clustering
Clinton Cabello
2023-06
CASO - USO TARJETA DE CREDITO
Este caso requiere desarrollar una segmentación de clientes para definir la estrategia de marketing.
El conjunto de datos de muestra resume el comportamiento de uso de 8950 titulares de tarjetas de crédito activos durante los últimos 6 meses.
El archivo este a nivel de cliente con 18 variables de comportamiento.
- BALANCE : Saldo que queda en la cuenta del cliente para realizar compras
- BALANCE_FREQUENCY : frecuencia con la que se actualiza el saldo, puntuación entre 0 y 1
- PURCHASES : Importe de las compras realizadas desde la cuenta
- ONEOFF_PURCHASES : importe máximo de compra realizado de una sola vez
- INSTALLMENTS_PURCHASES: Importe de la compra realizada a plazos
- CASH_ADVANCE : Anticipo dado por el usuario
- PURCHASES_FREQUENCY : frecuencia con la que se realizan las compras, puntuación entre 0 y 1
- ONEOFFPURCHASESFREQUENCY : Con qué frecuencia se realizan compras de una sola vez
- PURCHASESINSTALLMENTSFREQUENCY : Frecuencia con la que se realizan compras a plazos.
- CASHADVANCEFREQUENCY : Con qué frecuencia se paga el anticipo en efectivo
- CASHADVANCETRX : Número de transacciones realizadas con “Cash in Advanced”
- PURCHASES_TRX : número de transacciones de compra realizadas
- CREDIT_LIMIT: límite de tarjeta de crédito para el usuario
- PAYMENTS : Monto del pago realizado por el usuario
- MINIMUM_PAYMENTS: cantidad mínima de pagos realizados por el usuario
- PRCFULLPAYMENT : porcentaje del pago total pagado por el usuario
- TENURE : Tenencia del servicio de tarjeta de crédito para el usuario
# Cargamos las librerías adecuadas
library(ggplot2)
library(cluster)
library(cowplot)
library(factoextra)
library(tidyr)
library(klaR)
library(clustMixType)# Cargamos el conjunto de datos
credito<-read.csv("https://raw.githubusercontent.com/VictorGuevaraP/Multivariado_Analisis/master/credit_card.csv",
sep = ";",
stringsAsFactors = T)#Mostramos los datos
head(credito)## CUST_ID BALANCE BALANCE_FREQUENCY PURCHASES ONEOFF_PURCHASES
## 1 C10001 40.90075 0.818182 95.40 0.00
## 2 C10002 3202.46742 0.909091 0.00 0.00
## 3 C10003 2495.14886 1.000000 773.17 773.17
## 4 C10004 1666.67054 0.636364 1499.00 1499.00
## 5 C10005 817.71434 1.000000 16.00 16.00
## 6 C10006 1809.82875 1.000000 1333.28 0.00
## INSTALLMENTS_PURCHASES CASH_ADVANCE PURCHASES_FREQUENCY
## 1 95.40 0.000 0.166667
## 2 0.00 6442.945 0.000000
## 3 0.00 0.000 1.000000
## 4 0.00 205.788 0.083333
## 5 0.00 0.000 0.083333
## 6 1333.28 0.000 0.666667
## ONEOFF_PURCHASES_FREQUENCY PURCHASES_INSTALLMENTS_FREQUENCY
## 1 0.000000 0.083333
## 2 0.000000 0.000000
## 3 1.000000 0.000000
## 4 0.083333 0.000000
## 5 0.083333 0.000000
## 6 0.000000 0.583333
## CASH_ADVANCE_FREQUENCY CASH_ADVANCE_TRX PURCHASES_TRX CREDIT_LIMIT PAYMENTS
## 1 0.000000 0 2 1000 201.8021
## 2 0.250000 4 0 7000 4103.0326
## 3 0.000000 0 12 7500 622.0667
## 4 0.083333 1 1 7500 0.0000
## 5 0.000000 0 1 1200 678.3348
## 6 0.000000 0 8 1800 1400.0578
## MINIMUM_PAYMENTS PRC_FULL_PAYMENT TENURE
## 1 139.5098 0.000000 12
## 2 1072.3402 0.222222 12
## 3 627.2848 0.000000 12
## 4 NA 0.000000 12
## 5 244.7912 0.000000 12
## 6 2407.2460 0.000000 12#Verificamos la estructura de los datos
str(credito)## 'data.frame': 8950 obs. of 18 variables:
