'
Project: "Clustering Project for customer online retail"
Name: "Hamed Ahmed Hamed Ahmed"
StudentId: "454827"
Problem Statement:
"A Company wants to increase their annual profit by selecting suitable customers
who had better transactions and got good Revenue"
Dataset:
"Online retail is a transnational data set which contains all the transactions
occurring between **01/12/2010 and 09/12/2011** for a UK-based and registered non-store online retail.
The company mainly sells unique all-occasion gifts. Many customers of the company are wholesalers."
'
## [1] " \nProject: \"Clustering Project for customer online retail\"\nName: \"Hamed Ahmed Hamed Ahmed\"\nStudentId: \"454827\"\n\nProblem Statement: \n\"A Company wants to increase their annual profit by selecting suitable customers\n who had better transactions and got good Revenue\"\n\nDataset:\n\"Online retail is a transnational data set which contains all the transactions\n occurring between **01/12/2010 and 09/12/2011** for a UK-based and registered non-store online retail.\n The company mainly sells unique all-occasion gifts. Many customers of the company are wholesalers.\"\n"
'so We are going to analysis the Customers based on below 3 factors:'
## [1] "so We are going to analysis the Customers based on below 3 factors:"
'R (Recency): Number of days since last purchase'
## [1] "R (Recency): Number of days since last purchase"
'F (Frequency): Number of tracsactions'
## [1] "F (Frequency): Number of tracsactions"
'M (Monetary): Total amount of transactions (revenue contributed)'
## [1] "M (Monetary): Total amount of transactions (revenue contributed)"
# changing the language to English
Sys.setlocale("LC_ALL","English")
## Warning in Sys.setlocale("LC_ALL", "English"): using locale code page other than
## 65001 ("UTF-8") may cause problems
## [1] "LC_COLLATE=English_United States.1252;LC_CTYPE=English_United States.1252;LC_MONETARY=English_United States.1252;LC_NUMERIC=C;LC_TIME=English_United States.1252"
Sys.setenv(LANGUAGE='en')
#load packages for data manipulation
library(tidyverse, quietly = TRUE)
## -- Attaching packages --------------------------------------- tidyverse 1.3.2 --
## v ggplot2 3.4.0 v purrr 1.0.1
## v tibble 3.1.8 v dplyr 1.0.10
## v tidyr 1.2.1 v stringr 1.5.0
## v readr 2.1.3 v forcats 1.0.0
## -- Conflicts ------------------------------------------ tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()
library(lubridate)
##
## Attaching package: 'lubridate'
##
## The following objects are masked from 'package:base':
##
## date, intersect, setdiff, union
library(stats)
library(factoextra)
## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa
library(flexclust)
## Loading required package: grid
## Loading required package: lattice
## Loading required package: modeltools
## Loading required package: stats4
library(fpc)
library(clustertend)
## Package `clustertend` is deprecated. Use package `hopkins` instead.
library(cluster)
library(ClusterR)
library("PerformanceAnalytics")
## Loading required package: xts
## Loading required package: zoo
##
## Attaching package: 'zoo'
##
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
##
##
## Attaching package: 'xts'
##
## The following objects are masked from 'package:dplyr':
##
## first, last
##
##
## Attaching package: 'PerformanceAnalytics'
##
## The following object is masked from 'package:graphics':
##
## legend
library(corrplot)
## corrplot 0.92 loaded
library(rmarkdown)
library(scales)
##
## Attaching package: 'scales'
##
## The following object is masked from 'package:purrr':
##
## discard
##
## The following object is masked from 'package:readr':
##
## col_factor
# Load data
myRetailData <- read_csv("OnlineRetail.csv")
## Rows: 541909 Columns: 8
## -- Column specification --------------------------------------------------------
## Delimiter: ","
## chr (5): InvoiceNo, StockCode, Description, InvoiceDate, Country
## dbl (3): Quantity, UnitPrice, CustomerID
##
## i Use `spec()` to retrieve the full column specification for this data.
## i Specify the column types or set `show_col_types = FALSE` to quiet this message.
# Observing Datatypes, Columns and Rows¶
## View the rows
head(myRetailData)
## # A tibble: 6 x 8
## InvoiceNo StockCode Description Quant~1 Invoi~2 UnitP~3 Custo~4 Country
## <chr> <chr> <chr> <dbl> <chr> <dbl> <dbl> <chr>
## 1 536365 85123A WHITE HANGING HEA~ 6 01-12-~ 2.55 17850 United~
## 2 536365 71053 WHITE METAL LANTE~ 6 01-12-~ 3.39 17850 United~
## 3 536365 84406B CREAM CUPID HEART~ 8 01-12-~ 2.75 17850 United~
## 4 536365 84029G KNITTED UNION FLA~ 6 01-12-~ 3.39 17850 United~
## 5 536365 84029E RED WOOLLY HOTTIE~ 6 01-12-~ 3.39 17850 United~
## 6 536365 22752 SET 7 BABUSHKA NE~ 2 01-12-~ 7.65 17850 United~
## # ... with abbreviated variable names 1: Quantity, 2: InvoiceDate,
## # 3: UnitPrice, 4: CustomerID
## Datatypes and columns
str(myRetailData)
## spc_tbl_ [541,909 x 8] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
## $ InvoiceNo : chr [1:541909] "536365" "536365" "536365" "536365" ...
## $ StockCode : chr [1:541909] "85123A" "71053" "84406B" "84029G" ...
## $ Description: chr [1:541909] "WHITE HANGING HEART T-LIGHT HOLDER" "WHITE METAL LANTERN" "CREAM CUPID HEARTS COAT HANGER" "KNITTED UNION FLAG HOT WATER BOTTLE" ...
