice)
library(dplyr)
customers_df$Channel <- with(customers_data, factor(Channel, levels = c(1,2),labels = c("restaurant", "retail")))
customers_df$Region <- with(customers_data, factor(Region, levels = c(1,2,3), labels = c("Lisbon", "Porto", "Other region")))
#
#confirming the changes
head(customers_df)## # A tibble: 6 x 8
## Channel Region Fresh Milk Grocery Frozen Detergents_Paper Delicassen
## <fct> <fct> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 retail Other region 12669 9656 7561 214 2674 1338
## 2 retail Other region 7057 9810 9568 1762 3293 1776
## 3 retail Other region 6353 8808 7684 2405 3516 7844
## 4 restaurant Other region 13265 1196 4221 6404 507 1788
## 5 retail Other region 22615 5410 7198 3915 1777 5185
## 6 retail Other region 9413 8259 5126 666 1795 1451observation: we converted encoded variable to categorical variable.
###checking dataset summary after data cleaning
# getting the main summary
summary(customers_df)## Channel Region Fresh Milk
## restaurant:298 Lisbon : 77 Min. : 3 Min. : 55
## retail :142 Porto : 47 1st Qu.: 3128 1st Qu.: 1533
## Other region:316 Median : 8504 Median : 3627
## Mean : 12000 Mean : 5796
## 3rd Qu.: 16934 3rd Qu.: 7190
## Max. :112151 Max. :73498
## Grocery Frozen Detergents_Paper Delicassen
## Min. : 3 Min. : 25.0 Min. : 3.0 Min. : 3.0
## 1st Qu.: 2153 1st Qu.: 742.2 1st Qu.: 256.8 1st Qu.: 408.2
## Median : 4756 Median : 1526.0 Median : 816.5 Median : 965.5
## Mean : 7951 Mean : 3071.9 Mean : 2881.5 Mean : 1524.9
## 3rd Qu.:10656 3rd Qu.: 3554.2 3rd Qu.: 3922.0 3rd Qu.: 1820.2
## Max. :92780 Max. :60869.0 Max. :40827.0 Max. :47943.0the above shows the mean, median, max, and quantile for numerical variables and frequences for categorical variables.
##getting the dataset description
library(psych)##
## Attaching package: 'psych'## The following objects are masked from 'package:ggplot2':
##
## %+%, alphadescribe(customers_df)## vars n mean sd median trimmed mad min max
## Channel* 1 440 1.32 0.47 1.0 1.28 0.00 1 2
## Region* 2 440 2.54 0.77 3.0 2.68 0.00 1 3
## Fresh 3 440 12000.30 12647.33 8504.0 9864.61 8776.25 3 112151
## Milk 4 440 5796.27 7380.38 3627.0 4375.52 3647.20 55 73498
## Grocery 5 440 7951.28 9503.16 4755.5 6158.43 4586.42 3 92780
## Frozen 6 440 3071.93 4854.67 1526.0 2144.07 1607.88 25 60869
## Detergents_Paper 7 440 2881.49 4767.85 816.5 1849.73 1060.80 3 40827
## Delicassen 8 440 1524.87 2820.11 965.5 1113.24 945.16 3 47943
## range skew kurtosis se
## Channel* 1 0.76 -1.43 0.02
## Region* 2 -1.27 -0.13 0.04
## Fresh 112148 2.54 11.33 602.94
## Milk 73443 4.03 24.25 351.85
## Grocery 92777 3.56 20.56 453.05
## Frozen 60844 5.87 53.80 231.44
## Detergents_Paper 40824 3.61 18.68 227.30
## Delicassen 47940 11.08 167.97 134.44observation: it gives us the a glimpse of the variance,mean,variance,max and so on.
Univariate Analysis
univariate Analysis for Numerical data
#preview of the numerical columns
#
library(dplyr) # alternatively, this also loads %>%
data.num<- customers_df %>% select_if(is.numeric)
head(data.num)## # A tibble: 6 x 6
## Fresh Milk Grocery Frozen Detergents_Paper Delicassen
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 12669 9656 7561 214 2674 1338
## 2 7057 9810 9568 1762 3293 1776
## 3 6353 8808 7684 2405 3516 7844
## 4 13265 1196 4221 6404 507 1788
## 5 22615 5410 7198 3915 1777 5185
## 6 9413 8259 5126 666 1795 1451previewing the numerical variables using histograms to check skewness.
#3.3ai installing ggplot2 package for visualization.
