Motivations

Customer Segments (or Market Segmentation) allow the companies to be able to utilize their resources (time, finance) to serve their’s goals: increasing sales, increasing profits, retaining important customers as well as implementing marketing campaigns more effectively, which based on the understanding of their customer’s behavior, habits, and preferences.

Method and Data

RFM is a method used for analyzing customer value. It is commonly used in database marketing and direct marketing and has received particular attention in retail and professional services industries.

RFM stands for the three dimensions: - R (Recency) The value of how recently a customer purchased at the establishment. - F (Frequency) How frequent the customer’s transactions are at the establishment. - M (Monetary) The dollar (or pounds in our case) value of all the transactions that the customer made at the establishment.

F and M are inputs for a period (1 year, a month, a period). Particularly R depends on the modeler preference and it does not affect the model’s results.

Data can be download here. First, let’s have a look at the data:

# Load data: 
rm(list = ls())
library(tidyverse)
library(magrittr)
library(knitr)
my_df <- read_csv("/Users/jennynguyen/Downloads/data.csv")

# See the first 10 transaction with the first 4 columns
set.seed(29)
my_df %>% 
  sample_n(10) %>% 
  select(1:4) %>% 
  kable()

InvoiceNo	StockCode	Description	Quantity
561197	22120	WELCOME WOODEN BLOCK LETTERS	4
542174	21326	AGED GLASS SILVER T-LIGHT HOLDER	36
553009	23191	BUNDLE OF 3 RETRO NOTE BOOKS	2
576837	84661B	BLACK SQUARE TABLE CLOCK	1
539836	85232D	SET/3 DECOUPAGE STACKING TINS	1
556187	47590A	BLUE HAPPY BIRTHDAY BUNTING	3
578664	23267	SET OF 4 SANTA PLACE SETTINGS	2
577358	21240	BLUE POLKADOT CUP	1
575324	23130	MISTLETOE HEART WREATH GREEN	4
554512	21390	FILIGRIS HEART WITH BUTTERFLY	1

# See the first 10 transaction with the last 4 columns
my_df %>% 
  sample_n(10) %>% 
  select(5:8) %>% 
  kable()

InvoiceDate	UnitPrice	CustomerID	Country
9/20/2011 11:32	1.85	13767	United Kingdom
3/28/2011 11:34	1.25	17841	United Kingdom
10/12/2011 12:54	2.55	12691	France
6/23/2011 11:38	0.42	13268	United Kingdom
12/15/2010 15:50	8.50	17980	United Kingdom
5/27/2011 12:41	8.50	16275	United Kingdom
12/7/2011 14:01	1.65	16426	United Kingdom
8/1/2011 11:23	2.10	14408	United Kingdom
6/23/2011 18:44	1.25	15023	United Kingdom
7/7/2011 16:30	4.13	NA	United Kingdom

The variables are really descriptive. We should also make a preliminary assessment of the quality of the data. First of all, let have a look at the missing rate:

na_rate <- function(x) {100*sum(is.na(x)) / length(x)}

my_df %>%
  summarise_all(na_rate)

## # A tibble: 1 x 8
##   InvoiceNo StockCode Description Quantity InvoiceDate UnitPrice CustomerID
##       <dbl>     <dbl>       <dbl>    <dbl>       <dbl>     <dbl>      <dbl>
## 1         0         0       0.268        0           0         0       24.9
## # … with 1 more variable: Country <dbl>

Approximately 27% of stockcode is without description. Similarly, ~ 25% customters are not labled with IDs, but it’s not quite important in this situation.

The measures in this data set - if they are quantitative variables, must be non-negative. So we also need to check whether we have any negative record or not.

negative_dectect <- function(x) {100*sum(x <= 0) / length(x)}


sapply(my_df %>% select(Quantity, UnitPrice), negative_dectect)

##  Quantity UnitPrice 
## 1.9604768 0.4644691

# Remove negative records
my_df %>% 
  filter(Quantity > 0, UnitPrice > 0) -> my_df

Because we need an exact time to calculate R so that InvoiceDate will need to be modifed.

library(lubridate)

my_df %>% 
  mutate(time_ymd_hm = mdy_hm(InvoiceDate), 
         time_hour = hour(time_ymd_hm), 
         time_min = minute(time_ymd_hm), 
         w_day = wday(time_ymd_hm, label = TRUE, abbr = TRUE), 
         time_mon = month(time_ymd_hm, label = TRUE, abbr = TRUE), 
         time_ymd = InvoiceDate %>% str_split(" ", simplify = TRUE) %>% data.frame() %>% pull(X1) %>% mdy) -> my_df

Exploratory Data Analysis

This analysis is taken to look for some insights. For example, sales (accurate to the minute) have two spike times over 70,000 records. These are unusual:

library(hrbrthemes)
theme_set(theme_modern_rc())

my_df %>% 
  group_by(time_ymd_hm) %>% 
  summarise(sales = sum(Quantity)) %>% 
  ungroup() -> sales_byTime_hm

sales_byTime_hm %>% 
  ggplot(aes(time_ymd_hm, sales)) + 
  geom_line() + 
  labs(title = "Figure 1: Unit Sales by Min", x = "Time", y = "Quantity")

Sales by day tended to increase in the last stage. On the other hand, there are two days of abnormal sales (which is predictable):

my_df %>% 
  group_by(time_ymd) %>% 
  summarise(sales = sum(Quantity)) %>% 
  ungroup() -> sales_byTime

sales_byTime %>% 
  ggplot(aes(time_ymd, sales)) + 
  geom_line() + 
  geom_point(color = "firebrick") + 
  labs(title = "Figure 2: Unit Sales by Day", x = "Time", y = "Quantity")