## $ Quantity : num [1:541909] 6 6 8 6 6 2 6 6 6 32 ...
## $ InvoiceDate: chr [1:541909] "01-12-2010 08:26" "01-12-2010 08:26" "01-12-2010 08:26" "01-12-2010 08:26" ...
## $ UnitPrice : num [1:541909] 2.55 3.39 2.75 3.39 3.39 7.65 4.25 1.85 1.85 1.69 ...
## $ CustomerID : num [1:541909] 17850 17850 17850 17850 17850 ...
## $ Country : chr [1:541909] "United Kingdom" "United Kingdom" "United Kingdom" "United Kingdom" ...
## - attr(*, "spec")=
## .. cols(
## .. InvoiceNo = col_character(),
## .. StockCode = col_character(),
## .. Description = col_character(),
## .. Quantity = col_double(),
## .. InvoiceDate = col_character(),
## .. UnitPrice = col_double(),
## .. CustomerID = col_double(),
## .. Country = col_character()
## .. )
## - attr(*, "problems")=<externalptr>
## Summary for the data
summary(myRetailData)
## InvoiceNo StockCode Description Quantity
## Length:541909 Length:541909 Length:541909 Min. :-80995.00
## Class :character Class :character Class :character 1st Qu.: 1.00
## Mode :character Mode :character Mode :character Median : 3.00
## Mean : 9.55
## 3rd Qu.: 10.00
## Max. : 80995.00
##
## InvoiceDate UnitPrice CustomerID Country
## Length:541909 Min. :-11062.06 Min. :12346 Length:541909
## Class :character 1st Qu.: 1.25 1st Qu.:13953 Class :character
## Mode :character Median : 2.08 Median :15152 Mode :character
## Mean : 4.61 Mean :15288
## 3rd Qu.: 4.13 3rd Qu.:16791
## Max. : 38970.00 Max. :18287
## NA's :135080
## Dataset dimension
dim(myRetailData)
## [1] 541909 8
# Data Cleaning and Preparing
# As we can see we have 135080 in CustomerId and 1454 in Description missing values
colSums((is.na(myRetailData)))
## InvoiceNo StockCode Description Quantity InvoiceDate UnitPrice
## 0 0 1454 0 0 0
## CustomerID Country
## 135080 0
# Start remove these missing values
myRetailDataCleaned <- na.omit(myRetailData)
# Now check again
colSums((is.na(myRetailDataCleaned)))
## InvoiceNo StockCode Description Quantity InvoiceDate UnitPrice
## 0 0 0 0 0 0
## CustomerID Country
## 0 0
#convert the invoiceDate to datetime
myRetailDataCleaned$InvoiceDate = as_datetime(myRetailDataCleaned$InvoiceDate, format="%d-%m-%Y %H:%M")
# Check the dimension
dim(myRetailDataCleaned)
## [1] 406829 8
# Data Head
head(myRetailDataCleaned)
## # A tibble: 6 x 8
## InvoiceNo StockC~1 Descr~2 Quant~3 InvoiceDate UnitP~4 Custo~5 Country
## <chr> <chr> <chr> <dbl> <dttm> <dbl> <dbl> <chr>
## 1 536365 85123A WHITE ~ 6 2010-12-01 08:26:00 2.55 17850 United~
## 2 536365 71053 WHITE ~ 6 2010-12-01 08:26:00 3.39 17850 United~
## 3 536365 84406B CREAM ~ 8 2010-12-01 08:26:00 2.75 17850 United~
## 4 536365 84029G KNITTE~ 6 2010-12-01 08:26:00 3.39 17850 United~
## 5 536365 84029E RED WO~ 6 2010-12-01 08:26:00 3.39 17850 United~
## 6 536365 22752 SET 7 ~ 2 2010-12-01 08:26:00 7.65 17850 United~
## # ... with abbreviated variable names 1: StockCode, 2: Description,
## # 3: Quantity, 4: UnitPrice, 5: CustomerID
# As we can see our data now is cleaned from the null value and we changed the InvoiceDate column format from char to datetime
#And Since we will work on FRM for the dataset we need to check the outlier for the following columns
#Let's check for outliers on the following colums [UnitPrice,InvoiceDate,Quantity]
#Checking for outlires before scaling
summary(myRetailDataCleaned)
## InvoiceNo StockCode Description Quantity
## Length:406829 Length:406829 Length:406829 Min. :-80995.00
## Class :character Class :character Class :character 1st Qu.: 2.00
## Mode :character Mode :character Mode :character Median : 5.00
## Mean : 12.06
## 3rd Qu.: 12.00
## Max. : 80995.00
## InvoiceDate UnitPrice CustomerID
## Min. :2010-12-01 08:26:00.00 Min. : 0.00 Min. :12346
## 1st Qu.:2011-04-06 15:02:00.00 1st Qu.: 1.25 1st Qu.:13953
## Median :2011-07-31 11:48:00.00 Median : 1.95 Median :15152
## Mean :2011-07-10 16:30:57.88 Mean : 3.46 Mean :15288
## 3rd Qu.:2011-10-20 13:06:00.00 3rd Qu.: 3.75 3rd Qu.:16791
## Max. :2011-12-09 12:50:00.00 Max. :38970.00 Max. :18287
## Country
## Length:406829
## Class :character
## Mode :character
##
##
##
'Actually from the summary i can see that we have outlier in Quantity and UnitPrice'
## [1] "Actually from the summary i can see that we have outlier in Quantity and UnitPrice"
'Let\'s first visualize these 3 columns '
## [1] "Let's first visualize these 3 columns "
# As we can see the data for the unitPrice column is right skewed and contain outliers
hist(myRetailDataCleaned$UnitPrice, freq = T)
boxplot(myRetailDataCleaned$UnitPrice)
# As we can see the data for the Quantity column contain outliers
hist(myRetailDataCleaned$Quantity, freq = T)
boxplot(myRetailDataCleaned$Quantity)
# for date it contain some outliers but not high as much the others columns
hist(as.numeric(myRetailDataCleaned$InvoiceDate) , freq = T)
## Warning in breaks[-1L] + breaks[-nB]: NAs produced by integer overflow
boxplot(as.numeric(myRetailDataCleaned$InvoiceDate))
# Removing outliers
'After viewing the columns i found out that the best option to handle these outliers by taking a subset of the data'
## [1] "After viewing the columns i found out that the best option to handle these outliers by taking a subset of the data"
'that contain the most distruted values'
## [1] "that contain the most distruted values"
#Take subset
myRetailDataCleaned <- myRetailDataCleaned[myRetailDataCleaned$UnitPrice <5 & myRetailDataCleaned$Quantity <= 12 & myRetailDataCleaned$Quantity >= 0 , ]
#check the summary of the data after removing the outliers
summary(myRetailDataCleaned)
## InvoiceNo StockCode Description Quantity
## Length:282422 Length:282422 Length:282422 Min. : 1.000
## Class :character Class :character Class :character 1st Qu.: 2.000
## Mode :character Mode :character Mode :character Median : 4.000
## Mean : 5.601
## 3rd Qu.:10.000
## Max. :12.000
## InvoiceDate UnitPrice CustomerID
## Min. :2010-12-01 08:26:00.00 Min. :0.000 Min. :12347
## 1st Qu.:2011-04-08 08:39:00.00 1st Qu.:1.250 1st Qu.:14056
## Median :2011-08-04 15:04:00.00 Median :1.650 Median :15311
## Mean :2011-07-13 09:55:34.10 Mean :2.102 Mean :15373
## 3rd Qu.:2011-10-24 16:20:00.00 3rd Qu.:2.950 3rd Qu.:16895
## Max. :2011-12-09 12:50:00.00 Max. :4.960 Max. :18287
## Country
## Length:282422
## Class :character
## Mode :character
##
##
##
#check the dimension of the data after removing the outliers