#install.packages('ggplot2')
#
#installing ggplot2 library
#
library(ggplot2)
#
#note: the above have been installed in the console section.univariate analysis
1. Numerical variables distribution
#visualizing the Fresh colunm to check for skewness
#
qplot(data = data.num, x = Fresh)## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
#visualizing the milk colunm to check for skewness
#
qplot(data = data.num, x = Milk,)## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
#visualizing the grocery colunm to check for skewness
#
qplot(data = data.num, x = Grocery)## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
#visualizing the Frozen colunm to check for skewness
#
qplot(data = data.num, x = Frozen)## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
#visualizing the Detergents_Paper colunm to check for skewness
#
qplot(data = data.num, x = Detergents_Paper)## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
#visualizing the Delicassen column to check for skewness
#
qplot(data = data.num, x = Delicassen)## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Observation: All our numerical variables are positively skewed.This means the variable mean is greater than the mode.
we can check skewness for numerical values at once as below
## we can check skewness for numerical values at once as below
library(caret)
library(ggplot2)
library(dplyr) # alternatively, this also loads %>%
library(tidyr)##
## Attaching package: 'tidyr'## The following object is masked from 'package:magrittr':
##
## extractcustomers_df%>%
gather(attributes, value, 3:8) %>%
ggplot(aes(x = value)) +
geom_histogram(fill = 'lightblue2', color = 'black') +
facet_wrap(~attributes, scales = 'free_x') +
labs(x="Values", y="Frequency") +
theme_bw()## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
observation: shows skewness to the right(positive skewness meaning the tail on the right side is bigger than the left side).
2. univariate Analysis for categorical Data
## Identifying the categorical class in the data
#
df_cat<- customers_df %>% select_if(is.factor)
df_cat## # A tibble: 440 x 2
## Channel Region
## <fct> <fct>
## 1 retail Other region
## 2 retail Other region
## 3 retail Other region
## 4 restaurant Other region
## 5 retail Other region
## 6 retail Other region
## 7 retail Other region
## 8 retail Other region
## 9 restaurant Other region
## 10 retail Other region
## # ... with 430 more rowscreating tables for bar plots.
# create tables of all categorical variables to be able to create bar plots with them
Channel_table <- table(customers_df$Channel)
Region_table <- table(customers_df$Region)adjusting plot size bf plotting.
# function for adjusting plot size
set_plot_dimensions <- function(width_choice, height_choice) {
options(repr.plot.width = width_choice, repr.plot.height = height_choice)
}# barplot for channel variable
set_plot_dimensions(5, 4)
Channel_table##
## restaurant retail
## 298 142barplot(Channel_table, ylab = "count", xlab="Channel", col="dark red")
observation: restaurant has more sales compared to retail variable.
# barplot of the region representation.
set_plot_dimensions(5, 4)
Region_table##
## Lisbon Porto Other region
## 77 47 316barplot(Region_table, ylab = "count", xlab="Region", col="sky blue")
observation:other regions has more sales, followed by Lisbon city, and finally Porto.
Bivariate Analysis
# previewing numerical data once again.
#
head(data.num)## # A tibble: 6 x 6
## Fresh Milk Grocery Frozen Detergents_Paper Delicassen
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 12669 9656 7561 214 2674 1338
## 2 7057 9810 9568 1762 3293 1776
## 3 6353 8808 7684 2405 3516 7844
## 4 13265 1196 4221 6404 507 1788
## 5 22615 5410 7198 3915 1777 5185
## 6 9413 8259 5126 666 1795 1451plotting scatter plots for numerical data
for (i in 1:(ncol(data.num)/2)) {
for (j in 4:ncol(data.num)) {
plot(as.numeric(unlist(data.num[, j]))
, as.numeric(unlist(data.num[, i]))
, xlab = names(as.vector(data.num[, i]))
, ylab = names(as.vector(data.num[, j])))
}
}
#scatterplot observation:
- Frozen vs Fresh. As the expenditures for frozen products go up those of fresh products equally go up though not correspondingly. For both products most customers spent averagely small amounts of money and those who spent more were few.
- Detergents and Fresh Products. The amount spent on these products don’t have a direct relationship. As the expenditures of detergents goes up, that of Fresh products don’t necessarily go up also and vice versa.
