/ #Clustering #Customer Segmentation 

A gentle Introduction to Customer Segmentation - Using K-Means Clustering to Understand Marketing Response

Market segmentation refers to the process of dividing a consumer market of existing and/or potential customers into groups (or segments) based on shared attributes, interests, and behaviours.

For this mini-project I will use the popular K-Means clustering algorithm to segment customers based on their response to a series of marketing campaigns. The basic concept is that consumers who share common traits would respond to marketing communication in a similar way so that companies can reach out for each group in a relevant and effective way.

What is K-Means Clustering?

K-Means clustering is part of the Unsupervised Learning modelling family, a set of techniques used to find patterns in data that has not been labelled, classified or categorized. As this method does not require to have a target for clustering, it can be of great help in the exploratory phase of customer segmentation.

The fundamental idea is that customers assigned to a group are as similar as possible, whereas customers belonging to different groups are as dissimilar as possible. Each cluster is represented by its centre, corresponding to the mean of elements assigned to the cluster.

To illustrate the principle, suppose that you have a set of elements like those in the picture below and want to classify them into 3 clusters

What K-Means would do for you is to group them up around the middle or centre of each cluster, represented here by the “X”’s, in a way that minimises the distance of each element to its centre

So how does that help you to better understand your customers? Well, in this case you can use their behavior (specifically, which offer they did or did not go for) as a way to grouping them up with similar minded customers. You can now look into each of those groups to unearth trends and patterns and use them for shaping future offers.

On a slightly more technical note, it’s important to mention that there are many K-Means algorithms available ( Hartigan-Wong, Lloyd, MacQueen to name but a few) but they all share the same basic concept: each element is assigned to a cluster so that it minimises the sum of squares Euclidean Distance to the centre - a process also referred to as minimising the total within-cluster sum of squares (tot.withinss).

Loading the Packages

library(tidyverse)
library(lubridate)
library(knitr)
library(readxl)
library(broom)
library(umap)
library(ggrepel)

The Data

The dataset comes from John Foreman’s book, Data Smart. It contains sales promotion data for a fictional wine retailer and includes details of 32 promotions (including wine variety, minimum purchase quantity, percentage discount, and country of origin) and a list of 100 customers and the promotions they responded to.

offers_tbl <- read_excel('WineKMC.xlsx', sheet = 'OfferInformation')

offers_tbl <- offers_tbl %>% 
        set_names(c('offer', 'campaign', 'varietal', 'min_qty_kg', 
                    'disc_pct','origin', 'past_peak'))

head(offers_tbl)
## # A tibble: 6 x 7
##   offer campaign varietal          min_qty_kg disc_pct origin     past_peak
##   <dbl> <chr>    <chr>                  <dbl>    <dbl> <chr>      <chr>    
## 1     1 January  Malbec                    72       56 France     FALSE    
## 2     2 January  Pinot Noir                72       17 France     FALSE    
## 3     3 February Espumante                144       32 Oregon     TRUE     
## 4     4 February Champagne                 72       48 France     TRUE     
## 5     5 February Cabernet Sauvign~        144       44 New Zeala~ TRUE     
## 6     6 March    Prosecco                 144       86 Chile      FALSE
transac_tbl <- read_excel('WineKMC.xlsx', sheet = 'Transactions')

transac_tbl <- transac_tbl %>% 
        set_names(c('customer', 'offer'))

head(transac_tbl)
## # A tibble: 6 x 2
##   customer offer
##   <chr>    <dbl>
## 1 Smith        2
## 2 Smith       24
## 3 Johnson     17
## 4 Johnson     24
## 5 Johnson     26
## 6 Williams    18

The data needs to be converted to a User-Item format(a.k.a. Customer-Product matrix), featuring customers across the top and offers down the side. The cells are populated with 0’s and 1’s, where 1’s indicate if a customer responded to a specific offer.