dim(myRetailDataCleaned)
## [1] 282422 8
# Visualize the columns after removing the outliers
#After removing the outlier
hist(myRetailDataCleaned$UnitPrice, freq = T)
boxplot(myRetailDataCleaned$UnitPrice)
hist(myRetailDataCleaned$Quantity, freq = T)
boxplot(myRetailDataCleaned$Quantity)
hist(as.numeric(myRetailDataCleaned$InvoiceDate) , freq = T)
## Warning in breaks[-1L] + breaks[-nB]: NAs produced by integer overflow
boxplot(as.numeric(myRetailDataCleaned$InvoiceDate))
# we will create data frame based on customer Recency, Frequency and customer Spending
#Customer Spending
customerSpending <- myRetailDataCleaned %>% group_by(CustomerID) %>% summarize(Spending = sum((UnitPrice * Quantity)) )
# frequency of the customer
customerFrequency <- myRetailDataCleaned %>% group_by(CustomerID) %>% summarize(Frequency = n())
# recency of the customer
recency <- myRetailDataCleaned %>% group_by(CustomerID)%>% summarise(Recency = as.numeric(difftime(max(myRetailDataCleaned$InvoiceDate),max(InvoiceDate)), units = "days") )
#Merge the dataFrame
merged_df <- merge(customerSpending,customerFrequency, by = "CustomerID", all.x = TRUE, all.y = TRUE)
merged_df <- merge(merged_df,recency, by = "CustomerID", all.x = TRUE, all.y = TRUE)
# summary and dataset dimension
dim(merged_df)
## [1] 4104 4
summary(merged_df)
## CustomerID Spending Frequency Recency
## Min. :12347 Min. : 0.0 Min. : 1.00 Min. : 0.00
## 1st Qu.:13816 1st Qu.: 150.2 1st Qu.: 11.00 1st Qu.: 17.99
## Median :15288 Median : 334.9 Median : 29.00 Median : 51.03
## Mean :15293 Mean : 717.5 Mean : 68.82 Mean : 93.10
## 3rd Qu.:16774 3rd Qu.: 819.4 3rd Qu.: 74.00 3rd Qu.:147.06
## Max. :18287 Max. :58540.9 Max. :6872.00 Max. :373.12
# let's visualize our Data
hist(merged_df$Spending, freq = T)
boxplot(merged_df$Spending) #0.1
hist(merged_df$Frequency, freq = T)
boxplot(merged_df$Frequency) # 0.15
hist(merged_df$Recency, freq = T)
boxplot(merged_df$Recency) #0.4
# It seems that our data is highly skewed , concentrated in one area and also contain outliers
# Let's applu scaling and check again
#let's scale the data to have a better overview of the outliers and spread the data
##scaling ===>
data_scaled <- merged_df %>% mutate_all(~ rescale(., to = c(0, 1)))
# after scaling
hist(data_scaled$Spending, freq = T)
boxplot(data_scaled$Spending) #0.1
hist(data_scaled$Frequency, freq = T)
boxplot(data_scaled$Frequency) # 0.15
hist(data_scaled$Recency, freq = T)
boxplot(data_scaled$Recency) #0.4
# Same the data still skewed , concentrated in one area and also contain outliers
# so Let's take a subset of the data based on the graph most of data is distributed around values
data_scaled <- data_scaled[data_scaled$Spending <0.1 & data_scaled$Frequency <= 0.1 & data_scaled$Recency <= 0.4 , ]
# after removing the outliers
#We still got some outliers and skewed distrubtion but it's much better than before
hist(data_scaled$Spending, freq = T)
boxplot(data_scaled$Spending) #0.2
hist(data_scaled$Frequency, freq = T)
boxplot(data_scaled$Frequency) # 0.2
hist(data_scaled$Recency, freq = T)
boxplot(data_scaled$Recency) #0.4
# checking the summary and dimension of the data
summary(data_scaled)
## CustomerID Spending Frequency Recency
## Min. :0.0000 Min. :0.000000 Min. :0.000000 Min. :0.00000
## 1st Qu.:0.2466 1st Qu.:0.003418 1st Qu.:0.002329 1st Qu.:0.03745
## Median :0.4956 Median :0.007698 Median :0.005530 Median :0.08308
## Mean :0.4940 Mean :0.013182 Mean :0.010071 Mean :0.11435
## 3rd Qu.:0.7421 3rd Qu.:0.017411 3rd Qu.:0.012662 3rd Qu.:0.17151
## Max. :1.0000 Max. :0.099188 Max. :0.098385 Max. :0.39978
dim(data_scaled)
## [1] 3061 4
# Let's Apply clustering but first we need to check how many clusters our data can fit
# Elbow method
opt<-Optimal_Clusters_KMeans(data_scaled, max_clusters=10, plot_clusters = TRUE)
'It seems that our data can be in 3-4 clusters'
## [1] "It seems that our data can be in 3-4 clusters"
# check by using Silhouette width
silhouette_score = function(k){
km = kmeans(data_scaled, centers = k, nstart=25)
ss = silhouette(km$cluster, dist(data_scaled))
mean(ss[, 3])}
k = 2:10
avg_sil = sapply(k,silhouette_score)
plot(k, type = 'b', avg_sil, xlab = 'number of clusters', ylab ='average silhouette scores', frame = 'False')
'It seems that our data can be in 4 clusters'
## [1] "It seems that our data can be in 4 clusters"
# Gap statistics
library("factoextra")
fviz_nbclust(data_scaled, kmeans, method = "gap_stat")
'It seems that our data can be in 4 clusters'
## [1] "It seems that our data can be in 4 clusters"
# So let's try to cluster our dataset by 3 clusters
clusterNo = 3
# I will use Kmean and clara
# Convert the data frame into a matrix
data <- as.matrix(data_scaled[, c("Spending", "Frequency", "Recency")])
# Kmean
cluster_3 <- kmeans(data,centers = clusterNo,nstart = 10)
cluster_3$cluster <- as.factor(cluster_3$cluster)
# Clustering in different graph
fviz_cluster(list(data=data, cluster=cluster_3$cluster),
ellipse.type="norm", geom="point", stand=FALSE, palette="jco", ggtheme=theme_classic())
# Boxblot
groupBWplot(data, cluster_3$cluster, alpha=0.05)
## Warning in data.frame(..., check.names = FALSE): row names were found from a
## short variable and have been discarded
# Try out with Clara 3 clusters
clara_flex<-eclust(data, "clara", k=clusterNo)
summary(clara_flex)