- Delicatessen vs Fresh Products. For Delicatessen and fresh products, the amounts spent on delicatessen by customers progressively increases without much significant increase in that of fresh products. There is a chance customers prefer more delicatessen from this wholesale compared to milk products therefore the marketing team should focus on ensuring that supply delicatessen products is constant and look into bettering quality of milk products maybe that could encourage customers to purchase their milk products as much as they do delicassens.
- Frozen products vs Milk. For both of these products, most customers spend less on them them but purchases of both don’t have a relation.
- Detergent paper and milk products. Both have a positive correlation. As the amount spent on either increases so does the amount spent on the other.
- Delicassen and Milk. For both these two most customers spend about the same amount of money.
- Frozen and Grocery. Most customers for both products spend the least amount spendable then individually increase without any correlation.
- Delicatessen and Grocery. When these two are compared, the amounts spend on groceries remain low as that spent on groceries increase. Marketing focus should be put on groceries in this case. The marketing team should probably come up with advertisements for healthy eating habits to push the grocery sales or even have them in the same position at the store with fresh products this could prompt buyers who prefer fresh products to buy them.
cor(data.num)## Fresh Milk Grocery Frozen Detergents_Paper
## Fresh 1.00000000 0.1005098 -0.01185387 0.34588146 -0.1019529
## Milk 0.10050977 1.0000000 0.72833512 0.12399376 0.6618157
## Grocery -0.01185387 0.7283351 1.00000000 -0.04019274 0.9246407
## Frozen 0.34588146 0.1239938 -0.04019274 1.00000000 -0.1315249
## Detergents_Paper -0.10195294 0.6618157 0.92464069 -0.13152491 1.0000000
## Delicassen 0.24468997 0.4063683 0.20549651 0.39094747 0.0692913
## Delicassen
## Fresh 0.2446900
## Milk 0.4063683
## Grocery 0.2054965
## Frozen 0.3909475
## Detergents_Paper 0.0692913
## Delicassen 1.0000000plotting correlation of the numerical variables.
#install.packages("corrplot")
library(corrplot)## corrplot 0.88 loaded#
## Let’s build a correlation matrix to understand the relation between each attributes
corrplot(cor(data.num), type = 'upper', method = 'number', tl.cex = 0.9, bg="black")
observation: There is a strong linear correlation between a couple of variables.
1.Grocery and Detergent_papers have a high positive correlation of 0.92.
Milk and Grocery have a high positive correlation of 0.73.
Detergent and Milk have a high positive correlated of 0.66,
Delicassen and Milk have a high positive correlation of 0.41.
Frozen and Detergent_paper have a negative correlation of -0.13.
clustering
we will use unsupervised learning
Feature Selection
1.filter method
# Calculating the correlation matrix
# ---
#
feature_num<-data.num
cor_Matrix <- cor(feature_num)
cor_Matrix## Fresh Milk Grocery Frozen Detergents_Paper
## Fresh 1.00000000 0.1005098 -0.01185387 0.34588146 -0.1019529
## Milk 0.10050977 1.0000000 0.72833512 0.12399376 0.6618157
## Grocery -0.01185387 0.7283351 1.00000000 -0.04019274 0.9246407
## Frozen 0.34588146 0.1239938 -0.04019274 1.00000000 -0.1315249
## Detergents_Paper -0.10195294 0.6618157 0.92464069 -0.13152491 1.0000000
## Delicassen 0.24468997 0.4063683 0.20549651 0.39094747 0.0692913
## Delicassen
## Fresh 0.2446900
## Milk 0.4063683
## Grocery 0.2054965
## Frozen 0.3909475
## Detergents_Paper 0.0692913
## Delicassen 1.0000000# Find attributes that are highly correlated
# ---
#
high_cor <- findCorrelation(cor_Matrix, cutoff=0.75)
high_cor## [1] 3#
names(data.num[,high_cor])## [1] "Grocery"observation; grocery variable is highly correlated.
Dropping variable with high correlation.