## $ CUST_ID : Factor w/ 8950 levels "C10001","C10002",..: 1 2 3 4 5 6 7 8 9 10 ...
## $ BALANCE : num 40.9 3202.5 2495.1 1666.7 817.7 ...
## $ BALANCE_FREQUENCY : num 0.818 0.909 1 0.636 1 ...
## $ PURCHASES : num 95.4 0 773.2 1499 16 ...
## $ ONEOFF_PURCHASES : num 0 0 773 1499 16 ...
## $ INSTALLMENTS_PURCHASES : num 95.4 0 0 0 0 ...
## $ CASH_ADVANCE : num 0 6443 0 206 0 ...
## $ PURCHASES_FREQUENCY : num 0.1667 0 1 0.0833 0.0833 ...
## $ ONEOFF_PURCHASES_FREQUENCY : num 0 0 1 0.0833 0.0833 ...
## $ PURCHASES_INSTALLMENTS_FREQUENCY: num 0.0833 0 0 0 0 ...
## $ CASH_ADVANCE_FREQUENCY : num 0 0.25 0 0.0833 0 ...
## $ CASH_ADVANCE_TRX : int 0 4 0 1 0 0 0 0 0 0 ...
## $ PURCHASES_TRX : int 2 0 12 1 1 8 64 12 5 3 ...
## $ CREDIT_LIMIT : num 1000 7000 7500 7500 1200 1800 13500 2300 7000 11000 ...
## $ PAYMENTS : num 202 4103 622 0 678 ...
## $ MINIMUM_PAYMENTS : num 140 1072 627 NA 245 ...
## $ PRC_FULL_PAYMENT : num 0 0.222 0 0 0 ...
## $ TENURE : int 12 12 12 12 12 12 12 12 12 12 ...# Seleccionamos solo las numericas
numericos = sapply(credito,is.numeric)# Me quedo solo con las numericas
creditonum<- credito[ ,numericos]
head(creditonum)## BALANCE BALANCE_FREQUENCY PURCHASES ONEOFF_PURCHASES
## 1 40.90075 0.818182 95.40 0.00
## 2 3202.46742 0.909091 0.00 0.00
## 3 2495.14886 1.000000 773.17 773.17
## 4 1666.67054 0.636364 1499.00 1499.00
## 5 817.71434 1.000000 16.00 16.00
## 6 1809.82875 1.000000 1333.28 0.00
## INSTALLMENTS_PURCHASES CASH_ADVANCE PURCHASES_FREQUENCY
## 1 95.40 0.000 0.166667
## 2 0.00 6442.945 0.000000
## 3 0.00 0.000 1.000000
## 4 0.00 205.788 0.083333
## 5 0.00 0.000 0.083333
## 6 1333.28 0.000 0.666667
## ONEOFF_PURCHASES_FREQUENCY PURCHASES_INSTALLMENTS_FREQUENCY
## 1 0.000000 0.083333
## 2 0.000000 0.000000
## 3 1.000000 0.000000
## 4 0.083333 0.000000
## 5 0.083333 0.000000
## 6 0.000000 0.583333
## CASH_ADVANCE_FREQUENCY CASH_ADVANCE_TRX PURCHASES_TRX CREDIT_LIMIT PAYMENTS
## 1 0.000000 0 2 1000 201.8021
## 2 0.250000 4 0 7000 4103.0326
## 3 0.000000 0 12 7500 622.0667
## 4 0.083333 1 1 7500 0.0000
## 5 0.000000 0 1 1200 678.3348
## 6 0.000000 0 8 1800 1400.0578
## MINIMUM_PAYMENTS PRC_FULL_PAYMENT TENURE
## 1 139.5098 0.000000 12
## 2 1072.3402 0.222222 12
## 3 627.2848 0.000000 12
## 4 NA 0.000000 12
## 5 244.7912 0.000000 12
## 6 2407.2460 0.000000 12—-ANÁLISIS EXPLORATORIO—-
verificamos que existen datos perdidos, por lo tanto se debe realizar una corrección de tales datos.