## Object of class 'clara' from call:
## fun_clust(x = x, k = k)
## Medoids:
## Spending Frequency Recency
## 1947 0.019251508 0.008877893 0.03795852
## 885 0.006247772 0.002765245 0.17164250
## 235 0.005710882 0.003201863 0.34598555
## Objective function: 0.03582964
## Numerical information per cluster:
## size max_diss av_diss isolation
## [1,] 1754 0.11486855 0.03425603 0.8543337
## [2,] 996 0.09939795 0.03785266 0.7392713
## [3,] 311 0.08389501 0.03822573 0.4812027
## Average silhouette width per cluster:
## [1] 0.6155814 0.4744204 0.6739031
## Average silhouette width of best sample: 0.5755754
##
## Best sample:
## [1] 31 46 66 120 122 222 235 245 276 291 383 610 753 885 1319
## [16] 1369 1399 1449 1742 1747 1798 1852 1853 1947 2075 2191 2232 2240 2372 2401
## [31] 2448 2606 2623 2661 2811 2844 3387 3429 3441 3451 3515 3631 3692 3701 3786
## [46] 3797
## Clustering vector:
## 1 2 4 9 11 12 14 15 16 18 19 20 21 23 24 26
## 1 1 1 1 2 2 1 3 1 1 2 2 2 1 1 3
## 27 28 29 31 33 34 35 36 38 39 40 41 44 45 46 47
## 2 1 1 1 1 2 1 2 1 1 2 3 2 3 1 2
## 48 49 51 52 54 55 56 57 58 59 60 62 64 65 66 67
## 1 2 2 2 2 1 3 2 1 2 1 2 1 1 1 2
## 68 69 70 71 72 73 74 76 77 78 79 81 82 84 85 86
## 1 2 1 2 3 1 1 1 1 1 2 2 1 1 1 3
## 87 88 89 90 92 93 94 95 97 98 99 100 101 102 103 104
## 2 2 2 2 1 2 3 1 1 1 2 1 2 1 1 1
## 105 106 107 108 109 110 112 113 114 116 117 118 120 122 123 126
## 1 1 1 1 1 1 1 1 2 1 1 2 2 3 1 2
## 127 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144
## 3 2 1 1 2 2 3 2 1 1 1 2 1 2 1 1
## 145 146 147 148 149 150 151 152 153 154 157 159 160 161 162 164
## 3 2 2 1 1 1 1 1 2 2 2 2 1 2 1 1
## 166 169 170 171 172 173 176 177 178 179 181 183 184 186 187 188
## 1 2 1 1 2 1 1 1 1 2 2 1 1 1 1 2
## 189 191 192 193 194 195 196 197 198 200 201 202 203 204 205 206
## 1 2 3 2 2 1 1 1 1 2 1 2 2 2 1 2
## 207 208 210 211 212 213 214 215 216 219 221 222 223 224 225 226
## 2 2 1 2 1 1 1 1 1 3 1 1 1 1 2 2
## 227 228 229 231 232 233 235 236 237 238 240 241 244 245 246 247
## 2 2 1 1 3 1 3 1 1 1 3 1 3 1 1 1
## 248 249 250 251 252 254 255 257 259 260 261 262 264 267 268 269
## 1 1 1 1 2 2 1 1 1 1 1 2 1 1 1 1
## 271 272 274 275 276 277 278 279 280 281 282 283 284 286 287 288
## 3 1 2 3 2 1 1 1 2 1 2 1 1 1 1 2
## 289 290 291 292 293 295 296 297 298 299 300 301 303 304 305 306
## 1 1 1 3 1 2 1 1 1 3 1 1 1 1 2 3
## 307 312 313 314 315 316 318 319 320 321 324 325 326 327 330 332
## 1 3 2 3 2 1 1 3 2 3 1 3 2 1 1 2
## 333 334 335 336 337 338 339 341 345 346 349 352 353 354 357 359
## 1 1 1 2 1 1 1 1 2 1 1 2 3 2 1 2
## 360 361 362 363 366 367 369 371 372 373 374 375 377 379 380 381
## 2 1 1 1 1 3 2 1 1 3 1 2 1 1 1 2
## 383 384 386 388 389 390 392 394 396 397 399 401 402 403 404 406
## 3 2 1 2 3 1 1 2 2 1 2 1 2 2 2 1
## 407 408 410 412 413 414 415 416 417 418 419 420 421 424 425 426
## 1 2 1 1 2 1 1 2 1 3 3 1 1 2 2 1
## 427 429 430 431 432 433 434 435 436 437 438 440 441 442 443 444
## 1 2 2 1 1 1 1 1 2 3 1 3 1 1 1 1
## 445 446 447 449 450 451 452 453 455 456 457 461 463 464 465 467
## 1 1 1 1 1 1 2 1 3 1 1 1 1 1 2 1
## 468 469 470 471 472 475 478 482 483 484 485 486 487 488 489 490
## 1 1 1 1 1 1 1 1 1 1 2 2 1 1 2 1
## 491 492 493 494 496 497 498 499 500 503 504 505 506 508 510 511
## 1 1 1 2 2 2 3 2 1 3 1 1 1 1 2 2
## 514 516 518 519 520 523 524 525 526 529 530 533 534 537 538 539
## 2 1 1 2 1 3 1 1 1 3 1 1 1 2 1 1
## 541 542 543 544 546 547 548 549 550 551 552 556 557 558 559 560
## 1 2 1 2 2 1 1 1 3 1 1 2 1 2 2 1
## 563 564 565 566 567 568 569 570 572 573 574 575 577 578 579 580
## 2 2 1 1 1 3 2 1 2 1 1 1 1 1 2 2
## 581 582 584 585 587 588 589 590 591 592 593 594 595 596 597 598
## 1 1 3 2 1 1 2 1 1 1 1 2 2 1 2 1
## 599 600 602 603 604 605 606 607 608 609 610 612 613 614 615 616
## 1 1 1 2 2 3 1 1 2 1 1 2 1 2 1 1
## 617 619 620 623 627 628 629 631 632 634 635 637 638 639 640 641
## 2 3 2 2 1 1 2 1 1 2 3 2 2 1 1 3
## 642 644 645 646 647 650 651 652 653 654 655 656 657 658 659 660
## 2 1 1 2 2 2 1 1 1 1 1 1 3 2 2 2
## 661 662 663 665 667 670 671 674 676 677 678 679 680 681 682 683
## 3 1 2 1 1 3 1 3 1 3 1 1 1 1 1 1
## 684 685 686 688 689 690 691 692 693 694 696 697 698 699 700 703
## 1 2 1 2 2 1 1 1 2 1 1 2 1 2 2 2
## 706 708 709 710 711 712 713 714 715 718 719 720 721 722 726 727
## 2 2 1 1 2 2 2 3 2 2 1 1 2 1 2 2
## 728 729 730 731 733 735 736 737 738 740 741 743 744 745 746 747
## 2 3 1 1 1 3 1 2 1 1 2 3 1 1 2 1
## 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763
## 1 3 3 2 1 1 2 3 2 2 3 1 1 1 1 1
## 764 765 766 767 768 770 771 772 773 774 775 777 778 779 780 781
## 2 2 1 1 1 2 1 1 1 1 1 1 1 1 1 1
## 783 785 786 787 788 789 793 795 797 799 800 801 803 804 807 808
## 2 1 1 3 1 2 1 2 2 2 2 1 2 3 1 1
## 810 811 813 814 815 816 818 820 821 823 824 825 826 827 828 829
## 1 1 1 2 2 2 1 1 1 3 2 2 2 2 2 2
## 830 831 832 833 834 835 836 837 839 841 842 843 844 845 846 847
## 2 1 1 1 2 1 1 2 1 1 1 2 2 1 2 1
## 848 849 850 851 852 854 855 857 858 860 862 864 865 866 867 868
## 2 2 1 1 1 2 2 1 2 1 1 2 1 1 1 1
## 872 873 874 875 876 877 878 879 880 881 882 884 885 886 887 888
## 2 1 1 1 2 1 3 2 1 2 1 2 2 1 1 2
## 889 890 891 893 895 896 898 899 900 902 903 904 905 906 907 908
## 1 2 1 2 3 1 2 3 1 1 1 2 1 2 1 2
## 910 911 912 913 915 916 917 918 919 921 922 924 926 927 928 929
## 1 1 3 1 1 2 2 2 3 1 1 2 2 3 1 3
## 930 932 934 935 938 940 941 942 943 944 945 947 948 949 953 954
## 2 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1
## 959 961 962 963 964 966 967 968 969 970 972 973 974 977 978 979
## 1 1 3 1 3 2 1 1 1 3 1 1 1 2 1 1
## 980 982 985 988 989 990 991 992 993 995 996 997 998 999 1000 1001
## 2 2 3 1 1 1 2 2 2 2 1 1 2 1 2 1
## 1002 1003 1005 1008 1009 1010 1011 1012 1014 1017 1018 1020 1022 1023 1024 1025
## 3 1 1 2 1 2 1 3 2 1 2 1 1 2 1 2
## 1026 1027 1028 1030 1031 1032 1033 1035 1036 1037 1038 1040 1042 1043 1044 1045
## 1 1 1 3 1 1 1 2 1 1 1 1 1 2 1 2
## 1046 1047 1048 1049 1050 1051 1053 1055 1056 1058 1059 1060 1061 1062 1063 1064
## 1 2 3 2 2 1 2 1 1 2 2 1 1 3 1 1
## 1065 1067 1068 1069 1070 1071 1072 1073 1074 1075 1077 1079 1080 1081 1082 1084
## 3 2 2 2 2 1 2 1 1 1 2 3 2 1 2 1
## 1085 1086 1088 1090 1091 1092 1093 1094 1095 1096 1097 1099 1100 1101 1102 1103
## 1 2 1 2 1 2 3 1 2 2 2 2 1 2 1 2
## 1104 1106 1107 1109 1113 1114 1115 1116 1118 1120 1121 1124 1125 1127 1128 1129
## 1 2 2 