# We can remove the variables with a higher correlation
# and comparing the results graphically as shown below
#
# Removing Redundant Features
# ---
#
new_num<-feature_num[-high_cor]
new_num## # A tibble: 440 x 5
## Fresh Milk Frozen Detergents_Paper Delicassen
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 12669 9656 214 2674 1338
## 2 7057 9810 1762 3293 1776
## 3 6353 8808 2405 3516 7844
## 4 13265 1196 6404 507 1788
## 5 22615 5410 3915 1777 5185
## 6 9413 8259 666 1795 1451
## 7 12126 3199 480 3140 545
## 8 7579 4956 1669 3321 2566
## 9 5963 3648 425 1716 750
## 10 6006 11093 1159 7425 2098
## # ... with 430 more rowsvariable Grocery has been dropped
###. performing the comparison
# Performing our graphical comparison
# ---
#
par(mfrow = c(1, 2))
corrplot(cor_Matrix, order = "hclust")
corrplot(cor(new_num), order = "hclust")
removing one variable reduce Multicollinearity as it remove redundancy
##1. Wrapper Methods for feature selection we use the clustvarsel function will implement variable section methodology for model-based clustering to find the optimal subset of variables in a dataset.
#preview of dataset
#
head(new_num)## # A tibble: 6 x 5
## Fresh Milk Frozen Detergents_Paper Delicassen
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 12669 9656 214 2674 1338
## 2 7057 9810 1762 3293 1776
## 3 6353 8808 2405 3516 7844
## 4 13265 1196 6404 507 1788
## 5 22615 5410 3915 1777 5185
## 6 9413 8259 666 1795 1451scaling the datset.
# scaling our dataset by use of scale function.
#
library(dplyr)
wrapper_norm <- as.data.frame(scale(new_num))
#
#previewing the scaled dataset.
head(wrapper_norm)## Fresh Milk Frozen Detergents_Paper Delicassen
## 1 0.05287300 0.52297247 -0.5886970 -0.04351919 -0.06626363
## 2 -0.39085706 0.54383861 -0.2698290 0.08630859 0.08904969
## 3 -0.44652098 0.40807319 -0.1373793 0.13308016 2.24074190
## 4 0.09999758 -0.62331041 0.6863630 -0.49802132 0.09330484
## 5 0.83928412 -0.05233688 0.1736612 -0.23165413 1.29786952
## 6 -0.20457266 0.33368675 -0.4955909 -0.22787885 -0.02619421observation: our data is now scaled and is now on the same scale.
installing the packages to be used
# Installing package
# install.packages("mclust")
# Install.packages("clustvarsel")
#
#loading libraries
library(mclust) ## Package 'mclust' version 5.4.7
## Type 'citation("mclust")' for citing this R package in publications.##
## Attaching package: 'mclust'## The following object is masked from 'package:psych':
##
## simlibrary(clustvarsel)## Package 'clustvarsel' version 2.3.4## Type 'citation("clustvarsel")' for citing this R package in publications.selecting the best features
# Sequential forward greedy search (default)
# ---
#
out = clustvarsel(wrapper_norm, G = 1:5)
out## ------------------------------------------------------
## Variable selection for Gaussian model-based clustering
## Stepwise (forward/backward) greedy search
## ------------------------------------------------------
##
## Variable proposed Type of step BICclust Model G BICdiff Decision
## Detergents_Paper Add -313.9955 V 5 945.84285 Accepted
## Delicassen Add -868.2711 VVI 5 705.56265 Accepted
## Frozen Add -1445.6586 VVI 5 608.31377 Accepted
## Frozen Remove -868.2711 VVI 5 608.31377 Rejected
## Milk Add -1958.6442 VVI 5 389.11513 Accepted
## Milk Remove -1445.6586 VVI 5 389.11513 Rejected
## Fresh Add -3112.8447 VVI 5 54.62052 Accepted
## Fresh Remove -1958.6442 VVI 5 54.62052 Rejected
## Fresh Remove -1958.6442 VVI 5 54.62052 Rejected
##
## Selected subset: Detergents_Paper, Delicassen, Frozen, Milk, Freshobservation: surprisingly all the 5 features in our dataset were accepted.
finding the best features
# Having identified the variables that we use, we proceed to build the clustering model:
# ---
#
# Building the model
Subset1 = wrapper_norm[out$subset]
mod = Mclust(Subset1, G = 1:5)
summary(mod)## ----------------------------------------------------
## Gaussian finite mixture model fitted by EM algorithm
## ----------------------------------------------------
##
## Mclust VVI (diagonal, varying volume and shape) model with 5 components:
##
## log-likelihood n df BIC ICL
## -1392.079 440 54 -3112.845 -3201.723
##
## Clustering table:
## 1 2 3 4 5
## 165 90 94 60 31###2. Embedded Methods future selection
We will use the ewkm function from the wskm package.