# Resumen de los datos
summary(creditonum)## BALANCE BALANCE_FREQUENCY PURCHASES ONEOFF_PURCHASES
## Min. : 0.0 Min. :0.0000 Min. : 0.00 Min. : 0.0
## 1st Qu.: 128.3 1st Qu.:0.8889 1st Qu.: 39.63 1st Qu.: 0.0
## Median : 873.4 Median :1.0000 Median : 361.28 Median : 38.0
## Mean : 1564.5 Mean :0.8773 Mean : 1003.20 Mean : 592.4
## 3rd Qu.: 2054.1 3rd Qu.:1.0000 3rd Qu.: 1110.13 3rd Qu.: 577.4
## Max. :19043.1 Max. :1.0000 Max. :49039.57 Max. :40761.2
##
## INSTALLMENTS_PURCHASES CASH_ADVANCE PURCHASES_FREQUENCY
## Min. : 0.0 Min. : 0.0 Min. :0.00000
## 1st Qu.: 0.0 1st Qu.: 0.0 1st Qu.:0.08333
## Median : 89.0 Median : 0.0 Median :0.50000
## Mean : 411.1 Mean : 978.9 Mean :0.49035
## 3rd Qu.: 468.6 3rd Qu.: 1113.8 3rd Qu.:0.91667
## Max. :22500.0 Max. :47137.2 Max. :1.00000
##
## ONEOFF_PURCHASES_FREQUENCY PURCHASES_INSTALLMENTS_FREQUENCY
## Min. :0.00000 Min. :0.0000
## 1st Qu.:0.00000 1st Qu.:0.0000
## Median :0.08333 Median :0.1667
## Mean :0.20246 Mean :0.3644
## 3rd Qu.:0.30000 3rd Qu.:0.7500
## Max. :1.00000 Max. :1.0000
##
## CASH_ADVANCE_FREQUENCY CASH_ADVANCE_TRX PURCHASES_TRX CREDIT_LIMIT
## Min. :0.0000 Min. : 0.000 Min. : 0.00 Min. : 50
## 1st Qu.:0.0000 1st Qu.: 0.000 1st Qu.: 1.00 1st Qu.: 1600
## Median :0.0000 Median : 0.000 Median : 7.00 Median : 3000
## Mean :0.1351 Mean : 3.249 Mean : 14.71 Mean : 4494
## 3rd Qu.:0.2222 3rd Qu.: 4.000 3rd Qu.: 17.00 3rd Qu.: 6500
## Max. :1.5000 Max. :123.000 Max. :358.00 Max. :30000
## NA's :1
## PAYMENTS MINIMUM_PAYMENTS PRC_FULL_PAYMENT TENURE
## Min. : 0.0 Min. : 0.02 Min. :0.0000 Min. : 6.00
## 1st Qu.: 383.3 1st Qu.: 169.12 1st Qu.:0.0000 1st Qu.:12.00
## Median : 856.9 Median : 312.34 Median :0.0000 Median :12.00
## Mean : 1733.1 Mean : 864.21 Mean :0.1537 Mean :11.52
## 3rd Qu.: 1901.1 3rd Qu.: 825.49 3rd Qu.:0.1429 3rd Qu.:12.00
## Max. :50721.5 Max. :76406.21 Max. :1.0000 Max. :12.00
## NA's :313# Verificacion de datos perdidos
library(DataExplorer)
plot_missing(creditonum)
# Para ver las variables con valores perdidos
which(colSums(is.na(creditonum))!=0)## CREDIT_LIMIT MINIMUM_PAYMENTS
## 13 15# Graficar la cantidad de valores perdidos
library(VIM)
#windows()
graf_perdidos1 <- aggr(creditonum,prop = F,
numbers = TRUE,
sortVars=T,
cex.axis=0.5)
##
## Variables sorted by number of missings:
## Variable Count
## MINIMUM_PAYMENTS 313
## CREDIT_LIMIT 1
## BALANCE 0
## BALANCE_FREQUENCY 0
## PURCHASES 0
## ONEOFF_PURCHASES 0
## INSTALLMENTS_PURCHASES 0
## CASH_ADVANCE 0
## PURCHASES_FREQUENCY 0
## ONEOFF_PURCHASES_FREQUENCY 0
## PURCHASES_INSTALLMENTS_FREQUENCY 0
## CASH_ADVANCE_FREQUENCY 0
## CASH_ADVANCE_TRX 0
## PURCHASES_TRX 0
## PAYMENTS 0
## PRC_FULL_PAYMENT 0
## TENURE 0library(visdat)
#Visualización gráfica de proporción de datos perdidos y donde se producen.
vis_dat(credito)
#Determinación del porcentaje de datos perdidos.
library(visdat)
vis_miss(credito ,sort_miss = TRUE) 
# Resumen de datos perdidos
summary(graf_perdidos1)##
## Missings per variable:
## Variable Count
## BALANCE 0
## BALANCE_FREQUENCY 0
## PURCHASES 0
## ONEOFF_PURCHASES 0
## INSTALLMENTS_PURCHASES 0
## CASH_ADVANCE 0
## PURCHASES_FREQUENCY 0
## ONEOFF_PURCHASES_FREQUENCY 0
## PURCHASES_INSTALLMENTS_FREQUENCY 0
## CASH_ADVANCE_FREQUENCY 0
## CASH_ADVANCE_TRX 0
## PURCHASES_TRX 0
## CREDIT_LIMIT 1
## PAYMENTS 0
## MINIMUM_PAYMENTS 313
## PRC_FULL_PAYMENT 0
## TENURE 0
##
## Missings in combinations of variables:
## Combinations Count Percent
## 0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0 8636 96.49162011
## 0:0:0:0:0:0:0:0:0:0:0:0:0:0:1:0:0 313 3.49720670
## 0:0:0:0:0:0:0:0:0:0:0:0:1:0:0:0:0 1 0.01117318De la libreria DMwR2 con la funcion centralImputation() + Si la variable es numerica (numeric o integer) reemplaza los valores faltantes con la mediana. + Si la variable es categorica (factor) reemplaza los valores faltantes con la moda.