From Figure 2 we also see that there is another anomaly: there are two times where the data is not continuous. Specifically, from 2010-12-22 to 2011-01-03, there are 12 consecutive days of data missing.

sales_byTime %>% 
  mutate(lag1 = lag(time_ymd, n = 1L)) %>% 
  mutate(duration_date = time_ymd - lag1) %>% 
  mutate(duration_date = as.numeric(duration_date)) %>% 
  slice(which.max(duration_date))

## # A tibble: 1 x 4
##   time_ymd   sales lag1       duration_date
##   <date>     <dbl> <date>             <dbl>
## 1 2011-01-04  8639 2010-12-23            12

my_df %>% 
  mutate(money = Quantity*UnitPrice) -> my_df

my_df %>% 
  group_by(time_ymd_hm) %>% 
  summarise(moneySales = sum(money)) %>% 
  ungroup() -> sales_byTime_hm_money

sales_byTime_hm_money %>% 
  ggplot(aes(time_ymd_hm, moneySales)) + 
  geom_line() + 
  labs(title = "Figure 3: Monetary Sales by Min", x = "Time", y = "")

my_df %>% 
  group_by(time_ymd) %>% 
  summarise(moneySales = sum(money)) %>% 
  ungroup() -> sales_byTime_money

sales_byTime_money %>% 
  ggplot(aes(time_ymd, moneySales)) + 
  geom_line() + 
  geom_point(color = "firebrick") + 
  labs(title = "Figure 4: Monetary Sales by Day", x = "Time", y = "")

Doanh thu cả theo số lượng bán và tiền ở 4 tháng cuối năm cao hơn hẳn các tháng còn lại trong năm:

my_df %>% 
  group_by(time_mon) %>% 
  summarise_each(funs(sum), Quantity) %>% 
  mutate(Quantity = Quantity / 1000) %>% 
  ggplot(aes(time_mon, Quantity)) + 
  geom_col() + 
  theme(panel.grid.major.x = element_blank()) + 
  labs(title = "Figure 5: Unit Sales in thousands by Month", x = "Time", y = "Quanlity") + 
  scale_y_continuous(limits = c(0, 800))

my_df %>% 
  group_by(time_mon) %>% 
  summarise_each(funs(sum), money) %>% 
  mutate(money = money / 1000) %>% 
  ggplot(aes(time_mon, money)) + 
  geom_col() + 
  theme(panel.grid.major.x = element_blank()) + 
  labs(title = "Figure 6: Monetary Sales in thousands by Month", x = "Time", y = "")

More than 4000 items are being sold, but the revenue distribution is not even:

my_df %>% 
  group_by(Description) %>% 
  summarise(sales = sum(money)) %>% 
  ungroup() %>% 
  arrange(-sales) %>% 
  mutate(Description = factor(Description, levels = Description)) %>% 
  mutate(total = sum(sales)) %>% 
  mutate(money_percent = sales / total) %>% 
  mutate(cum_money = cumsum(money_percent)) -> moneySales_Item

moneySales_Item %>% 
  ggplot(aes(Description, sales)) + 
  geom_col() + 
  theme(panel.grid.major.x = element_blank()) + 
  theme(axis.text.x = element_blank()) + 
  labs(title = "Figure 6: Money Sales by Product", x = "", y = "")

Once again we can see the presence of principle 80 - 20: 80% of the sales of this online retailer comes from 827 product codes (corresponding to 20.59% of product codes):

moneySales_Item %>% 
  filter(cum_money <= 0.8) -> top80_sales

top80_sales %>% nrow() / nrow(moneySales_Item)

## [1] 0.2059776

Products which bring the most revenue:

moneySales_Item %>% 
  select(-total) %>% 
  head() %>% 
  kable()

Description	sales	money_percent	cum_money
DOTCOM POSTAGE	206248.77	0.0193358	0.0193358
REGENCY CAKESTAND 3 TIER	174484.74	0.0163579	0.0356937
PAPER CRAFT , LITTLE BIRDIE	168469.60	0.0157940	0.0514877
WHITE HANGING HEART T-LIGHT HOLDER	106292.77	0.0099649	0.0614526
PARTY BUNTING	99504.33	0.0093285	0.0707812
JUMBO BAG RED RETROSPOT	94340.05	0.0088444	0.0796255

The company may use this information for its business purposes. For example, the company may prioritize shipping for orders listed above or prioritize preparing inventory for these codes. In other words, it is necessary to focus on logistics (logistics - warehousing - transportation) for the brands that bring up to 80% of the revenue for the company.

Customer Segments

Apply the K-means Clustering for Customer Segmentation with RFM method:

y <- as.duration(ymd_hm("2011-12-31 24:59") - my_df$time_ymd_hm) %>% as.numeric()
y <- round(y / (3600*24), 0)

# Create Recency: 
my_df %>% mutate(recency = y) -> my_df

# Purchase ammount for individual customers: 
my_df %>% 
  group_by(CustomerID) %>% 
  summarise_each(funs(sum), money) %>% 
  ungroup() -> df_money

# R: 
my_df %>% 
  group_by(CustomerID) %>% 
  summarise_each(funs(min), recency) %>% 
  ungroup() -> df_recency

# F: 
my_df %>% 
  group_by(CustomerID) %>% 
  count() %>% 
  ungroup() %>% 
  rename(freq = n) -> df_freq

# Data for EDA:  

df_money %>% 
  full_join(df_recency, by = "CustomerID") %>% 
  full_join(df_freq, by = "CustomerID") %>% 
  mutate(CustomerID = as.character(CustomerID)) -> final_df

 
final_df %>% 
  head() %>% 
  kable()