This is a weighted subspace clustering algorithm that is well suited to very high dimensional data.
installing the package to use
# We install and load our wskm package
#install.packages("wskm")
#
#loading library
library(wskm)## Loading required package: latticeExtra##
## Attaching package: 'latticeExtra'## The following object is masked from 'package:ggplot2':
##
## layer## Loading required package: fpcmodel building
embed_data <-wrapper_norm
set.seed(6)
model <- ewkm(embed_data[1:5], 2, lambda=2, maxiter=1000)
model## K-means clustering with 2 clusters of sizes 204, 236
##
## Cluster means:
## Fresh Milk Frozen Detergents_Paper Delicassen
## 1 -0.2744347 0.3146299 -0.3696722 0.5510653 -0.03458459
## 2 0.2372232 -0.2719682 0.3195471 -0.4763446 0.02989516
##
## Clustering vector:
## [1] 1 1 1 2 2 1 1 1 1 1 1 2 1 1 1 2 1 2 1 1 1 2 2 2 1 1 2 2 1 1 1 2 2 2 2 1 2
## [38] 1 1 2 2 1 1 1 1 1 1 1 1 1 2 2 1 1 2 1 1 1 2 1 1 1 1 1 2 1 1 1 2 2 2 2 2 2
## [75] 1 2 2 1 2 1 2 1 1 2 1 1 1 2 2 2 2 2 1 2 1 2 1 1 1 2 1 1 1 2 1 1 1 1 1 2 2
## [112] 1 2 2 2 2 1 2 2 2 2 2 2 1 2 2 2 1 2 2 2 2 2 2 1 1 2 2 2 2 2 2 2 2 2 1 1 1
## [149] 2 1 1 2 2 2 2 1 1 2 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1 1 2 1 2 1 1 2 2 2 1 2 2
## [186] 2 2 2 1 1 2 1 2 1 2 2 2 1 2 2 1 1 2 2 1 1 2 1 1 1 2 1 1 1 1 1 1 2 1 2 1 1
## [223] 2 2 1 2 1 2 1 2 2 1 2 2 2 1 2 2 1 2 2 2 2 1 1 1 2 2 2 2 2 1 2 2 2 2 2 2 2
## [260] 2 2 2 2 2 1 2 1 2 1 2 2 1 2 2 2 1 2 2 2 1 1 1 2 2 2 2 1 2 2 1 2 2 2 1 2 1
## [297] 2 1 1 2 1 1 1 1 1 1 1 1 2 1 2 2 1 2 1 1 2 2 2 1 2 2 2 1 2 2 2 2 2 2 2 1 2
## [334] 1 2 1 2 2 2 2 1 1 1 1 2 1 1 1 1 1 2 1 1 1 2 2 2 1 2 2 2 1 2 2 2 1 1 1 2 1
## [371] 2 2 2 1 1 2 2 1 2 2 2 2 2 2 2 2 2 2 1 2 2 1 2 2 1 2 1 2 2 2 2 2 2 2 2 2 2
## [408] 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 2 1 1 2 1 2 2 2 2 2 2 2 1 2 2 1 1 2
##
## Within cluster sum of squares by cluster:
## [1] 755.1876 1205.5871
## (between_SS / total_SS = 10.7 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss"
## [5] "tot.withinss" "betweenss" "size" "iterations"
## [9] "total.iterations" "restarts" "weights"##Loading and installing our cluster package to be used
#
#install.packages("cluster")
#
# loading the library
library("cluster")# Cluster Plot against 1st 2 principal components
# ---
#
clusplot(embed_data[1:5], model$cluster, color=TRUE, shade=TRUE,
labels=6, lines=1,main='Cluster Analysis for wholesale dataset')
observation, with 2 clusters, the two components explains 72.46% of the point variability.
The red cluster shows that some customers spending habits increases significantly over different products. Blue cluster shows these customers spending habits on one product increases where as their spending habits decreases on other products.
calculating weight for each cluster
Weights are calculated for each variable and cluster.
They are a measure of the relative importance of each variable with regards to the membership of the observations to that cluster.
The weights are incorporated into the distance function, typically reducing the distance for more important variables.