#Imputacion con el paquete DMwR
library(DMwR2)
creditonum_im <- centralImputation(creditonum)
plot_missing(creditonum_im) 
Estandarización de datos
# Para estandarizar los datos (center y scale)
credito_st <- as.data.frame(scale(creditonum_im))
str(credito_st)## 'data.frame': 8950 obs. of 17 variables:
## $ BALANCE : num -0.7319 0.7869 0.4471 0.0491 -0.3588 ...
## $ BALANCE_FREQUENCY : num -0.249 0.134 0.518 -1.017 0.518 ...
## $ PURCHASES : num -0.425 -0.47 -0.108 0.232 -0.462 ...
## $ ONEOFF_PURCHASES : num -0.357 -0.357 0.109 0.546 -0.347 ...
## $ INSTALLMENTS_PURCHASES : num -0.349 -0.455 -0.455 -0.455 -0.455 ...
## $ CASH_ADVANCE : num -0.467 2.605 -0.467 -0.369 -0.467 ...
## $ PURCHASES_FREQUENCY : num -0.806 -1.222 1.27 -1.014 -1.014 ...
## $ ONEOFF_PURCHASES_FREQUENCY : num -0.679 -0.679 2.673 -0.399 -0.399 ...
## $ PURCHASES_INSTALLMENTS_FREQUENCY: num -0.707 -0.917 -0.917 -0.917 -0.917 ...
## $ CASH_ADVANCE_FREQUENCY : num -0.675 0.574 -0.675 -0.259 -0.675 ...
## $ CASH_ADVANCE_TRX : num -0.476 0.11 -0.476 -0.33 -0.476 ...
## $ PURCHASES_TRX : num -0.511 -0.592 -0.109 -0.552 -0.552 ...
## $ CREDIT_LIMIT : num -0.96 0.689 0.826 0.826 -0.905 ...
## $ PAYMENTS : num -0.529 0.819 -0.384 -0.599 -0.364 ...
## $ MINIMUM_PAYMENTS : num -0.3024 0.0975 -0.0933 -0.2283 -0.2573 ...
## $ PRC_FULL_PAYMENT : num -0.526 0.234 -0.526 -0.526 -0.526 ...
## $ TENURE : num 0.361 0.361 0.361 0.361 0.361 ...head(credito_st)## BALANCE BALANCE_FREQUENCY PURCHASES ONEOFF_PURCHASES
## 1 -0.7319485 -0.2494205 -0.4248760 -0.3569141
## 2 0.7869169 0.1343172 -0.4695256 -0.3569141
## 3 0.4471102 0.5180549 -0.1076622 0.1088824
## 4 0.0490964 -1.0168960 0.2320449 0.5461589
## 5 -0.3587553 0.5180549 -0.4620372 -0.3472749
## 6 0.1178718 0.5180549 0.1544837 -0.3569141
## INSTALLMENTS_PURCHASES CASH_ADVANCE PURCHASES_FREQUENCY
## 1 -0.3490593 -0.4667595 -0.8064453
## 2 -0.4545508 2.6054589 -1.2216898
## 3 -0.4545508 -0.4667595 1.2697723
## 4 -0.4545508 -0.3686327 -1.0140688
## 5 -0.4545508 -0.4667595 -1.0140688
## 6 1.0197650 -0.4667595 0.4392858
## ONEOFF_PURCHASES_FREQUENCY PURCHASES_INSTALLMENTS_FREQUENCY
## 1 -0.6786229 -0.7072736
## 2 -0.6786229 -0.9169440
## 3 2.6733017 -0.9169440
## 4 -0.3992970 -0.9169440
## 5 -0.3992970 -0.9169440
## 6 -0.6786229 0.5507533
## CASH_ADVANCE_FREQUENCY CASH_ADVANCE_TRX PURCHASES_TRX CREDIT_LIMIT PAYMENTS
## 1 -0.6753111 -0.4760432 -0.5113047 -0.9603247 -0.5289492
## 2 0.5739307 0.1100677 -0.5917628 0.6886400 0.8185964
## 3 -0.6753111 -0.4760432 -0.1090140 0.8260537 -0.3837833
## 4 -0.2588989 -0.3295155 -0.5515337 0.8260537 -0.5986548
## 5 -0.6753111 -0.4760432 -0.5515337 -0.9053593 -0.3643474
## 6 -0.6753111 -0.4760432 -0.2699303 -0.7404628 -0.1150531
## MINIMUM_PAYMENTS PRC_FULL_PAYMENT TENURE
## 1 -0.30238310 -0.5255216 0.3606594
## 2 0.09749408 0.2342138 0.3606594
## 3 -0.09328819 -0.5255216 0.3606594
## 4 -0.22829414 -0.5255216 0.3606594
## 5 -0.25725202 -0.5255216 0.3606594
## 6 0.66972926 -0.5255216 0.3606594# Histograma para las variables numuricas
plot_histogram(credito_st)
# Gráfico de variables numéricas
library(funModeling)