CustomerID	money	recency	freq
12346	77183.60	348	1
12347	4310.00	24	182
12348	1797.24	97	31
12349	1757.55	41	73
12350	334.40	332	17
12352	2506.04	58	85

# Scaling dataset: 
final_df %>% 
  mutate_if(is.numeric, function(x) {(x - min(x)) / (max(x) - min(x))}) %>% 
  select(-CustomerID) -> final_df_scaled

Optimal K will be chosen following this method: Elbow Method:

set.seed(29)
wss <- sapply(1:10, 
              function(k){kmeans(final_df_scaled %>% sample_frac(0.2), 
                                 k, nstart = 30)$tot.withinss})


u <- data.frame(k = 1:10, WSS = wss)

u %>% 
  ggplot(aes(k, WSS)) + 
  geom_line() + 
  geom_point() + 
  geom_point(data = u %>% filter(k == 3), color = "red", size = 3) + 
  scale_x_continuous(breaks = seq(1, 10, by = 1)) + 
  labs(title = "Figure 7: The Optimal Number of Clusters, Elbow Method", x = "Number of Clusters (K)") + 
  theme(panel.grid.minor = element_blank())

# Cluster with K = 3 
set.seed(123)
km.res <- kmeans(final_df_scaled, 3, nstart = 30)

final_df %>% 
  mutate(Group = km.res$cluster) %>% 
  mutate(Group = paste("Group", Group)) -> final_df_clustered


# Groups of customer: 
final_df_clustered %>% 
  group_by(Group) %>% 
  summarise_each(funs(mean), money, recency, freq) %>% 
  ungroup() %>% 
  mutate_if(is.numeric, function(x) {round(x, 0)}) %>% 
  arrange(-money)

## # A tibble: 3 x 4
##   Group   money recency  freq
##   <chr>   <dbl>   <dbl> <dbl>
## 1 Group 2  3308      54   165
## 2 Group 1   799     176    41
## 3 Group 3   607     316    24

Based on the results of the K-Means Clustering, customers will be classified into the following 3 groups:

Group 2 Group has those customers who spend a lot, make the purchase very often, and have the smallest Recency. This group is called * Champions *. The way of “taking care” of these customers is well described [here] (https://www.putler.com/rfm-analysis/). On average, each customer in this group spends £ 3308.
Group 1 This is Loyal Customers. This is a group of customers with the potential to turn into Champions if the company knows how to implement customer care and promotion strategies appropriately.
Group 3 Less purchase, and bring less money to the company.

Before we can use the above Insights to cater to the business strategies, we should consider these following points: the K-means clustering algorithm is very sensitive to outliers. Although the data has been scaled to minimize the impact of these outliers, it does not guarantee that the results will not be deformed.

final_df %>% 
  ggplot(aes(CustomerID, money)) + 
  geom_col() + 
  theme(panel.grid.minor.x = element_blank()) + 
  theme(panel.grid.major.x = element_blank()) + 
  theme(panel.grid.minor.y = element_blank()) + 
  theme(axis.text.x = element_blank()) + 
  labs(title = "Figure 8: Spending by Customer", y = "")

Figure 8 shows some customers with massive spending. They may not be individual customers but maybe the form of a small store to buy and resell. Similarly, the buying frequency (Figure 9, the unit on the Y-axis is 1000):

final_df %>% 
  mutate(freq = freq / 1000) %>% 
  ggplot(aes(CustomerID, freq)) + 
  geom_col() + 
  theme(panel.grid.minor.x = element_blank()) + 
  theme(panel.grid.major.x = element_blank()) + 
  theme(panel.grid.minor.y = element_blank()) + 
  theme(axis.text.x = element_blank()) + 
  labs(title = "Figure 9: Frequency by Customer", y = "")

Because the K-Means Clustering is very sensitive to outliers, so we should split these outliers for separate analysis while focusing on those common customers.

# Identify Outlier: 
outlier_label <- function(x) {
  a <- mean(x)
  b <- sd(x)
  th1 <- a - 3*b
  th2 <- a + 3*b
  y <- case_when(x >= th1 & x <= th2 ~ "Normal", TRUE ~ "Outlier")
  return(y)
  
}

# Only apply Normal Observation for K-means Clustering: 

final_df %>% 
  mutate(nor_money = outlier_label(money), nor_freq = outlier_label(freq)) %>% 
  filter(nor_money == "Normal", nor_freq == "Normal") %>% 
  select(1:4) -> final_df_normal

final_df_normal %>% 
  mutate_if(is.numeric, function(x) {(x - min(x)) / (max(x) - min(x))}) -> final_df_normal_scaled

Re-apply K means clustering - Find the optimal K:

set.seed(29)
wss <- sapply(1:10, 
              function(k){kmeans(final_df_normal_scaled %>% select(-CustomerID) %>% sample_frac(0.2), 
                                 k, nstart = 30)$tot.withinss})


u <- data.frame(k = 1:10, WSS = wss)

u %>% 
  ggplot(aes(k, WSS)) + 
  geom_line() + 
  geom_point() + 
  geom_point(data = u %>% filter(k == 4), color = "red", size = 3) + 
  scale_x_continuous(breaks = seq(1, 10, by = 1)) + 
  labs(title = "Figure 10: The Optimal Number of Clusters, Elbow Method", 
       subtitle = "Outliers are are removed from sample.", 
       x = "Number of Clusters (K)") + 
  theme(panel.grid.minor = element_blank())

After removing outliers, optimal K is 4.