3 1 1 1 1 2 1 1 1 1 1 2 1
## 1130 1132 1133 1136 1137 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1150
## 1 1 1 2 1 2 2 2 1 1 1 1 1 1 2 1
## 1151 1152 1153 1154 1155 1157 1158 1159 1160 1161 1164 1165 1166 1168 1169 1172
## 1 2 1 1 1 2 3 2 1 3 3 2 2 2 1 1
## 1173 1174 1175 1176 1177 1178 1179 1180 1183 1184 1185 1187 1189 1191 1192 1193
## 3 2 2 1 1 1 1 1 2 1 2 1 1 1 1 1
## 1194 1196 1197 1199 1201 1202 1203 1205 1207 1208 1209 1210 1211 1212 1213 1214
## 1 2 3 1 1 1 1 2 1 1 1 3 2 3 3 1
## 1217 1218 1219 1220 1221 1222 1223 1225 1226 1227 1229 1232 1233 1234 1235 1236
## 1 1 1 1 2 1 1 1 1 3 1 2 1 2 1 2
## 1237 1238 1240 1241 1242 1243 1244 1245 1246 1248 1249 1250 1251 1252 1253 1254
## 1 1 1 1 1 1 3 2 1 1 3 1 1 2 1 1
## 1256 1257 1258 1261 1262 1266 1267 1271 1272 1274 1275 1276 1277 1278 1280 1281
## 3 1 2 1 2 1 2 2 2 1 3 1 1 2 2 1
## 1282 1283 1284 1286 1287 1288 1289 1291 1292 1294 1295 1296 1298 1299 1300 1301
## 2 1 2 1 1 1 2 3 1 2 1 1 2 1 3 2
## 1302 1303 1304 1305 1306 1307 1309 1311 1312 1313 1314 1315 1317 1318 1319 1320
## 1 1 1 1 2 1 2 2 3 1 1 2 2 2 1 2
## 1321 1324 1325 1328 1330 1333 1334 1336 1338 1339 1340 1342 1346 1347 1348 1349
## 2 2 1 1 3 1 1 2 3 2 1 3 2 2 3 1
## 1351 1352 1353 1354 1355 1357 1358 1359 1360 1361 1362 1363 1365 1366 1367 1369
## 1 1 1 1 1 1 1 1 1 1 2 1 1 1 3 2
## 1370 1371 1372 1374 1375 1376 1377 1379 1380 1383 1384 1385 1386 1387 1388 1389
## 2 2 1 2 3 2 2 1 3 1 3 1 2 1 1 1
## 1393 1394 1395 1396 1397 1399 1404 1406 1407 1408 1409 1410 1411 1418 1419 1420
## 2 1 3 1 3 1 1 2 2 1 1 1 3 2 2 1
## 1421 1422 1424 1425 1426 1427 1429 1430 1431 1432 1433 1435 1436 1437 1438 1439
## 1 1 1 1 2 1 1 2 1 3 1 1 3 3 1 2
## 1440 1442 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1456 1457 1461
## 2 2 2 1 1 1 1 3 2 1 1 2 1 1 3 1
## 1462 1464 1465 1466 1467 1468 1470 1471 1476 1477 1479 1480 1481 1482 1483 1484
## 1 2 1 1 1 1 2 1 3 2 1 1 1 3 2 2
## 1485 1488 1490 1492 1493 1494 1495 1498 1499 1500 1503 1504 1505 1507 1508 1509
## 2 1 1 2 1 1 2 1 1 2 2 1 2 1 1 2
## 1511 1512 1513 1514 1517 1518 1519 1520 1521 1522 1523 1524 1525 1526 1527 1528
## 1 2 1 1 2 1 1 2 1 2 3 1 1 1 1 2
## 1529 1531 1532 1533 1535 1536 1537 1538 1539 1541 1542 1543 1544 1546 1547 1549
## 1 1 1 2 2 2 1 1 2 1 1 1 1 1 1 1
## 1550 1551 1552 1553 1554 1555 1556 1557 1558 1560 1563 1564 1565 1566 1567 1569
## 1 2 2 1 2 1 2 2 1 1 1 1 1 2 1 2
## 1571 1572 1573 1574 1575 1576 1577 1578 1580 1582 1583 1584 1587 1589 1590 1592
## 1 1 1 1 1 1 1 2 1 1 1 1 1 1 2 1
## 1593 1594 1595 1598 1599 1600 1601 1602 1603 1605 1607 1609 1610 1611 1612 1613
## 2 1 2 1 2 2 1 1 2 2 1 1 2 2 1 1
## 1615 1616 1617 1618 1619 1620 1621 1622 1623 1624 1628 1629 1630 1631 1632 1633
## 1 1 1 2 1 1 1 2 1 1 1 1 3 2 2 1
## 1634 1635 1637 1638 1639 1641 1643 1645 1646 1647 1648 1649 1650 1651 1652 1653
## 3 1 2 1 3 1 1 1 1 1 1 1 1 1 1 1
## 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1666 1667 1668 1669 1670 1671
## 2 1 1 1 2 1 1 3 1 1 1 2 1 1 1 1
## 1672 1673 1675 1676 1677 1679 1680 1681 1682 1683 1684 1685 1686 1687 1689 1691
## 2 1 1 2 3 1 2 2 2 1 1 2 3 1 2 2
## 1692 1693 1694 1697 1698 1699 1700 1702 1704 1705 1706 1707 1708 1709 1710 1711
## 1 1 1 3 2 2 3 2 1 1 1 1 1 2 1 1
## 1714 1715 1716 1717 1719 1720 1721 1722 1723 1725 1727 1728 1729 1732 1733 1734
## 2 2 2 2 1 1 2 1 1 1 2 2 1 1 1 1
## 1735 1736 1737 1738 1740 1741 1742 1743 1744 1746 1747 1748 1749 1750 1751 1752
## 2 1 1 2 2 2 2 3 1 1 2 1 2 3 1 2
## 1753 1754 1755 1756 1757 1758 1759 1761 1762 1764 1766 1767 1768 1769 1770 1771
## 1 1 2 1 1 1 3 1 1 1 3 1 2 1 1 1
## 1776 1777 1778 1781 1782 1783 1784 1785 1786 1788 1789 1790 1792 1793 1794 1795
## 3 1 2 1 1 1 1 1 1 1 2 1 1 1 2 2
## 1796 1798 1799 1801 1802 1803 1805 1806 1807 1808 1809 1810 1811 1812 1813 1814
## 3 1 2 1 3 1 2 1 2 1 1 2 1 1 2 2
## 1815 1816 1818 1819 1820 1821 1823 1825 1826 1827 1828 1829 1830 1831 1832 1833
## 1 1 3 2 1 1 1 2 1 2 1 2 1 3 3 1
## 1834 1835 1836 1838 1841 1842 1844 1845 1846 1848 1850 1851 1852 1853 1855 1856
## 2 2 2 1 1 2 2 3 3 2 1 1 2 2 1 1
## 1858 1859 1860 1861 1862 1863 1864 1865 1866 1868 1869 1870 1871 1872 1876 1878
## 1 1 1 1 1 2 1 1 1 1 1 2 2 2 1 1
## 1880 1882 1883 1885 1886 1888 1889 1890 1892 1894 1895 1896 1897 1899 1900 1901
## 2 1 1 1 1 1 2 1 2 1 2 2 2 2 1 3
## 1902 1906 1909 1910 1912 1914 1915 1916 1917 1918 1920 1922 1923 1925 1927 1928
## 2 1 1 1 2 1 3 2 1 2 1 1 1 3 1 1
## 1929 1930 1931 1932 1933 1935 1936 1937 1938 1939 1940 1941 1942 1943 1945 1946
## 1 1 1 1 1 3 2 3 1 1 3 2 2 2 1 3
## 1947 1949 1951 1952 1954 1955 1958 1959 1960 1961 1962 1963 1964 1965 1968 1969
## 1 1 2 2 1 1 1 3 1 1 1 2 1 1 1 2
## 1972 1973 1975 1977 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
## 1 1 2 1 1 2 1 1 1 3 2 1 1 2 2 1
## 1994 1995 1996 1998 2001 2002 2003 2005 2010 2011 2013 2017 2018 2019 2020 2021
## 2 3 1 2 1 2 1 2 1 2 3 1 1 1 2 2
## 2022 2023 2024 2026 2027 2028 2029 2030 2031 2034 2035 2037 2038 2041 2042 2043
## 2 2 3 1 1 1 3 2 3 3 3 3 2 3 1 2
## 2044 2045 2046 2047 2050 2051 2052 2053 2054 2055 2056 2058 2059 2060 2061 2062
## 1 1 2 2 2 2 2 2 1 1 1 2 1 1 2 2
## 2064 2065 2066 2069 2071 2072 2074 2075 2076 2077 2079 2080 2084 2085 2086 2087
## 2 2 2 2 2 1 2 2 2 3 2 1 2 2 3 2
## 2088 2089 2092 2095 2097 2098 2100 2103 2104 2105 2106 2107 2108 2109 2110 2112
## 2 2 2 1 2 1 2 2 1 2 2 2 1 3 2 1
## 2114 2116 2119 2120 2121 2123 2125 2126 2127 2128 2130 2131 2133 2134 2136 2138
## 1 2 1 1 1 3 1 1 3 3 1 1 2 1 1 2
## 2139 2140 2141 2144 2145 2146 2147 2148 2150 2151 2152 2154 2155 2156 2157 2161
## 2 1 2 1 1 1 1 1 1 1 1 3 2 1 1 1
## 2162 2163 2164 2168 2170 2171 2173 2174 2175 2176 2177 2178 2179 2180 2181 2182
## 1 1 1 1 2 1 1 2 1 2 2 1 3 2 2 3
## 2183 2185 2186 2187 2188 2189 2190 2191 2192 2193 2194 2196 2197 2198 2201 2203
## 1 1 1 1 2 1 1 1 1 1 1 2 2 1 1 1
## 2204 2205 2207 2208 2209 2210 2211 2212 2213 2214 2216 2217 2218 2219 2220 2223
## 1 2 2 1 2 1 2 1 1 1 1 1 1 1 1 1
## 2224 2225 2227 2228 2229 2230 2231 2232 2234 2237 2238 2239 