# checking the Weights
#
round(model$weights*100,2)## Fresh Milk Frozen Detergents_Paper Delicassen
## 1 0 0 99.99 0.00 0
## 2 0 0 0.00 99.99 0observation:
In cluster 1, Frozen has a high weight of 1
In cluster 2, Detergent_paper has a high weigh of 1
4. Feature ranking
We use the FSelector Package. This is a package containing functions for selecting attributes from a given dataset.
installing packages and loading the library required
#Feature Ranking
#
#install.packages("FSelector")
#
library(FSelector)
#checking correlation.
library(caret)
library(corrplot)
#
corrplot(cor(embed_data), type = 'upper', method = 'number', tl.cex = 0.9)
### ranking the features
# From the FSelector package, we use the correlation coefficient as a unit of valuation.
# This would be one of the several algorithms contained
# in the FSelector package that can be used rank the variables.
# ---
#
Scores <- linear.correlation(embed_data)
Scores## attr_importance
## Milk 0.1005098
## Frozen 0.3458815
## Detergents_Paper 0.1019529
## Delicassen 0.2446900explanation: From the output above, we observe a list containing rows of variables on the left and score on the right.
we will now make decision
our decision will be based on cuttoff k=4
# In order to make a decision, we define a cutoff.
# we want to use the top 5 representative variables,
# through the use of the cutoff.k function included in the FSelector package.
# Alternatively, we could define our cutoff visually
# but in cases where there are few variables than in high dimensional datasets.
#
# cutoff.k: The algorithms select a subset from a ranked attributes.
Subset <- cutoff.k(Scores, 4)
as.data.frame(Subset)## Subset
## 1 Frozen
## 2 Delicassen
## 3 Detergents_Paper
## 4 Milkobservation: the top 4 features are frozen,delicassen,Detergents_paper, milk and Grocery.
cutoff based on percentage
# We set cutoff as a percentage which would indicate
# that we would want to work with the percentage of the best variables.
# ---
#
Subset2 <-cutoff.k.percent(Scores, 0.6)
Subset2## [1] "Frozen" "Delicassen"observation: at 60% we get 3 variables as the best to work with.
##K-mean clustering
confirmating all the datatypes are numerical
#previewing the dataset to be
embed_data<-
head(customers_df)k-means method
getting numerical variables for clustering
head(new_num)## # A tibble: 6 x 5
## Fresh Milk Frozen Detergents_Paper Delicassen
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 12669 9656 214 2674 1338
## 2 7057 9810 1762 3293 1776
## 3 6353 8808 2405 3516 7844
## 4 13265 1196 6404 507 1788
## 5 22615 5410 3915 1777 5185
## 6 9413 8259 666 1795 1451observation: variables have the right datatypes.
###1. k-means clustering
# using already scaled data.
#
summary(new_num)## Fresh Milk Frozen Detergents_Paper
## Min. : 3 Min. : 55 Min. : 25.0 Min. : 3.0
## 1st Qu.: 3128 1st Qu.: 1533 1st Qu.: 742.2 1st Qu.: 256.8
## Median : 8504 Median : 3627 Median : 1526.0 Median : 816.5
## Mean : 12000 Mean : 5796 Mean : 3071.9 Mean : 2881.5
## 3rd Qu.: 16934 3rd Qu.: 7190 3rd Qu.: 3554.2 3rd Qu.: 3922.0
## Max. :112151 Max. :73498 Max. :60869.0 Max. :40827.0
## Delicassen
## Min. : 3.0
## 1st Qu.: 408.2
## Median : 965.5
## Mean : 1524.9
## 3rd Qu.: 1820.2
## Max. :47943.0our dataset is in different dimension.we will scale it before we do clustering
# normalizing our dataset by use of scale function.
#
library(dplyr)
df_Normalize <- as.data.frame(scale(new_num))
#
#previewing the scaled dataset.
head(df_Normalize)## Fresh Milk Frozen Detergents_Paper Delicassen
## 1 0.05287300 0.52297247 -0.5886970 -0.04351919 -0.06626363
## 2 -0.39085706 0.54383861 -0.2698290 0.08630859 0.08904969
## 3 -0.44652098 0.40807319 -0.1373793 0.13308016 2.24074190
## 4 0.09999758 -0.62331041 0.6863630 -0.49802132 0.09330484
## 5 0.83928412 -0.05233688 0.1736612 -0.23165413 1.29786952
## 6 -0.20457266 0.33368675 -0.4955909 -0.22787885 -0.02619421observation: our data has been scaled and is now on the same scale.