plot_num(credito_st)
# Descripción de los datos
df_status(credito_st)## variable q_zeros p_zeros q_na p_na q_inf p_inf
## 1 BALANCE 0 0 0 0 0 0
## 2 BALANCE_FREQUENCY 0 0 0 0 0 0
## 3 PURCHASES 0 0 0 0 0 0
## 4 ONEOFF_PURCHASES 0 0 0 0 0 0
## 5 INSTALLMENTS_PURCHASES 0 0 0 0 0 0
## 6 CASH_ADVANCE 0 0 0 0 0 0
## 7 PURCHASES_FREQUENCY 0 0 0 0 0 0
## 8 ONEOFF_PURCHASES_FREQUENCY 0 0 0 0 0 0
## 9 PURCHASES_INSTALLMENTS_FREQUENCY 0 0 0 0 0 0
## 10 CASH_ADVANCE_FREQUENCY 0 0 0 0 0 0
## 11 CASH_ADVANCE_TRX 0 0 0 0 0 0
## 12 PURCHASES_TRX 0 0 0 0 0 0
## 13 CREDIT_LIMIT 0 0 0 0 0 0
## 14 PAYMENTS 0 0 0 0 0 0
## 15 MINIMUM_PAYMENTS 0 0 0 0 0 0
## 16 PRC_FULL_PAYMENT 0 0 0 0 0 0
## 17 TENURE 0 0 0 0 0 0
## type unique
## 1 numeric 8871
## 2 numeric 43
## 3 numeric 6203
## 4 numeric 4014
## 5 numeric 4452
## 6 numeric 4323
## 7 numeric 47
## 8 numeric 47
## 9 numeric 47
## 10 numeric 54
## 11 numeric 65
## 12 numeric 173
## 13 numeric 205
## 14 numeric 8711
## 15 numeric 8636
## 16 numeric 47
## 17 numeric 7# Descripción de las variables numéricas
profiling_num(credito_st)## variable mean std_dev variation_coef
## 1 BALANCE -4.166148e-17 1 -2.400299e+16
## 2 BALANCE_FREQUENCY 1.634398e-16 1 6.118459e+15
## 3 PURCHASES -1.950644e-18 1 -5.126512e+17
## 4 ONEOFF_PURCHASES 4.059523e-17 1 2.463344e+16
## 5 INSTALLMENTS_PURCHASES 1.865327e-17 1 5.360991e+16
## 6 CASH_ADVANCE -1.604997e-17 1 -6.230541e+16
## 7 PURCHASES_FREQUENCY 2.502245e-17 1 3.996411e+16
## 8 ONEOFF_PURCHASES_FREQUENCY -1.315382e-17 1 -7.602355e+16
## 9 PURCHASES_INSTALLMENTS_FREQUENCY 6.405602e-17 1 1.561133e+16
## 10 CASH_ADVANCE_FREQUENCY 1.353447e-17 1 7.388545e+16
## 11 CASH_ADVANCE_TRX -1.933616e-17 1 -5.171657e+16
## 12 PURCHASES_TRX -1.239018e-17 1 -8.070909e+16
## 13 CREDIT_LIMIT 7.231110e-17 1 1.382914e+16
## 14 PAYMENTS -3.326757e-17 1 -3.005930e+16
## 15 MINIMUM_PAYMENTS 3.083174e-18 1 3.243411e+17
## 16 PRC_FULL_PAYMENT 1.128662e-17 1 8.860051e+16
## 17 TENURE 2.960341e-16 1 3.377989e+15
## p_01 p_05 p_25 p_50 p_75 p_95
## 1 -0.7515665 -0.7473632 -0.68996921 -0.33201009 0.235242714 2.0872306
## 2 -3.3193265 -2.5518510 0.04904212 0.51805488 0.518054879 0.5180549
## 3 -0.4695256 -0.4695256 -0.45097545 -0.30043732 0.050043726 1.4019311
## 4 -0.3569141 -0.3569141 -0.35691408 -0.33402097 -0.009056257 1.2522873
## 5 -0.4545508 -0.4545508 -0.45455083 -0.35613632 0.063659658 1.4806629
## 6 -0.4667595 -0.4667595 -0.46675948 -0.46675948 0.064348823 1.7491709
## 7 -1.2216898 -1.2216898 -1.01406879 0.02404124 1.062151276 1.2697723
## 8 -0.6786229 -0.6786229 -0.67862289 -0.39929696 0.326954491 2.6733017
## 9 -0.9169440 -0.9169440 -0.91694396 -0.49760082 0.970096395 1.5991098
## 10 -0.6753111 -0.6753111 -0.67531113 -0.67531113 0.435124903 2.2395847
## 11 -0.4760432 -0.4760432 -0.47604322 -0.47604322 0.110067702 1.7218727
## 12 -0.5917628 -0.5917628 -0.55153375 -0.31015935 0.092131303 1.7012939
## 13 -1.0977385 -0.9603247 -0.79542828 -0.41066984 0.551226236 2.0627772
## 14 -0.5986548 -0.5675712 -0.46626527 -0.30266771 0.058026516 1.5021938
## 15 -0.3535961 -0.3301891 -0.28894519 -0.22829414 -0.024088413 