2240 2241 2242 2243
## 1 3 1 2 1 2 1 1 2 1 1 1 1 2 1 1
## 2244 2245 2246 2247 2248 2250 2253 2254 2255 2256 2258 2260 2261 2262 2264 2265
## 3 1 1 1 1 1 2 3 1 1 2 2 2 1 1 2
## 2266 2267 2268 2269 2270 2271 2273 2275 2276 2277 2278 2279 2280 2281 2282 2283
## 1 1 1 2 1 2 2 2 1 1 1 1 2 1 2 3
## 2284 2285 2286 2287 2288 2289 2290 2291 2292 2293 2294 2295 2298 2301 2302 2303
## 3 3 2 1 2 1 1 2 2 3 1 3 1 1 2 3
## 2304 2306 2308 2309 2311 2312 2314 2315 2317 2318 2319 2320 2321 2322 2323 2324
## 1 2 2 1 3 2 2 2 1 2 2 2 1 2 2 1
## 2325 2326 2327 2328 2329 2330 2331 2332 2334 2335 2337 2339 2341 2342 2343 2345
## 1 1 3 1 3 1 1 1 1 1 1 3 2 1 1 1
## 2346 2347 2348 2351 2352 2353 2356 2357 2359 2362 2363 2364 2365 2366 2367 2368
## 3 1 3 1 1 1 1 1 2 3 1 1 2 2 1 1
## 2369 2370 2371 2372 2373 2374 2375 2376 2377 2378 2380 2381 2382 2383 2384 2386
## 3 1 2 1 1 2 1 2 2 1 2 1 2 2 3 1
## 2387 2389 2392 2393 2394 2395 2396 2397 2399 2400 2401 2402 2403 2404 2405 2406
## 2 3 1 1 1 1 2 1 1 2 3 1 2 3 2 2
## 2407 2408 2409 2410 2412 2413 2414 2415 2417 2418 2419 2421 2422 2424 2425 2426
## 1 1 2 2 1 2 1 3 1 2 2 2 1 2 2 3
## 2427 2428 2430 2431 2432 2433 2434 2435 2436 2438 2439 2440 2441 2443 2444 2445
## 1 2 2 2 2 2 1 2 2 2 1 1 1 2 1 3
## 2446 2447 2448 2449 2450 2451 2452 2453 2454 2455 2456 2458 2459 2460 2461 2465
## 1 1 1 2 1 1 1 2 2 3 1 1 1 2 1 1
## 2466 2467 2468 2472 2474 2476 2477 2478 2479 2480 2481 2483 2485 2488 2494 2495
## 2 2 2 3 1 1 1 1 1 1 1 1 1 1 2 1
## 2496 2498 2499 2500 2501 2503 2504 2505 2506 2507 2508 2509 2510 2511 2512 2513
## 1 2 3 2 3 2 1 1 1 1 1 1 1 1 2 1
## 2514 2515 2516 2518 2520 2521 2523 2524 2525 2526 2527 2528 2529 2530 2531 2532
## 1 1 1 2 1 2 1 2 2 1 1 1 3 1 1 1
## 2533 2534 2535 2536 2537 2538 2539 2540 2542 2543 2544 2546 2547 2548 2549 2550
## 2 1 1 2 2 1 1 1 2 1 2 1 1 1 1 1
## 2551 2552 2553 2554 2555 2557 2558 2559 2560 2561 2562 2564 2567 2569 2570 2571
## 1 2 2 2 1 2 1 1 2 3 2 2 2 1 2 1
## 2572 2573 2575 2577 2578 2579 2581 2582 2583 2584 2587 2588 2589 2591 2592 2593
## 1 3 2 2 1 3 2 1 2 1 1 1 2 1 1 2
## 2594 2595 2597 2598 2600 2601 2604 2605 2606 2607 2608 2609 2611 2612 2613 2615
## 2 3 1 2 3 1 2 2 2 2 2 2 2 1 2 2
## 2616 2619 2622 2623 2624 2625 2626 2629 2630 2631 2632 2633 2634 2636 2637 2638
## 3 1 1 2 2 3 2 1 2 1 2 1 1 2 1 2
## 2639 2641 2642 2644 2645 2646 2648 2649 2650 2652 2654 2655 2656 2657 2658 2659
## 2 1 1 3 1 2 2 1 1 1 1 1 1 2 2 2
## 2660 2661 2662 2663 2664 2665 2666 2667 2668 2669 2670 2671 2672 2673 2674 2675
## 1 3 2 2 3 2 3 2 2 2 2 1 1 1 2 1
## 2676 2677 2679 2680 2681 2683 2684 2685 2686 2687 2688 2689 2690 2691 2692 2693
## 2 1 2 1 1 2 1 1 2 1 2 2 1 2 1 2
## 2695 2698 2699 2701 2702 2705 2707 2708 2709 2710 2711 2712 2713 2714 2715 2717
## 2 1 1 2 2 2 2 2 2 2 2 1 1 1 1 1
## 2719 2720 2722 2723 2725 2726 2727 2728 2729 2730 2732 2733 2737 2738 2739 2741
## 2 2 2 1 2 2 1 1 2 2 1 3 3 1 2 1
## 2742 2744 2745 2746 2748 2749 2750 2751 2753 2754 2755 2757 2758 2759 2761 2762
## 1 3 1 1 1 3 1 3 3 1 1 2 3 1 2 1
## 2763 2764 2765 2766 2767 2768 2769 2772 2773 2774 2775 2776 2777 2778 2780 2782
## 3 2 1 1 1 1 1 3 1 2 1 2 1 1 1 1
## 2783 2784 2786 2787 2788 2789 2790 2791 2792 2793 2794 2795 2796 2797 2798 2799
## 1 2 1 1 1 1 1 1 2 1 1 1 1 1 1 2
## 2800 2801 2802 2804 2805 2806 2807 2808 2809 2811 2813 2814 2815 2817 2818 2819
## 1 2 1 1 2 2 2 2 1 2 1 2 2 1 2 1
## 2822 2824 2825 2826 2827 2828 2829 2830 2831 2832 2833 2834 2835 2836 2838 2840
## 2 1 1 1 1 2 2 1 2 1 2 3 1 1 1 3
## 2841 2843 2844 2845 2846 2847 2848 2849 2850 2851 2853 2856 2857 2858 2859 2860
## 2 2 1 1 1 1 2 1 2 1 3 3 2 2 2 3
## 2862 2863 2865 2866 2867 2868 2869 2872 2873 2874 2875 2876 2877 2878 2881 2882
## 1 1 1 1 1 1 2 1 3 2 1 1 2 1 2 1
## 2883 2884 2886 2887 2888 2891 2892 2893 2894 2897 2898 2899 2900 2902 2903 2905
## 2 2 1 1 2 1 3 1 2 1 1 2 1 2 1 1
## 2906 2908 2909 2911 2912 2913 2914 2915 2916 2920 2921 2924 2925 2926 2927 2928
## 1 2 1 1 1 1 3 1 2 3 2 2 1 2 1 1
## 2929 2930 2931 2932 2934 2935 2936 2937 2938 2939 2941 2943 2946 2947 2948 2949
## 1 1 2 1 1 1 1 3 2 2 3 2 2 2 1 2
## 2950 2951 2952 2953 2955 2956 2957 2958 2959 2960 2963 2964 2966 2968 2970 2971
## 2 2 1 1 1 2 1 2 1 1 1 2 1 1 1 2
## 2973 2975 2976 2977 2978 2979 2981 2982 2983 2984 2985 2989 2990 2991 2992 2993
## 2 1 2 1 2 1 1 1 1 3 1 2 2 2 1 3
## 2994 2995 2996 2998 3000 3001 3002 3003 3004 3005 3006 3007 3008 3010 3011 3012
## 1 3 1 1 1 2 1 1 1 1 2 1 1 2 2 1
## 3013 3014 3015 3016 3017 3018 3019 3022 3023 3024 3025 3026 3027 3028 3029 3030
## 3 2 2 1 2 2 2 1 1 1 1 2 2 1 1 1
## 3031 3033 3034 3036 3037 3039 3040 3042 3044 3045 3046 3047 3048 3049 3052 3053
## 1 2 1 1 1 2 3 1 2 1 2 1 2 2 1 1
## 3054 3055 3056 3057 3058 3059 3061 3062 3065 3066 3067 3068 3070 3072 3073 3075
## 2 1 1 1 2 1 2 3 2 1 2 1 1 1 2 2
## 3076 3077 3078 3079 3080 3081 3082 3083 3084 3086 3087 3088 3089 3090 3091 3093
## 1 2 2 1 2 2 2 1 3 1 1 3 1 1 1 2
## 3094 3096 3097 3099 3100 3102 3103 3104 3105 3107 3109 3110 3111 3112 3113 3114
## 1 2 1 2 1 3 3 3 1 1 1 1 3 1 1 2
## 3116 3117 3118 3119 3121 3123 3125 3126 3127 3129 3130 3131 3132 3133 3134 3135
## 1 1 2 3 1 1 3 2 1 1 1 3 2 2 2 2
## 3138 3139 3140 3141 3143 3144 3145 3146 3147 3148 3149 3150 3151 3152 3153 3154
## 1 1 1 1 3 2 1 3 1 1 1 2 1 2 1 2
## 3156 3157 3158 3160 3161 3163 3165 3166 3167 3168 3169 3170 3171 3172 3173 3174
## 1 1 1 1 1 2 1 1 1 3 1 1 1 2 1 2
## 3175 3176 3178 3179 3180 3181 3183 3184 3185 3188 3189 3190 3192 3193 3194 3195
## 1 1 1 1 1 2 2 1 1 2 1 1 2 1 2 1
## 3196 3197 3198 3200 3202 3203 3204 3205 3206 3207 3208 3210 3212 3213 3214 3217
## 1 2 1 1 3 1 2 3 3 1 2 1 2 1 3 2
## 3219 3220 3221 3222 3223 3225 3226 3227 3228 3229 3230 3231 3232 3233 3235 3236
## 1 2 1 2 1 2 1 2 1 1 1 1 1 1 3 1
## 3237 3238 3239 3240 3241 3242 3243 3244 3245 3246 3247 3248 3249 3252 3253 3254
## 1 2 2 1 2 1 1 1 1 1 2 1 1 2 2 1
## 3255 3256 3258 3259 3260 3261 3262 3263 3264 3266 3267 3268 3269 3271 3272 3273
## 2 1 2 1 3 1 1 1 3 2 3 1 2 1 3 1
## 3274 3275 3277 3279 3280 