Getting the optimal clusters.
###installing the packages to be used
library(factoextra)## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBalibrary(cluster)
library(gridExtra) # for grid.arrange##
## Attaching package: 'gridExtra'## The following object is masked from 'package:dplyr':
##
## combinelibrary(dplyr)###1.a Elbow method
Getting the optimal cluster for k-means elbow method
# Determining Optimal clusters (k) Using Elbow method
fviz_nbclust(x = df_Normalize,FUNcluster = kmeans, method = 'wss' )
observation: elbow methods gives 2 as the optimal cluster, we will check other methods.
###1.b k-means silhouette method optimal cluster
# Determining Optimal clusters (k) Using Average Silhouette Method
fviz_nbclust(x = df_Normalize,FUNcluster = kmeans, method = 'silhouette' )
observation; silhouette method chooses 2 as optimal cluster.
###1.c K-means Gap-Statistic method
#loading libraries required
library(factoextra)
library(cluster)
# compute gap statistic
set.seed(1234)
gap_stat <- clusGap(x = df_Normalize, FUN = kmeans, K.max = 15, nstart = 25,iter.max=100)
# Print the result
print(gap_stat, method = "firstmax")## Clustering Gap statistic ["clusGap"] from call:
## clusGap(x = df_Normalize, FUNcluster = kmeans, K.max = 15, nstart = 25, iter.max = 100)
## B=100 simulated reference sets, k = 1..15; spaceH0="scaledPCA"
## --> Number of clusters (method 'firstmax'): 1
## logW E.logW gap SE.sim
## [1,] 5.548652 7.129865 1.581213 0.009219731
## [2,] 5.449888 6.995793 1.545905 0.009991787
## [3,] 5.384440 6.922024 1.537584 0.009804606
## [4,] 5.261183 6.859947 1.598764 0.009421083
## [5,] 5.145344 6.808299 1.662955 0.009489560
## [6,] 5.096112 6.763149 1.667037 0.009795126
## [7,] 5.037667 6.722761 1.685094 0.009570377
## [8,] 4.973473 6.687051 1.713578 0.009486315
## [9,] 4.937628 6.656072 1.718444 0.010033475
## [10,] 4.892399 6.628184 1.735785 0.010190786
## [11,] 4.839106 6.601789 1.762683 0.010451775
## [12,] 4.815152 6.577865 1.762713 0.010595444
## [13,] 4.785596 6.556162 1.770566 0.010839477
## [14,] 4.748170 6.535631 1.787461 0.010797960
## [15,] 4.708260 6.516785 1.808525 0.010884256#visualizing to get the optimal cluster
# plot the result to determine the optimal number of clusters.
fviz_gap_stat(gap_stat)
gap statistics method gives as 1 as the optimal cluster.
# Compute k-means clustering with k = 2, optimal cluster
set.seed(123)
kmean_df <- kmeans(new_num, centers = 2, nstart = 25)
print(kmean_df)## K-means clustering with 2 clusters of sizes 376, 64
##
## Cluster means:
## Fresh Milk Frozen Detergents_Paper Delicassen
## 1 7962.609 5279.63 2477.753 3005.846 1228.902
## 2 35721.719 8831.50 6562.734 2150.922 3263.688
##
## Clustering vector:
## [1] 1 1 1 1 2 1 1 1 1 1 1 1 2 1 2 1 1 1 1 1 1 1 2 2 2 1 1 1 1 2 1 1 1 2 1 1 2
## [38] 1 1 2 2 1 1 1 1 1 1 2 1 1 1 1 2 1 2 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1
## [75] 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1
## [112] 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1
## [149] 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 2 1 2 1
## [186] 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [223] 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 1 2
## [260] 2 1 1 2 1 1 1 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1 2 2 2 2 1 1 1 2 1 1 1 1 1 1
## [297] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1
## [334] 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [371] 2 1 1 1 1 1 1 2 1 1 2 1 2 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2 2 2 1 1 2
## [408] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 1 1 2 2 1 1 1
##
## Within cluster sum of squares by cluster:
## [1] 39030411454 34907223610
## (between_SS / total_SS = 37.3 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"We can visualize the results using the below code.
visualizing the kmeans clusters
library(factoextra)
library(cluster)
fviz_cluster(kmean_df, data = customers_data)
These are the 2 optimal clusters.these shows clients spend less and can be attributed to particular product buying,while others spend more which time for example restaurants.