# Grouping with k = 4: 
set.seed(123)
km.res4 <- kmeans(final_df_normal_scaled %>% select(-CustomerID), 4, nstart = 30)


final_df_normal %>% 
  mutate(Group = km.res4$cluster) %>% 
  mutate(Group = paste("Group", Group)) -> final_df_clustered

#  Groups of customers description: 
final_df_clustered %>% 
  group_by(Group) %>% 
  summarise_each(funs(mean), money, recency, freq) %>% 
  ungroup() %>% 
  mutate_if(is.numeric, function(x) {round(x, 0)}) %>% 
  arrange(-money) %>% 
  kable()

Group	money	recency	freq
Group 4	2668	41	136
Group 2	999	103	51
Group 3	726	214	35
Group 1	566	331	24

Calculate the proportion of revenue from these customer groups:

final_df_clustered %>% 
  group_by(Group) %>% 
  summarise_each(funs(sum, mean, median, min, max, sd, n()), money) %>% 
  ungroup() %>% 
  mutate(per_sale = round(100*sum / sum(sum), 2)) -> sale_group


library(ggthemes)

sale_group %>% 
  ggplot(aes(reorder(Group, per_sale), per_sale, fill = Group, color = Group)) + 
  geom_col(width = 0.5, show.legend = FALSE) + 
  coord_flip() + 
  geom_text(aes(label = paste(per_sale, paste0(paste0("(", "%")), ")")), 
            hjust = -0.05, color = "white", size = 5) + 
  scale_y_continuous(limits = c(0, 90), expand = c(0.01, 0)) + 
  scale_fill_tableau() + 
  scale_color_tableau() + 
  theme(axis.title.x = element_blank(),
        axis.text.x = element_blank(),
        axis.ticks.x = element_blank()) + 
  theme(panel.grid.major = element_blank()) + 
  theme(panel.grid.minor = element_blank()) + 
  labs(x = NULL, title = "Figure 11: Share of Sales by Customer Group")

Group 4 accounts for 49.1% of total customers and is the group that brings nearly 75% of revenue to the company:

sale_group %>% 
  select(Group, n) %>% 
  mutate(total = sum(n)) %>% 
  mutate(label = 100*n / total) %>% 
  mutate(label = paste(round(label, 1), "%")) %>% 
  ggplot(aes(Group, n, fill = Group, color = Group)) + 
  geom_col(width = 0.5, show.legend = FALSE) + 
  geom_text(aes(label = label), color = "white", vjust = 1.4, size = 5) + 
  scale_fill_tableau() + 
  scale_color_tableau() + 
  theme(panel.grid.minor = element_blank()) + 
  theme(panel.grid.major.x = element_blank()) + 
  labs(x = NULL, y = NULL, title = "Figure 12: Number of Customers by Group")

Group Labelling

To answer the question a consumer whose behavior is described by R, F and M, which group will this customer be?. Many approaches/models can be applied to this problem and one of them is to use classification algorithms, for example, Random Forest:

# Data for ML:  
df_forML <- final_df_clustered %>% 
  select(- CustomerID) %>% 
  mutate(Group = as.factor(Group))

# Split data into training, testing:

library(caret)
set.seed(1)
id <- createDataPartition(df_forML$Group, p = 0.8, list = FALSE)
df_train <- df_forML[id, ]
df_test <- df_forML[-id, ]

# Train Random Forest: 
set.seed(1)
my_rf <- train(Group ~., method = "rf", data = df_train)

## note: only 2 unique complexity parameters in default grid. Truncating the grid to 2 .

As the business getting imput for a new customer with M = 1757.55, R = 41, F = 73, which segmentation that customer will be:

cus1 <- df_test %>% 
  slice(1) %>% 
  select(-Group)

cus1 %>% 
  kable()

money	recency	freq
1757.55	41	73

That customer will be in group 4:

predict(my_rf, cus1) %>% as.character()

## [1] "Group 4"

Model evaluation:

pred <- predict(my_rf, df_test)


confusionMatrix(pred, df_test$Group)

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction Group 1 Group 2 Group 3 Group 4
##    Group 1      99       0       0       0
##    Group 2       0     217       0       1
##    Group 3       0       0     123       0
##    Group 4       0       0       0     424
## 
## Overall Statistics
##                                      
##                Accuracy : 0.9988     
##                  95% CI : (0.9936, 1)
##     No Information Rate : 0.4919     
##     P-Value [Acc > NIR] : < 2.2e-16  
##                                      
##                   Kappa : 0.9983     
##                                      
##  Mcnemar's Test P-Value : NA         
## 
## Statistics by Class:
## 
##                      Class: Group 1 Class: Group 2 Class: Group 3
## Sensitivity                  1.0000         1.0000         1.0000
## Specificity                  1.0000         0.9985         1.0000
## Pos Pred Value               1.0000         0.9954         1.0000
## Neg Pred Value               1.0000         1.0000         1.0000
## Prevalence                   0.1146         0.2512         0.1424
## Detection Rate               0.1146         0.2512         0.1424
## Detection Prevalence         0.1146         0.2523         0.1424
## Balanced Accuracy            1.0000         0.9992         1.0000
##                      Class: Group 4
## Sensitivity                  0.9976
## Specificity                  1.0000
## Pos Pred Value               1.0000
## Neg Pred Value               0.9977
## Prevalence                   0.4919
## Detection Rate               0.4907
## Detection Prevalence         0.4907
## Balanced Accuracy            0.9988