0.8036121
## 16 -0.5255216 -0.5255216 -0.52552161 -0.52552161 -0.037120268 2.8932912
## 17 -4.1225372 -2.6281384 0.36065939 0.36065939 0.360659394 0.3606594
## p_99 skewness kurtosis iqr
## 1 3.7349080 2.39298490 10.669794 0.9252119
## 2 0.5180549 -2.02292641 6.089972 0.4690128
## 3 3.7320768 8.14290404 114.325882 0.5010192
## 4 3.6734172 10.04339927 167.095191 0.3478578
## 5 3.8427805 7.29789654 99.520563 0.5182105
## 6 4.1052072 5.16574312 55.869216 0.5311083
## 7 1.2697723 0.06015415 1.361614 2.0762201
## 8 2.6733017 1.53535541 4.160526 1.0055774
## 9 1.5991098 0.50911582 1.601479 1.8870404
## 10 3.4888265 1.82837977 6.332201 1.1104360
## 11 3.7732610 5.72033928 64.611758 0.5861109
## 12 4.0953256 4.62987914 37.772995 0.6436651
## 13 3.4369145 1.52238075 5.835116 1.3466545
## 14 4.1020070 5.90662964 57.739472 0.5242918
## 15 3.3358241 13.85012475 296.555553 0.2648568
## 16 2.8932912 1.94249431 5.430366 0.4884013
## 17 0.3606594 -2.94252402 10.689855 0.0000000
## range_98
## 1 [-0.751566546987758, 3.73490796035832]
## 2 [-3.31932646420056, 0.518054878864647]
## 3 [-0.469525649414068, 3.73207683134817]
## 4 [-0.35691408120146, 3.67341720184473]
## 5 [-0.45455083424524, 3.84278047888461]
## 6 [-0.466759476151324, 4.10520719921743]
## 7 [-1.22168980074932, 1.26977228649778]
## 8 [-0.678622892777191, 2.67330172076504]
## 9 [-0.916943961286405, 1.59910984744428]
## 10 [-0.675311127842014, 3.4888264874028]
## 11 [-0.476043220613547, 3.77326096861664]
## 12 [-0.591762814625347, 4.09532563388242]
## 13 [-1.09773847265287, 3.43691447746774]
## 14 [-0.598654813004152, 4.10200696280094]
## 15 [-0.353596051481219, 3.33582406894981]
## 16 [-0.525521609873799, 2.89329120354813]
## 17 [-4.12253723970077, 0.360659393995693]
## range_80
## 1 [-0.740271774881679, 1.3327150337213]
## 2 [-1.7843756154221, 0.518054878864647]
## 3 [-0.469525649414068, 0.720487740600691]
## 4 [-0.35691408120146, 0.607066066608701]
## 5 [-0.45455083424524, 0.806117029763679]
## 6 [-0.466759476151324, 0.994993033579468]
## 7 [-1.22168980074932, 1.26977228649778]
## 8 [-0.678622892777191, 1.83532056737948]
## 9 [-0.916943961286405, 1.59910984744428]
## 10 [-0.675311127842014, 1.40676017826396]
## 11 [-0.476043220613547, 0.989234086017551]
## 12 [-0.591762814625347, 0.896712617481659]
## 13 [-0.905359256587151, 1.37570859104928]
## 14 [-0.536612286800153, 0.75672350398168]
## 15 [-0.315405461511987, 0.380138087021043]
## 16 [-0.525521609873799, 1.76508400076278]
## 17 [-1.13373948390313, 0.360659393995693]Graficando cada variable usando ggplot2
ggplot(credito_st, aes(x=" ",y=BALANCE )) +
geom_boxplot(fill="red") +
labs(title = "Monto del saldo que queda en su cuenta para realizar compras",x=" ") -> g1; g1
ggplot(credito_st, aes(x=" ",y=BALANCE_FREQUENCY)) +
geom_boxplot(fill="green") +
labs(title = "recuencia de actualizaci?n del saldo",x=" ") -> g2; g2
ggplot(credito_st, aes(x=" ",y=PURCHASES)) +
geom_boxplot(fill="blue") +
labs(title = "cantidad de compras realizadas desde la cuenta",x=" ") -> g3; g3
ggplot(credito_st, aes(x=" ",y=ONEOFF_PURCHASES)) +
geom_boxplot(fill="yellow") +