3281 3282 3283 3284 3285 3286 3287 3288 3289 3290 3291
## 2 1 2 1 2 1 1 3 1 1 1 1 1 2 1 1
## 3292 3293 3294 3295 3296 3297 3298 3299 3300 3302 3303 3304 3305 3306 3308 3309
## 1 3 1 3 1 1 2 1 2 1 1 1 1 1 1 1
## 3311 3312 3313 3316 3318 3321 3324 3325 3326 3327 3329 3332 3334 3335 3337 3338
## 2 1 1 1 3 2 1 1 3 1 1 1 1 2 1 2
## 3339 3340 3341 3342 3343 3344 3345 3346 3348 3349 3351 3352 3354 3357 3358 3359
## 1 1 1 1 1 1 2 1 1 2 2 1 2 2 2 1
## 3361 3362 3363 3364 3365 3367 3368 3369 3370 3372 3373 3374 3376 3377 3379 3380
## 1 3 2 1 1 1 1 2 1 2 2 1 2 2 1 1
## 3381 3382 3383 3386 3387 3388 3390 3391 3392 3394 3395 3396 3397 3399 3400 3401
## 1 1 2 1 1 2 1 1 1 1 1 1 1 3 1 2
## 3403 3404 3405 3408 3409 3410 3412 3415 3416 3417 3419 3420 3423 3425 3426 3427
## 1 3 1 1 1 2 3 3 1 3 2 1 2 2 1 1
## 3428 3429 3430 3431 3432 3433 3434 3435 3436 3437 3439 3440 3441 3443 3444 3445
## 1 1 1 1 1 1 3 1 1 1 1 2 2 1 1 3
## 3446 3447 3448 3450 3451 3452 3455 3456 3457 3460 3461 3462 3463 3465 3466 3467
## 2 1 1 1 2 2 1 2 1 2 1 1 1 1 1 2
## 3469 3471 3472 3473 3475 3476 3478 3479 3480 3481 3482 3485 3486 3487 3489 3490
## 1 1 1 2 1 1 1 2 1 2 2 2 1 1 1 1
## 3491 3492 3493 3494 3495 3498 3499 3500 3501 3502 3503 3505 3508 3509 3510 3511
## 1 1 1 2 1 3 1 3 3 1 1 1 1 1 1 2
## 3512 3513 3514 3515 3516 3517 3518 3519 3520 3521 3522 3524 3525 3526 3527 3529
## 1 2 1 2 1 2 2 1 1 3 1 1 2 1 1 1
## 3532 3533 3534 3535 3536 3540 3541 3542 3543 3544 3545 3546 3548 3549 3550 3552
## 2 1 1 1 1 3 1 2 2 1 2 1 1 1 2 2
## 3553 3554 3555 3557 3558 3559 3561 3563 3566 3567 3570 3573 3574 3575 3576 3577
## 2 1 2 2 1 1 1 2 1 1 2 2 1 1 2 3
## 3578 3579 3581 3582 3583 3584 3585 3588 3589 3590 3591 3593 3595 3596 3597 3599
## 1 1 1 2 1 1 1 1 2 1 1 2 1 1 1 2
## 3601 3604 3605 3606 3608 3610 3611 3612 3613 3614 3616 3617 3618 3620 3622 3624
## 2 2 1 1 1 1 1 1 1 1 2 2 1 1 1 1
## 3626 3627 3628 3629 3630 3631 3632 3633 3634 3635 3637 3639 3640 3642 3643 3644
## 1 3 3 2 1 2 1 2 1 1 1 1 2 1 2 1
## 3645 3646 3647 3648 3649 3651 3652 3653 3654 3655 3656 3657 3659 3660 3661 3662
## 2 1 2 3 1 2 1 1 1 1 2 1 1 1 1 1
## 3663 3665 3667 3669 3670 3671 3672 3673 3674 3675 3677 3678 3679 3680 3681 3682
## 1 3 1 2 2 3 1 1 1 1 1 2 1 1 3 1
## 3683 3684 3685 3686 3687 3689 3690 3691 3692 3694 3695 3697 3698 3699 3700 3701
## 1 1 2 1 2 1 2 1 2 1 1 2 1 1 2 1
## 3702 3703 3705 3706 3707 3708 3709 3712 3714 3715 3717 3718 3722 3723 3725 3727
## 1 1 3 3 3 3 1 1 1 1 1 1 1 2 1 1
## 3728 3729 3731 3732 3733 3734 3735 3736 3738 3739 3741 3742 3743 3744 3746 3749
## 1 2 2 1 1 1 1 2 1 2 3 1 1 1 1 1
## 3750 3751 3752 3753 3754 3755 3757 3759 3760 3761 3763 3764 3765 3766 3767 3769
## 1 1 1 1 1 1 2 1 1 1 2 1 2 1 1 2
## 3770 3771 3773 3775 3776 3777 3779 3780 3781 3782 3783 3784 3785 3786 3788 3789
## 2 2 3 1 1 1 2 1 1 1 2 2 1 1 1 1
## 3790 3791 3793 3794 3795 3797 3798 3799 3800 3801 3802 3803 3804 3807 3808 3811
## 1 1 2 1 1 1 1 2 1 2 2 1 2 3 3 1
## 3816 3819 3821 3822 3823 3824 3825 3826 3827 3829 3832 3836 3837 3838 3839 3840
## 1 1 2 1 1 3 1 3 1 2 2 1 1 1 1 3
## 3841 3845 3847 3848 3850 3853 3854 3858 3860 3861 3862 3863 3864 3865 3866 3867
## 2 2 2 2 2 1 1 1 2 1 2 2 1 2 2 3
## 3868 3869 3870 3871 3872 3873 3874 3875 3877 3879 3880 3881 3882 3884 3885 3887
## 2 1 3 1 2 3 1 1 1 1 2 2 1 2 3 1
## 3888 3889 3890 3897 3898 3899 3901 3903 3905 3906 3907 3909 3912 3914 3915 3916
## 3 1 1 2 1 1 1 1 3 1 2 1 3 2 1 1
## 3918 3919 3920 3925 3926 3927 3928 3929 3930 3932 3933 3935 3936 3937 3938 3940
## 1 1 2 1 1 1 3 2 1 3 1 2 1 1 1 1
## 3941 3942 3943 3944 3945 3948 3949 3951 3952 3954 3955 3956 3957 3958 3961 3963
## 1 2 1 1 2 2 1 1 1 3 1 2 2 1 3 1
## 3964 3966 3967 3968 3971 3972 3974 3976 3977 3978 3979 3980 3981 3982 3985 3986
## 1 2 1 1 2 1 2 1 1 3 1 1 1 1 1 1
## 3987 3989 3990 3994 3995 3996 3997 3998 3999 4001 4002 4003 4005 4007 4008 4009
## 1 2 1 3 1 1 1 2 1 1 1 2 1 3 1 1
## 4010 4011 4013 4014 4015 4016 4017 4018 4020 4021 4022 4024 4026 4027 4028 4029
## 3 3 1 3 1 2 1 1 2 1 1 1 2 1 2 1
## 4030 4032 4033 4034 4035 4036 4039 4040 4042 4044 4045 4046 4049 4050 4051 4052
## 2 1 3 1 1 1 1 2 2 2 1 3 2 1 1 1
## 4053 4056 4057 4058 4060 4061 4062 4063 4065 4066 4068 4069 4070 4072 4073 4074
## 1 2 1 1 1 1 2 1 1 2 2 1 1 2 2 1
## 4075 4077 4078 4079 4081 4082 4084 4085 4086 4087 4089 4090 4092 4094 4095 4096
## 1 1 2 1 3 1 2 2 1 1 2 3 2 1 1 1
## 4097 4098 4099 4102 4104
## 2 2 2 1 2
##
## Silhouette plot information for best sample:
## cluster neighbor sil_width
## 1783 1 2 0.751297368
## 785 1 2 0.750491513
## 1514 1 2 0.750155393
## 1379 1 2 0.749921569
## 3361 1 2 0.749801337
## 2370 1 2 0.749754666
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##
## 1035 dissimilarities, summarized :
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.001917 0.044045 0.105970 0.122330 0.168800 0.396860
## Metric : euclidean
## Number of objects : 46
##
## Available components:
## [1] "sample" "medoids" "i.med" "clustering" "objective"
## [6] "clusinfo" "diss" "call" "silinfo" "data"
## [11] "clust_plot" "nbclust"
fviz_cluster(clara_flex)
fviz_silhouette(clara_flex)
## cluster size ave.sil.width
## 1 1 1754 0.62
## 2 2 996 0.47
## 3 3 311 0.67
clara_labels = data.frame(clara_flex$clustering)
names(clara_labels)[1] = "Cluster"
# Analysis based on the clustering
'Based on silhouette width for 3 cluster we got 45% for kmeans and 58% for Clara
so it\'s better for this dataset to use Clara for clustering '
## [1] "Based on silhouette width for 3 cluster we got 45% for kmeans and 58% for Clara \n so it's better for this dataset to use Clara for clustering "
'Bind the cluster labels of clara with the dataset'
## [1] "Bind the cluster labels of clara with the dataset"
data_scaled_labeled = cbind(data_scaled,clara_labels)
'Check the data rows'
## [1] "Check the data rows"
head(data_scaled_labeled)