# Statistical description for the prediction on test data: 
df_test %>% 
  mutate(GroupPredicted = pred) %>% 
  group_by(GroupPredicted) %>% 
  summarise_each(funs(mean), money, recency, freq) %>% 
  mutate_if(is.numeric, function(x) {round(x, 0)}) %>% 
  kable()

GroupPredicted	money	recency	freq
Group 1	453	330	22
Group 2	1018	103	53
Group 3	505	217	29
Group 4	2753	42	147

# Statistical description for the prediction on train data compared to test data: 
df_train %>% 
  group_by(Group) %>% 
  summarise_each(funs(mean), money, recency, freq) %>% 
  mutate_if(is.numeric, function(x) {round(x, 0)}) %>% 
  kable()

Group	money	recency	freq
Group 1	594	331	24
Group 2	995	103	51
Group 3	782	213	36
Group 4	2647	41	133

References

Chapman, C., & Feit, E. M. (2019). R for marketing research and analytics. New York, NY: Springer.
Chen, D., Sain, S. L., & Guo, K. (2012). Data mining for the online retail industry: A case study of RFM model-based customer segmentation using data mining. Journal of Database Marketing & Customer Strategy Management, 19(3), 197-208.
Khajvand, M., & Tarokh, M. J. (2011). Estimating customer future value of different customer segments based on adapted RFM model in retail banking context. Procedia Computer Science, 3, 1327-1332.
Shmueli, G., Bruce, P. C., Yahav, I., Patel, N. R., & Lichtendahl Jr, K. C. (2017). Data mining for business analytics: concepts, techniques, and applications in R. John Wiley & Sons.
Zakrzewska, D., & Murlewski, J. (2005, September). Clustering algorithms for bank customer segmentation. In 5th International Conference on Intelligent Systems Design and Applications (ISDA’05) (pp. 197-202). IEEE.

---
title: "Market Segmentation: K-means Clustering Algorithm" 
subtitle: "Data Science for Marketing Series"
author: "Jenny"
output:
  html_document: 
    code_download: true
    #code_folding: hide
    highlight: zenburn
    # number_sections: yes
    theme: "flatly"
    toc: TRUE
    toc_float: TRUE
---

```{r setup,include=FALSE}
knitr::opts_chunk$set(echo = TRUE, warning = FALSE, message = FALSE, fig.width = 10, fig.height = 6)
```


# Motivations

Customer Segments (or Market Segmentation) allow the companies to be able to utilize their resources (time, finance) to serve their's goals: increasing sales, increasing profits, retaining important customers as well as implementing marketing campaigns more effectively, which  based on the understanding of their customer's behavior, habits, and preferences.


# Method and Data 

RFM is a method used for analyzing customer value. It is commonly used in database marketing and direct marketing and has received particular attention in retail and professional services industries.

RFM stands for the three dimensions: \n
- **R (Recency)** The value of how recently a customer purchased at the establishment.
- **F (Frequency)** How frequent the customer’s transactions are at the establishment.
- **M (Monetary)** The dollar (or pounds in our case) value of all the transactions that the customer made at the establishment.

F and M are inputs for a period (1 year, a month, a period). Particularly R depends on the modeler preference and it does not affect the model's results.

Data can be download [here](https://www.kaggle.com/carrie1/ecommerce-data). First, let's have a look at the data:

```{r}
# Load data: 
rm(list = ls())
library(tidyverse)
library(magrittr)
library(knitr)
my_df <- read_csv("/Users/jennynguyen/Downloads/data.csv")

# See the first 10 transaction with the first 4 columns
set.seed(29)
my_df %>% 
  sample_n(10) %>% 
  select(1:4) %>% 
  kable()

# See the first 10 transaction with the last 4 columns
my_df %>% 
  sample_n(10) %>% 
  select(5:8) %>% 
  kable()
```

The variables are really descriptive.  We should also make a preliminary assessment of the quality of the data. First of all, let have a look at the missing rate:

```{r}

na_rate <- function(x) {100*sum(is.na(x)) / length(x)}

my_df %>%
  summarise_all(na_rate)
```

Approximately 27% of stockcode is without description. Similarly, ~ 25% customters are not labled with IDs, but it's not quite important in this situation.

The measures in this data set - if they are quantitative variables, must be non-negative. So we also need to check whether we have any negative record or not. 


```{r}

negative_dectect <- function(x) {100*sum(x <= 0) / length(x)}


sapply(my_df %>% select(Quantity, UnitPrice), negative_dectect)

# Remove negative records
my_df %>% 
  filter(Quantity > 0, UnitPrice > 0) -> my_df
```


Because we need an exact time to calculate R so that InvoiceDate will need to be modifed.

```{r}
library(lubridate)

my_df %>% 
  mutate(time_ymd_hm = mdy_hm(InvoiceDate), 
         time_hour = hour(time_ymd_hm), 
         time_min = minute(time_ymd_hm), 
         w_day = wday(time_ymd_hm, label = TRUE, abbr = TRUE), 
         time_mon = month(time_ymd_hm, label = TRUE, abbr = TRUE), 
         time_ymd = InvoiceDate %>% str_split(" ", simplify = TRUE) %>% data.frame() %>% pull(X1) %>% mdy) -> my_df
```