labs(title = "cantidad m?xima de compra realizada",x=" ") -> g4; g4
ggplot(credito_st, aes(x=" ",y=INSTALLMENTS_PURCHASES)) +
geom_boxplot(fill="aliceblue") +
labs(title = "cantidad de compra a plazos",x=" ") -> g5; g5
ggplot(credito_st, aes(x=" ",y=CASH_ADVANCE)) +
geom_boxplot(fill="dodgerblue") +
labs(title = "pago por adelantado dado por el usuario",x=" ") -> g6; g6
ggplot(credito_st, aes(x=" ",y=PURCHASES_FREQUENCY)) +
geom_boxplot(fill="bisque2") +
labs(title = "Con qu? frecuencia se realizan las Compras",x=" ") -> g7; g7
ggplot(credito_st, aes(x=" ",y=ONEOFF_PURCHASES_FREQUENCY)) +
geom_boxplot(fill="brown1") +
labs(title = "Con qu? frecuencia se realizan Compras en one-go",x=" ") -> g8; g8
ggplot(credito_st, aes(x=" ",y=PURCHASES_INSTALLMENTS_FREQUENCY)) +
geom_boxplot(fill="burlywood") +
labs(title = "Frecuencia con la que se realizan las compras a plazos",x=" ") -> g9; g9 
ggplot(credito_st, aes(x=" ",y=CASH_ADVANCE_FREQUENCY)) +
geom_boxplot(fill="coral") +
labs(title = "Frecuencia con la que se paga el anticipo de efectivo",x=" ") -> g10; g10
ggplot(credito_st, aes(x=" ",y=CASH_ADVANCE_TRX )) +
geom_boxplot(fill="red") +
labs(title = "N?mero de transacciones realizadas con Efectivo en anticipo",x=" ") -> g11; g11
ggplot(credito_st, aes(x=" ",y=PURCHASES_TRX)) +
geom_boxplot(fill="green") +
labs(title = "N?mero de transacciones de compra realizado",x=" ") -> g12; g12
ggplot(credito_st, aes(x=" ",y=CREDIT_LIMIT)) +
geom_boxplot(fill="blue") +
labs(title = "L?mite de tarjeta de cr?dito",x=" ") -> g13; g13
ggplot(credito_st, aes(x=" ",y=PAYMENTS)) +
geom_boxplot(fill="yellow") +
labs(title = "Monto del pago realizado por el usuario",x=" ") -> g14; g14
ggplot(credito_st, aes(x=" ",y=MINIMUM_PAYMENTS)) +
geom_boxplot(fill="aliceblue") +
labs(title = "Monto m?nimo de los pagos realizados por el usuario",x=" ") -> g15; g15
ggplot(credito_st, aes(x=" ",y=PRC_FULL_PAYMENT)) +
geom_boxplot(fill="dodgerblue") +
labs(title = "Porcentaje del pago total pagado por el usuario",x=" ") -> g16; g16
ggplot(credito_st, aes(x=" ",y=TENURE)) +
geom_boxplot(fill="bisque2") +
labs(title = "Tenencia del servicio de tarjeta de cr?dito para el usuario",x=" ") -> g17; g17
library(cowplot)
plot_grid(g1,g2,g3,g4,g5,g6,g7,g8,g9, ncol = 3)
plot_grid(g10, g11,g12,g13,g14,g15,g16,g17, ncol = 3)
—CLUSTER DE PARTICIÓN—-
k-means. es una técnica para encontrar y clasificar K grupos de datos (clusters).
Determinando el número de clusters.- Criterio de la Suma de Cuadrados (SSE)
# Usando la función kmeans()
set.seed(123)
wss <- numeric()
for(k in 1:10){
b<-kmeans(credito_st,k)
wss[k]<-b$tot.withinss
}
wss## [1] 152133.00 127770.02 111960.85 99050.87 92121.04 86360.82 79491.90
## [8] 81335.79 73034.05 68183.62wss1 <- data.frame(cluster=c(1:10),wss)library(ggplot2)
ggplot(wss1,aes(cluster,wss)) + geom_line(color="red") +
geom_point(color="red") +
geom_vline(xintercept = 7, linetype = 2) +
labs(title = "Metodo Elbow") +
scale_x_continuous(breaks=1:10)
# Usando la función fviz_nbclust() del paquete factoextra
library(factoextra)
set.seed(123) # Iniciamos una semilla
fviz_nbclust(credito_st,
kmeans,