This type of matrix is also known as binary rating matrix and does NOT require normalisation.

wine_tbl <- transac_tbl %>% 
    left_join(offers_tbl) %>% 
    mutate(value = 1) %>%
    spread(customer,value, fill = 0) 

head(wine_tbl)
## # A tibble: 6 x 107
##   offer campaign varietal min_qty_kg disc_pct origin past_peak Adams Allen
##   <dbl> <chr>    <chr>         <dbl>    <dbl> <chr>  <chr>     <dbl> <dbl>
## 1     1 January  Malbec           72       56 France FALSE         0     0
## 2     2 January  Pinot N~         72       17 France FALSE         0     0
## 3     3 February Espuman~        144       32 Oregon TRUE          0     0
## 4     4 February Champag~         72       48 France TRUE          0     0
## 5     5 February Caberne~        144       44 New Z~ TRUE          0     0
## 6     6 March    Prosecco        144       86 Chile  FALSE         0     0
## # ... with 98 more variables: Anderson <dbl>, Bailey <dbl>, Baker <dbl>,
## #   Barnes <dbl>, Bell <dbl>, Bennett <dbl>, Brooks <dbl>, Brown <dbl>,
## #   Butler <dbl>, Campbell <dbl>, Carter <dbl>, Clark <dbl>,
## #   Collins <dbl>, Cook <dbl>, Cooper <dbl>, Cox <dbl>, Cruz <dbl>,
## #   Davis <dbl>, Diaz <dbl>, Edwards <dbl>, Evans <dbl>, Fisher <dbl>,
## #   Flores <dbl>, Foster <dbl>, Garcia <dbl>, Gomez <dbl>, Gonzalez <dbl>,
## #   Gray <dbl>, Green <dbl>, Gutierrez <dbl>, Hall <dbl>, Harris <dbl>,
## #   Hernandez <dbl>, Hill <dbl>, Howard <dbl>, Hughes <dbl>,
## #   Jackson <dbl>, James <dbl>, Jenkins <dbl>, Johnson <dbl>, Jones <dbl>,
## #   Kelly <dbl>, King <dbl>, Lee <dbl>, Lewis <dbl>, Long <dbl>,
## #   Lopez <dbl>, Martin <dbl>, Martinez <dbl>, Miller <dbl>,
## #   Mitchell <dbl>, Moore <dbl>, Morales <dbl>, Morgan <dbl>,
## #   Morris <dbl>, Murphy <dbl>, Myers <dbl>, Nelson <dbl>, Nguyen <dbl>,
## #   Ortiz <dbl>, Parker <dbl>, Perez <dbl>, Perry <dbl>, Peterson <dbl>,
## #   Phillips <dbl>, Powell <dbl>, Price <dbl>, Ramirez <dbl>, Reed <dbl>,
## #   Reyes <dbl>, Richardson <dbl>, Rivera <dbl>, Roberts <dbl>,
## #   Robinson <dbl>, Rodriguez <dbl>, Rogers <dbl>, Ross <dbl>,
## #   Russell <dbl>, Sanchez <dbl>, Sanders <dbl>, Scott <dbl>, Smith <dbl>,
## #   Stewart <dbl>, Sullivan <dbl>, Taylor <dbl>, Thomas <dbl>,
## #   Thompson <dbl>, Torres <dbl>, Turner <dbl>, Walker <dbl>, Ward <dbl>,
## #   Watson <dbl>, White <dbl>, Williams <dbl>, Wilson <dbl>, Wood <dbl>,
## #   Wright <dbl>, Young <dbl>

Clustering the Customers

The K-Means algorithm comes with the stats package, one of the Core System Libraries in R, and is fairly straightforward to use. I just need to pass a few parameters to the kmeans() function.

user_item_tbl <- wine_tbl[,8:107]

set.seed(196)             # for reproducibility of clusters visualisation with UMAP
kmeans_obj <- user_item_tbl %>%  
    kmeans(centers = 5,   # number of clusters to divide customer list into
           nstart = 100,  # specify number of random sets to be chosen
           iter.max = 50) # maximum number of iterations allowed - 

I can quickly inspect the model withglance()from the broompackage, which provides an summary of model-level statistics

glance(kmeans_obj) %>% glimpse()
## Observations: 1
## Variables: 4
## $ totss        <dbl> 283.1875
## $ tot.withinss <dbl> 189.7255
## $ betweenss    <dbl> 93.46201
## $ iter         <int> 3

The one metric to really keep an eye on is the total within-cluster sum of squares (or tot.withinss) as the optimal number of clusters is that which minimises the tot.withinss. So I want to fit the k-means model for different number of clusters and see where tot.withinss reaches its minimum.