# Exploratory Data Analysis

This analysis is taken to look for some insights. For example, sales (accurate to the minute) have two spike times over 70,000 records. These are unusual:


```{r}
library(hrbrthemes)
theme_set(theme_modern_rc())

my_df %>% 
  group_by(time_ymd_hm) %>% 
  summarise(sales = sum(Quantity)) %>% 
  ungroup() -> sales_byTime_hm

sales_byTime_hm %>% 
  ggplot(aes(time_ymd_hm, sales)) + 
  geom_line() + 
  labs(title = "Figure 1: Unit Sales by Min", x = "Time", y = "Quantity")
  
```

Sales by day tended to increase in the last stage. On the other hand, there are two days of abnormal sales (which is predictable):

```{r}
my_df %>% 
  group_by(time_ymd) %>% 
  summarise(sales = sum(Quantity)) %>% 
  ungroup() -> sales_byTime

sales_byTime %>% 
  ggplot(aes(time_ymd, sales)) + 
  geom_line() + 
  geom_point(color = "firebrick") + 
  labs(title = "Figure 2: Unit Sales by Day", x = "Time", y = "Quantity")

```

From Figure 2 we also see that there is another anomaly: there are two times where the data is not continuous. Specifically, from 2010-12-22 to 2011-01-03, there are 12 consecutive days of data missing.


```{r}
sales_byTime %>% 
  mutate(lag1 = lag(time_ymd, n = 1L)) %>% 
  mutate(duration_date = time_ymd - lag1) %>% 
  mutate(duration_date = as.numeric(duration_date)) %>% 
  slice(which.max(duration_date)) 

```



```{r}
my_df %>% 
  mutate(money = Quantity*UnitPrice) -> my_df

my_df %>% 
  group_by(time_ymd_hm) %>% 
  summarise(moneySales = sum(money)) %>% 
  ungroup() -> sales_byTime_hm_money

sales_byTime_hm_money %>% 
  ggplot(aes(time_ymd_hm, moneySales)) + 
  geom_line() + 
  labs(title = "Figure 3: Monetary Sales by Min", x = "Time", y = "")

my_df %>% 
  group_by(time_ymd) %>% 
  summarise(moneySales = sum(money)) %>% 
  ungroup() -> sales_byTime_money

sales_byTime_money %>% 
  ggplot(aes(time_ymd, moneySales)) + 
  geom_line() + 
  geom_point(color = "firebrick") + 
  labs(title = "Figure 4: Monetary Sales by Day", x = "Time", y = "")
  
```

Doanh thu cả theo số lượng bán và tiền ở 4 tháng cuối năm cao hơn hẳn các tháng còn lại trong năm: 


```{r}
my_df %>% 
  group_by(time_mon) %>% 
  summarise_each(funs(sum), Quantity) %>% 
  mutate(Quantity = Quantity / 1000) %>% 
  ggplot(aes(time_mon, Quantity)) + 
  geom_col() + 
  theme(panel.grid.major.x = element_blank()) + 
  labs(title = "Figure 5: Unit Sales in thousands by Month", x = "Time", y = "Quanlity") + 
  scale_y_continuous(limits = c(0, 800))

my_df %>% 
  group_by(time_mon) %>% 
  summarise_each(funs(sum), money) %>% 
  mutate(money = money / 1000) %>% 
  ggplot(aes(time_mon, money)) + 
  geom_col() + 
  theme(panel.grid.major.x = element_blank()) + 
  labs(title = "Figure 6: Monetary Sales in thousands by Month", x = "Time", y = "")
  
```

More than 4000 items are being sold, but the revenue distribution is not even:

```{r}
my_df %>% 
  group_by(Description) %>% 
  summarise(sales = sum(money)) %>% 
  ungroup() %>% 
  arrange(-sales) %>% 
  mutate(Description = factor(Description, levels = Description)) %>% 
  mutate(total = sum(sales)) %>% 
  mutate(money_percent = sales / total) %>% 
  mutate(cum_money = cumsum(money_percent)) -> moneySales_Item

moneySales_Item %>% 
  ggplot(aes(Description, sales)) + 
  geom_col() + 
  theme(panel.grid.major.x = element_blank()) + 
  theme(axis.text.x = element_blank()) + 
  labs(title = "Figure 6: Money Sales by Product", x = "", y = "")
  
```

Once again we can see the presence of **principle 80 - 20**: 80% of the sales of this online retailer comes from 827 product codes (corresponding to 20.59% of product codes):

```{r}
moneySales_Item %>% 
  filter(cum_money <= 0.8) -> top80_sales

top80_sales %>% nrow() / nrow(moneySales_Item)
```

Products which bring the most revenue:

```{r}
moneySales_Item %>% 
  select(-total) %>% 
  head() %>% 
  kable()
```

The company may use this information for its business purposes. For example, the company may prioritize shipping for orders listed above or prioritize preparing inventory for these codes. In other words, it is necessary to focus on logistics (logistics - warehousing - transportation) for the brands that bring up to 80% of the revenue for the company.