## CustomerID Spending Frequency Recency Cluster
## 1 0.0000000000 0.04245154 0.018629021 0.005021431 1
## 2 0.0003367003 0.01451396 0.006985883 0.048574624 1
## 4 0.0008417508 0.01615179 0.008004657 0.096283806 1
## 9 0.0016835017 0.02001781 0.006112647 0.088076055 1
## 11 0.0020202020 0.04414318 0.020521030 0.152770256 2
## 12 0.0021885522 0.02892680 0.015863775 0.139081365 2
'Visualizing each value of RFM on boxplot for analysis'
## [1] "Visualizing each value of RFM on boxplot for analysis"
boxplot(data_scaled_labeled$Recency ~ data_scaled_labeled$Cluster,
names = c("Cluster1", "Cluster2","Cluster3"),
xlab = "Clusters", ylab = "Recency",
main = "Visualizing Customer Recency")
boxplot(data_scaled_labeled$Frequency ~ data_scaled_labeled$Cluster,
names = c("Cluster1", "Cluster2","Cluster3"),
xlab = "Clusters", ylab = "Frequency",
main = "Visualizing Customer Frequency")
boxplot(data_scaled_labeled$Spending ~ data_scaled_labeled$Cluster,
names = c("Cluster1", "Cluster2","Cluster3"),
xlab = "Clusters", ylab = "Monetary",
main = "Visualizing Customer Monetary")
#Based on Clara Clustering
'
Let\'s discuss each of the customer segments in more detail:
1- Highly Engaged and Valuable Customers (Cluster 1)
This segment is comprised of customers who have recently made many purchases and with high monetary value.
These customers are highly engaged with the brand and are likely to continue making purchases in the future.
Businesses should focus on retaining these customers and maintaining their loyalty. This can be achieved through personalized promotions, exclusive offers, and by providing excellent customer service.
Consider implementing a loyalty program or VIP program for this segment to further incentivize repeat purchases.
This segment is a prime target for upselling and cross-selling opportunities. Offer these customers complementary products or services to enhance their experience with your brand.
2- Less Engaged and Moderate Purchasing Power Customers (Cluster 2)
This segment is comprised of customers who have a moderate level of recent purchases and monetary value.
These customers may be less engaged with the brand and may not be making purchases as frequently as the first cluster.
To increase engagement and drive repeat purchases, businesses should focus on providing targeted and relevant promotions, offers, and advertisements.
Consider gathering more information on these customers, such as their preferences and purchasing history, to create a more personalized experience.
This segment may also be open to trying new products or services, so businesses can use this as an opportunity to introduce new offerings and expand their customer base.
3- Less Engaged and Less Valuable Customers (Cluster 3)
This segment is comprised of customers who have made few purchases in recent times and with low monetary value.
These customers are less engaged and are not as valuable to the business as the other two clusters.
To increase engagement and drive repeat purchases, businesses can offer special promotions or discounts to this segment.
Consider gathering more information on these customers to determine what may be causing their lack of engagement and address any pain points.
This segment may also be a good target for re-engagement campaigns, such as sending a follow-up email or a special offer to encourage them to make a purchase.
By understanding and targeting each customer segment based on their
recency, frequency, and monetary value, businesses can improve customer engagement and retention,
and optimize their spending on customer acquisition and retention.
'
## [1] "\nLet's discuss each of the customer segments in more detail:\n \n1- Highly Engaged and Valuable Customers (Cluster 1)\nThis segment is comprised of customers who have recently made many purchases and with high monetary value.\nThese customers are highly engaged with the brand and are likely to continue making purchases in the future.\nBusinesses should focus on retaining these customers and maintaining their loyalty. This can be achieved through personalized promotions, exclusive offers, and by providing excellent customer service.\nConsider implementing a loyalty program or VIP program for this segment to further incentivize repeat purchases.\nThis segment is a prime target for upselling and cross-selling opportunities. Offer these customers complementary products or services to enhance their experience with your brand.\n\n2- Less Engaged and Moderate Purchasing Power Customers (Cluster 2)\nThis segment is comprised of customers who have a moderate level of recent purchases and monetary value.\nThese customers may be less engaged with the brand and may not be making purchases as frequently as the first cluster.\nTo increase engagement and drive repeat purchases, businesses should focus on providing targeted and relevant promotions, offers, and advertisements.\nConsider gathering more information on these customers, such as their preferences and purchasing history, to create a more personalized experience.\nThis segment may also be open to trying new products or services, so businesses can use this as an opportunity to introduce new offerings and expand their customer base.\n\n3- Less Engaged and Less Valuable Customers (Cluster 3)\nThis segment is comprised of customers who have made few purchases in recent times and with low monetary value.\nThese customers are less engaged and are not as valuable to the business as the other two clusters.\nTo increase engagement and drive repeat purchases, businesses can offer special promotions or discounts to this segment.\nConsider gathering more information on these customers to determine what may be causing their lack of engagement and address any pain points.\nThis segment may also be a good target for re-engagement campaigns, such as sending a follow-up email or a special offer to encourage them to make a purchase.\n\nBy understanding and targeting each customer segment based on their \nrecency, frequency, and monetary value, businesses can improve customer engagement and retention,\nand optimize their spending on customer acquisition and retention.\n\n"