First, I build a function for a set number of centers (4 in this case) and check that is working on glance().

kmeans_map <- function(centers = 4) {
    user_item_tbl %>%  
        kmeans(centers = centers, nstart = 100, iter.max = 50)
}
4 %>% kmeans_map() %>%  glance()
## # A tibble: 1 x 4
##   totss tot.withinss betweenss  iter
##   <dbl>        <dbl>     <dbl> <int>
## 1  283.         203.      80.0     2

Then, I create a nested tibble, which is a way of “nesting” columns inside a data frame. The great thing about nested data frames is that you can put essentially anything you want in them: lists, models, data frames, plots, etc!

kmeans_map_tbl <- tibble(centers = 1:15) %>%  # create column with centres 
          mutate(k_means = centers %>% 
                  map(kmeans_map)) %>%    # iterate `kmeans_map` row-wise to gather 
                                          # kmeans models for each centre in column 2
          mutate(glance = k_means %>%  
                  map(glance))            # apply `glance()` row-wise to gather each
                                          # model’s summary metrics in column 3

kmeans_map_tbl %>% glimpse()
## Observations: 15
## Variables: 3
## $ centers <int> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15
## $ k_means <list> [<1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
## $ glance  <list> [<tbl_df[1 x 4]>, <tbl_df[1 x 4]>, <tbl_df[1 x 4]>, <...

Last, I can build a scree plot and look for the “elbow” on the graph, the point where the number of additional clusters seem to level off. In this case 5 appears to be an optimal number as the drop in tot.withinss for 6 is not as pronounced as the previous one.

kmeans_map_tbl %>% 
    unnest(glance) %>%                           # unnest the glance column
    select(centers, tot.withinss) %>%            # select centers and tot.withinss
    
    ggplot(aes(x = centers, y = tot.withinss)) + 
    geom_line(colour = 'grey30', size = .8) +
    geom_point(colour = 'green4', size = 3) +
    geom_label_repel(aes(label = centers), 
                     colour = 'grey30') +
    theme_bw() +
    labs(title = 'Scree Plot')

Visualising the Segments

Now that I have identified the optimal number of clusters I want to visualise them. To do so, I use the UMAP ( Uniform Manifold Approximation and Projection ), a dimentionality reduction technique that can be used for cluster visualisation in a similar way to Principal Component Analysis and t-SNE.

First, I create a umap object and pull out the layout argument (containing coordinates that can be used to visualize the dataset), change its format to a tibble and attach the offer column from the wine_tbl.

umap_obj <- user_item_tbl %>%  umap() 

umap_tbl <- umap_obj$layout %>% 
    as_tibble() %>%                       # change to a tibble
    set_names(c('x', 'y')) %>%            # remane columns
    bind_cols(wine_tbl %>% select(offer)) # attach offer reference

Then, I pluck the 5th kmeans model from the nested tibble, attach the cluster argument from the kmeans function to the output, and join offer and cluster to the umap_tbl.

umap_kmeans_5_tbl <- kmeans_map_tbl %>% 
    pull(k_means) %>%
    pluck(5) %>%                          # pluck element 5 
    broom::augment(wine_tbl) %>%          # attach .cluster to the tibble 
    select(offer, .cluster) %>% 
    left_join(umap_tbl, by = 'offer')     # join umap_tbl to clusters by offer

At last, I can visualise the UMAP’ed projections of the clusters.

umap_kmeans_5_tbl %>% 
    mutate(label_text = str_glue('Offer: {offer}
                                  Cluster: {.cluster}')) %>%
    ggplot(aes(x,y, colour = .cluster)) +
    geom_point() +
    geom_label_repel(aes(label = label_text), size = 3) +
    theme_light() +
    labs(title    = 'UMAP 2D Projections of K-Means Clusters',
         caption  = "") +
    theme(legend.position = 'none')

Evaluating the Clusters

Now we can finally have a closer look at the single clusters to see what K-Means has identified.