# Customer Segments

Apply the K-means Clustering for Customer Segmentation with RFM method: 

```{r}

y <- as.duration(ymd_hm("2011-12-31 24:59") - my_df$time_ymd_hm) %>% as.numeric()
y <- round(y / (3600*24), 0)

# Create Recency: 
my_df %>% mutate(recency = y) -> my_df

# Purchase ammount for individual customers: 
my_df %>% 
  group_by(CustomerID) %>% 
  summarise_each(funs(sum), money) %>% 
  ungroup() -> df_money

# R: 
my_df %>% 
  group_by(CustomerID) %>% 
  summarise_each(funs(min), recency) %>% 
  ungroup() -> df_recency

# F: 
my_df %>% 
  group_by(CustomerID) %>% 
  count() %>% 
  ungroup() %>% 
  rename(freq = n) -> df_freq

# Data for EDA:  

df_money %>% 
  full_join(df_recency, by = "CustomerID") %>% 
  full_join(df_freq, by = "CustomerID") %>% 
  mutate(CustomerID = as.character(CustomerID)) -> final_df

 
final_df %>% 
  head() %>% 
  kable()

```



```{r}
# Scaling dataset: 
final_df %>% 
  mutate_if(is.numeric, function(x) {(x - min(x)) / (max(x) - min(x))}) %>% 
  select(-CustomerID) -> final_df_scaled
```


Optimal K will be chosen following this method: [Elbow Method](https://bl.ocks.org/rpgove/0060ff3b656618e9136b): 

```{r}
set.seed(29)
wss <- sapply(1:10, 
              function(k){kmeans(final_df_scaled %>% sample_frac(0.2), 
                                 k, nstart = 30)$tot.withinss})


u <- data.frame(k = 1:10, WSS = wss)

u %>% 
  ggplot(aes(k, WSS)) + 
  geom_line() + 
  geom_point() + 
  geom_point(data = u %>% filter(k == 3), color = "red", size = 3) + 
  scale_x_continuous(breaks = seq(1, 10, by = 1)) + 
  labs(title = "Figure 7: The Optimal Number of Clusters, Elbow Method", x = "Number of Clusters (K)") + 
  theme(panel.grid.minor = element_blank())
```



```{r}
# Cluster with K = 3 
set.seed(123)
km.res <- kmeans(final_df_scaled, 3, nstart = 30)

final_df %>% 
  mutate(Group = km.res$cluster) %>% 
  mutate(Group = paste("Group", Group)) -> final_df_clustered


# Groups of customer: 
final_df_clustered %>% 
  group_by(Group) %>% 
  summarise_each(funs(mean), money, recency, freq) %>% 
  ungroup() %>% 
  mutate_if(is.numeric, function(x) {round(x, 0)}) %>% 
  arrange(-money) 

```

Based on the results of the K-Means Clustering, customers will be classified into the following 3 groups: 

- **Group 2** Group has those customers who spend a lot, make the purchase very often, and have the smallest Recency. This group is called * Champions *. The way of "taking care" of these customers is well described [here] (https://www.putler.com/rfm-analysis/). On average, each customer in this group spends £ 3308.

- **Group 1** This is *Loyal Customers*. This is a group of customers with the potential to turn into Champions if the company knows how to implement customer care and promotion strategies appropriately.

- **Group 3** Less purchase, and bring less money to the company.

Before we can use the above Insights to cater to the business strategies, we should consider these following points: the K-means clustering algorithm is very sensitive to outliers. Although the data has been scaled to minimize the impact of these outliers, it does not guarantee that the results will not be deformed.

```{r}
final_df %>% 
  ggplot(aes(CustomerID, money)) + 
  geom_col() + 
  theme(panel.grid.minor.x = element_blank()) + 
  theme(panel.grid.major.x = element_blank()) + 
  theme(panel.grid.minor.y = element_blank()) + 
  theme(axis.text.x = element_blank()) + 
  labs(title = "Figure 8: Spending by Customer", y = "")
```

Figure 8 shows some customers with massive spending. They may not be individual customers but maybe the form of a small store to buy and resell. Similarly, the buying frequency (Figure 9, the unit on the Y-axis is 1000):


```{r}
final_df %>% 
  mutate(freq = freq / 1000) %>% 
  ggplot(aes(CustomerID, freq)) + 
  geom_col() + 
  theme(panel.grid.minor.x = element_blank()) + 
  theme(panel.grid.major.x = element_blank()) + 
  theme(panel.grid.minor.y = element_blank()) + 
  theme(axis.text.x = element_blank()) + 
  labs(title = "Figure 9: Frequency by Customer", y = "")
```


Because the K-Means Clustering is very sensitive to outliers, so we should split these outliers for separate analysis while focusing on those common customers.

```{r}
# Identify Outlier: 
outlier_label <- function(x) {
  a <- mean(x)
  b <- sd(x)
  th1 <- a - 3*b
  th2 <- a + 3*b
  y <- case_when(x >= th1 & x <= th2 ~ "Normal", TRUE ~ "Outlier")
  return(y)
  
}

# Only apply Normal Observation for K-means Clustering: 

final_df %>% 
  mutate(nor_money = outlier_label(money), nor_freq = outlier_label(freq)) %>% 
  filter(nor_money == "Normal", nor_freq == "Normal") %>% 
  select(1:4) -> final_df_normal

final_df_normal %>% 
  mutate_if(is.numeric, function(x) {(x - min(x)) / (max(x) - min(x))}) -> final_df_normal_scaled

```

Re-apply K means clustering - Find the optimal K: 


```{r}
set.seed(29)
wss <- sapply(1:10, 
              function(k){kmeans(final_df_normal_scaled %>% select(-CustomerID) %>% sample_frac(0.2), 
                                 k, nstart = 30)$tot.withinss})


u <- data.frame(k = 1:10, WSS = wss)

u %>% 
  ggplot(aes(k, WSS)) + 
  geom_line() + 
  geom_point() + 
  geom_point(data = u %>% filter(k == 4), color = "red", size = 3) + 
  scale_x_continuous(breaks = seq(1, 10, by = 1)) + 
  labs(title = "Figure 10: The Optimal Number of Clusters, Elbow Method", 
       subtitle = "Outliers are are removed from sample.", 
       x = "Number of Clusters (K)") + 
  theme(panel.grid.minor = element_blank())
```