head(kmean_df)## $cluster
## [1] 1 1 1 1 2 1 1 1 1 1 1 1 2 1 2 1 1 1 1 1 1 1 2 2 2 1 1 1 1 2 1 1 1 2 1 1 2
## [38] 1 1 2 2 1 1 1 1 1 1 2 1 1 1 1 2 1 2 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1
## [75] 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1
## [112] 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1
## [149] 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 2 1 2 1
## [186] 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [223] 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 1 2
## [260] 2 1 1 2 1 1 1 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1 2 2 2 2 1 1 1 2 1 1 1 1 1 1
## [297] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1
## [334] 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [371] 2 1 1 1 1 1 1 2 1 1 2 1 2 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2 2 2 1 1 2
## [408] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 1 1 2 2 1 1 1
##
## $centers
## Fresh Milk Frozen Detergents_Paper Delicassen
## 1 7962.609 5279.63 2477.753 3005.846 1228.902
## 2 35721.719 8831.50 6562.734 2150.922 3263.688
##
## $totss
## [1] 117949721617
##
## $withinss
## [1] 39030411454 34907223610
##
## $tot.withinss
## [1] 73937635063
##
## $betweenss
## [1] 44012086554observation: the above shows the means of the two clusters.
head(customers_df)## # A tibble: 6 x 8
## Channel Region Fresh Milk Grocery Frozen Detergents_Paper Delicassen
## <fct> <fct> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 retail Other region 12669 9656 7561 214 2674 1338
## 2 retail Other region 7057 9810 9568 1762 3293 1776
## 3 retail Other region 6353 8808 7684 2405 3516 7844
## 4 restaurant Other region 13265 1196 4221 6404 507 1788
## 5 retail Other region 22615 5410 7198 3915 1777 5185
## 6 retail Other region 9413 8259 5126 666 1795 1451# Verifying the results of clustering
# ---
#
par(mfrow = c(2,2), mar = c(5,4,2,2))
# Plotting to see how Sepal.Length and Sepal.Width data points have been distributed in clusters
plot(customers_df[c(5:6)], col = kmean_df$cluster)
plot(customers_df[c(4,5)], col = kmean_df$cluster)
plot(customers_df[c(3,4)], col = kmean_df$cluster)
# Plotting to see how Sepal.Length and Sepal.Width data points have been distributed
# originally as per "class" attribute in dataset
# ---
There are two clusters of customers according to spending habits; Those that spend more on fresh products and not groceries and vice versa. Those that spend more on fresh products and not milk and vice versa. Those whose spending habits are more on groceries and milk but that of milk is slightly higher than that of groceries.
# showing how the clusters respond to the region variable
table(kmean_df$cluster, customers_df$Region)##
## Lisbon Porto Other region
## 1 66 43 267
## 2 11 4 49observation: based on the above findings, lisbon has a higher representation compared to cluster Porto. thus the wholesale supplier should concentrate on Lisbon.
# showing how the clusters respond to the region variable
table(kmean_df$cluster, customers_df$Channel)##
## restaurant retail
## 1 246 130
## 2 52 12observation: restaurants has representation on cluster 1, note that cluster one is the high spending group.
We can extract the clusters and add to our initial data to do some descriptive statistics at the cluster level
library(tidyr)
#customers_df %>%
# mutate(Cluster = kmean_df$cluster) %>%
# group_by(Cluster) %>%
# summarize_all('median')##checking the cluster size.
# Cluster size
kmean_df$size## [1] 376 64observation: we can see customers in cluster one has a high spending habit.
Recommendation
Delicatessen and Milk There is a chance customers prefer more delicatessen from this wholesale compared to milk products therefore the marketing team should focus on ensuring that supply delicatessen products is constant and look into bettering quality of milk products maybe that could encourage customers to purchase their milk products as much as they do delicassens.
Delicatessen and Grocery. When these two are compared, the amounts spend on groceries remain low as that spent on groceries increase. Marketing focus should be put on groceries in this case. The marketing team should probably come up with advertisements for healthy eating habits to push the grocery sales or even have them in the same position at the store with fresh products this could prompt buyers who prefer fresh products to buy them.
3.Since Lisbon is a high representation on high spending customers, the wholesalers should focus on distributing products preferred by restaurant to maximize revenue.