But let’s first bring all information together in one data frame.

cluster_trends_tbl <- wine_tbl %>%
    left_join(umap_kmeans_5_tbl) %>%
    arrange(.cluster) %>%
    select(.cluster, offer:past_peak)

Cluster 1 & 2

Customers in cluster 1 purchase high volumes of sparkling wines (Champagne and Prosecco) whilts those in the second segment favour low volume purchases of different varieties.

cluster_trends_tbl %>% 
    filter(.cluster == 1 | .cluster == 2) %>% 
    count(.cluster, varietal, origin, min_qty_kg, disc_pct) %>%
    select(-n)
## # A tibble: 9 x 5
##   .cluster varietal     origin       min_qty_kg disc_pct
##   <fct>    <chr>        <chr>             <dbl>    <dbl>
## 1 1        Champagne    France               72       48
## 2 1        Champagne    New Zealand          72       88
## 3 1        Prosecco     Chile               144       86
## 4 2        Espumante    Oregon                6       50
## 5 2        Espumante    South Africa          6       45
## 6 2        Malbec       France                6       54
## 7 2        Merlot       Chile                 6       43
## 8 2        Pinot Grigio France                6       87
## 9 2        Prosecco     Australia             6       40

Cluster 3 & 4

Customers in these groups have very specific taste when it comes to wine: those in the third segment have a penchant for Pinot Noir, whereas group 4 only buys French Champagne in high volumes.

cluster_trends_tbl %>% 
    filter(.cluster == 3 | .cluster == 4 ) %>% 
    group_by() %>%
    count(.cluster, varietal, origin, min_qty_kg, disc_pct) %>%
    select(-n) 
## # A tibble: 6 x 5
##   .cluster varietal   origin    min_qty_kg disc_pct
##   <fct>    <chr>      <chr>          <dbl>    <dbl>
## 1 3        Pinot Noir Australia        144       83
## 2 3        Pinot Noir France            72       17
## 3 3        Pinot Noir Germany           12       47
## 4 3        Pinot Noir Italy              6       34
## 5 4        Champagne  France            72       63
## 6 4        Champagne  France            72       89

Cluster 5

The fifth segment is a little more difficult to categorise as it encompasses many different attributes. The only clear trend is that customers in this segment picked up all available Cabernet Sauvignon offers.

cluster_trends_tbl %>% 
    filter(.cluster == 5 ) %>% 
    count(.cluster, varietal, origin, min_qty_kg, disc_pct) %>%
    select(-n) 
## # A tibble: 17 x 5
##    .cluster varietal           origin       min_qty_kg disc_pct
##    <fct>    <chr>              <chr>             <dbl>    <dbl>
##  1 5        Cabernet Sauvignon France               12       56
##  2 5        Cabernet Sauvignon Germany              72       45
##  3 5        Cabernet Sauvignon Italy                72       82
##  4 5        Cabernet Sauvignon Italy               144       19
##  5 5        Cabernet Sauvignon New Zealand         144       44
##  6 5        Cabernet Sauvignon Oregon               72       59
##  7 5        Champagne          California           12       50
##  8 5        Champagne          France               72       85
##  9 5        Champagne          Germany              12       66
## 10 5        Chardonnay         Chile               144       57
## 11 5        Chardonnay         South Africa        144       39
## 12 5        Espumante          Oregon              144       32
## 13 5        Malbec             France               72       56
## 14 5        Merlot             California           72       88
## 15 5        Merlot             Chile                72       64
## 16 5        Prosecco           Australia            72       83
## 17 5        Prosecco           California           72       52

Final thoughts

Although it’s not going to give you all the answers, clustering is a powerful exploratory exercise that can help you reveal patterns in your consumer base, especially when you have a brand new market to explore and do not have any prior knowledge of it.

It’s very easy to implement and even on a small dataset like the one I used here, you can unearth interesting patterns of behaviour in your customer base.

With little effort we have leaned that some of our customers favour certain varieties of wine whereas others prefer to buy high or low quantities. Such information can be used to tailor your pricing strategies and marketing campaings towards those customers that are more inclined to respond. Moreover, customer segmentation allows for a more efficient allocation of marketing resources and the maximization of cross- and up-selling opportunities.

Segmentation can also be enriched by overlaying information such as a customers’ demographics (age, race, religion, gender, family size, ethnicity, income, education level), geography (where they live and work), and psychographic (social class, lifestyle and personality characteristics) but these go beyond the scope of this mini-project.

Code Repository

The full R code can be found on my GitHub profile

References