After removing outliers, optimal K is 4.

```{r}
# Grouping with k = 4: 
set.seed(123)
km.res4 <- kmeans(final_df_normal_scaled %>% select(-CustomerID), 4, nstart = 30)


final_df_normal %>% 
  mutate(Group = km.res4$cluster) %>% 
  mutate(Group = paste("Group", Group)) -> final_df_clustered

```



```{r}
#  Groups of customers description: 
final_df_clustered %>% 
  group_by(Group) %>% 
  summarise_each(funs(mean), money, recency, freq) %>% 
  ungroup() %>% 
  mutate_if(is.numeric, function(x) {round(x, 0)}) %>% 
  arrange(-money) %>% 
  kable()
```

Calculate the proportion of revenue from these customer groups:

```{r}
final_df_clustered %>% 
  group_by(Group) %>% 
  summarise_each(funs(sum, mean, median, min, max, sd, n()), money) %>% 
  ungroup() %>% 
  mutate(per_sale = round(100*sum / sum(sum), 2)) -> sale_group


library(ggthemes)

sale_group %>% 
  ggplot(aes(reorder(Group, per_sale), per_sale, fill = Group, color = Group)) + 
  geom_col(width = 0.5, show.legend = FALSE) + 
  coord_flip() + 
  geom_text(aes(label = paste(per_sale, paste0(paste0("(", "%")), ")")), 
            hjust = -0.05, color = "white", size = 5) + 
  scale_y_continuous(limits = c(0, 90), expand = c(0.01, 0)) + 
  scale_fill_tableau() + 
  scale_color_tableau() + 
  theme(axis.title.x = element_blank(),
        axis.text.x = element_blank(),
        axis.ticks.x = element_blank()) + 
  theme(panel.grid.major = element_blank()) + 
  theme(panel.grid.minor = element_blank()) + 
  labs(x = NULL, title = "Figure 11: Share of Sales by Customer Group")

```


Group 4 accounts for 49.1% of total customers and is the group that brings nearly 75% of revenue to the company:

```{r}
sale_group %>% 
  select(Group, n) %>% 
  mutate(total = sum(n)) %>% 
  mutate(label = 100*n / total) %>% 
  mutate(label = paste(round(label, 1), "%")) %>% 
  ggplot(aes(Group, n, fill = Group, color = Group)) + 
  geom_col(width = 0.5, show.legend = FALSE) + 
  geom_text(aes(label = label), color = "white", vjust = 1.4, size = 5) + 
  scale_fill_tableau() + 
  scale_color_tableau() + 
  theme(panel.grid.minor = element_blank()) + 
  theme(panel.grid.major.x = element_blank()) + 
  labs(x = NULL, y = NULL, title = "Figure 12: Number of Customers by Group")
  
```


# Group Labelling

To answer the question **a consumer whose behavior is described by R, F and M, which group will this customer be?**.  Many approaches/models can be applied to this problem and one of them is to use classification algorithms, for example, Random Forest:

```{r}
# Data for ML:  
df_forML <- final_df_clustered %>% 
  select(- CustomerID) %>% 
  mutate(Group = as.factor(Group))

# Split data into training, testing:

library(caret)
set.seed(1)
id <- createDataPartition(df_forML$Group, p = 0.8, list = FALSE)
df_train <- df_forML[id, ]
df_test <- df_forML[-id, ]

# Train Random Forest: 
set.seed(1)
my_rf <- train(Group ~., method = "rf", data = df_train)

```

As the business getting imput for a new customer with M = 1757.55, R = 41, F = 73, which segmentation that customer will be:   
```{r}

cus1 <- df_test %>% 
  slice(1) %>% 
  select(-Group)

cus1 %>% 
  kable()

```

That customer will be in group 4: 

```{r}
predict(my_rf, cus1) %>% as.character()
```

Model evaluation: 

```{r}

pred <- predict(my_rf, df_test)


confusionMatrix(pred, df_test$Group)
```


```{r}

# Statistical description for the prediction on test data: 
df_test %>% 
  mutate(GroupPredicted = pred) %>% 
  group_by(GroupPredicted) %>% 
  summarise_each(funs(mean), money, recency, freq) %>% 
  mutate_if(is.numeric, function(x) {round(x, 0)}) %>% 
  kable()

# Statistical description for the prediction on train data compared to test data: 
df_train %>% 
  group_by(Group) %>% 
  summarise_each(funs(mean), money, recency, freq) %>% 
  mutate_if(is.numeric, function(x) {round(x, 0)}) %>% 
  kable()

  
```



# References

1. Chapman, C., & Feit, E. M. (2019). R for marketing research and analytics. New York, NY: Springer.
2. Chen, D., Sain, S. L., & Guo, K. (2012). Data mining for the online retail industry: A case study of RFM model-based customer segmentation using data mining. Journal of Database Marketing & Customer Strategy Management, 19(3), 197-208.
3. Khajvand, M., & Tarokh, M. J. (2011). Estimating customer future value of different customer segments based on adapted RFM model in retail banking context. Procedia Computer Science, 3, 1327-1332.
4. Shmueli, G., Bruce, P. C., Yahav, I., Patel, N. R., & Lichtendahl Jr, K. C. (2017). Data mining for business analytics: concepts, techniques, and applications in R. John Wiley & Sons.
5. Zakrzewska, D., & Murlewski, J. (2005, September). Clustering algorithms for bank customer segmentation. In 5th International Conference on Intelligent Systems Design and Applications (ISDA'05) (pp. 197-202). IEEE.







Market Segmentation: K-means Clustering Algorithm

Data Science for Marketing Series