method = "wss") +
geom_vline(xintercept = 7, linetype = 2) +
labs(subtitle = "Método Elbow")
Evaluación de grupos con coeficiente de silueta
# Usando la función k-means
library(cluster)
set.seed(123)
distancias_tc <- daisy(credito_st)
par(mfrow=c(1,4))
for(h in 2:8){
clu=kmeans(credito_st,h)
plot(silhouette(clu$cluster,distancias_tc))
}
par(mfrow=c(1,1))
# Usando el paquete factoextra
library(factoextra)
set.seed(123)
fviz_nbclust(credito_st, kmeans, method = "silhouette") +
labs(subtitle = "Silhouette method")
# Criterio de C-H
library(fpc)
kmeansruns(credito_st,criterion="ch")## K-means clustering with 2 clusters of sizes 5237, 3713
##
## Cluster means:
## BALANCE BALANCE_FREQUENCY PURCHASES ONEOFF_PURCHASES
## 1 0.06257995 -0.2047935 -0.3397108 -0.2352350
## 2 -0.08826587 0.2888509 0.4791450 0.3317872
## INSTALLMENTS_PURCHASES CASH_ADVANCE PURCHASES_FREQUENCY
## 1 -0.3708736 0.1818311 -0.7334872
## 2 0.5230986 -0.2564636 1.0345469
## ONEOFF_PURCHASES_FREQUENCY PURCHASES_INSTALLMENTS_FREQUENCY
## 1 -0.3804022 -0.6539609
## 2 0.5365381 0.9223790
## CASH_ADVANCE_FREQUENCY CASH_ADVANCE_TRX PURCHASES_TRX CREDIT_LIMIT PAYMENTS
## 1 0.2713543 0.1902565 -0.4563959 -0.1187027 -0.1120354
## 2 -0.3827316 -0.2683472 0.6437235 0.1674241 0.1580202
## MINIMUM_PAYMENTS PRC_FULL_PAYMENT TENURE
## 1 -0.006065258 -0.2834074 -0.08520623
## 2 0.008554742 0.3997319 0.12017910
##
## Clustering vector:
## [1] 1 1 2 1 1 2 2 2 1 1 2 1 2 2 1 1 1 1 2 2 1 2 2 2 1 2 1 2 1 1 2 2 1 2 2 1 1
## [38] 2 1 1 1 1 1 1 2 1 1 1 2 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1 2 1 2 2 1 1
## [75] 1 2 2 2 1 1 2 1 1 2 2 2 2 2 1 1 2 1 1 1 1 1 2 1 1 1 1 2 2 2 1 1 2 1 1 2 2
## [112] 1 2 1 2 2 2 1 1 1 2 1 2 1 1 2 1 2 1 1 1 2 1 1 2 1 2 2 2 2 1 1 1 2 2 1 2 1
## [149] 1 2 2 2 2 2 2 1 2 1 2 1 1 1 2 1 2 1 2 2 2 2 1 2 1 1 2 1 1 1 2 1 2 1 1 1 2
## [186] 2 1 2 1 1 1 1 1 2 1 2 2 2 1 1 1 1 2 1 2 1 1 1 2 1 1 1 1 2 1 1 2 1 1 2 2 2
## [223] 1 2 2 1 2 2 1 2 2 2 2 1 2 2 1 1 1 1 1 2 2 1 2 1 2 2 1 2 1 2 1 2 1 1 1 2 2
## [260] 1 1 2 2 2 1 2 2 2 1 2 2 1 2 2 2 1 1 1 2 2 2 2 1 2 1 1 1 1 1 1 2 1 1 1 2 2
## [297] 1 1 2 2 1 2 1 2 1 2 2 2 1 2 2 2 2 1 1 1 1 2 2 2 1 1 1 1 1 2 2 2 1 2 1 2 2
## [334] 2 1 1 1 2 1 2 1 1 1 1 2 1 2 2 2 2 1 2 1 1 1 2 2 1 1 1 2 1 1 2 1 2 1 2 1 1
## [371] 2 2 1 2 2 1 2 2 1 1 1 1 1 1 2 1 1 1 2 1 1 2 1 2 1 1 2 1 1 2 2 2 1 2 1 1 1
## [408] 1 1 2 1 2 1 1 2 2 1 2 2 2 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 2 2 1 2 1 1 1 2
## [445] 2 2 2 1 1 1 2 2 2 1 2 2 2 2 1 2 2 2 2 2 1 1 2 2 2 1 1 1 2 1 1 1 2 2 1 1 1
## [482] 2 1 1 2 2 1 2 1 2 2 1 2 1 2 1 1 1 2 2 2 2 2 2 2 2 2 2 1 2 2 2 1 2 2 2 1 1
## [519] 2 1 1 2 1 2 2 1 1 1 2 2 2 2 1 1 2 1 2 1 1 2 2 1 1 1 2 2 2 2 2 1 2 2 1 2 1
## [556] 2 1 1 1 1 2 1 1 2 1 2 2 2 1 1 1 1 1 1 2 1 1 1 1 1 1 2 1 1 2 2 1 2 1 2 2 2
## [593] 1 1 1 1 1 2 2 1 1 1 1 2 2 1 1 2 1 2 2 1 2 2 1 1 2 2 1 2 2 1 2 2 2 1 2 2 2
## [630] 2 2 1 1 2 2 1 1 1 1 2 2 1 2 2 2 2 1 2 1 1 1 2 2 1 1 2 2 1 2 1 1 2 2 1 2 2
## [667] 2 1 2 2 1 1 2 1 1 2 1 2 1 1 1 1 2 2 2 1 2 1 1 2 2 2 2 2 1 2 1 2 2 2 1 1 1
## [704] 1 2 1 1 1 2 2 1 1 2 2 1 2 1 1 1 1 1 1 1 1 1 2 2 1 2 2 1 1 1 2 2 1 1 1 1 1
## [741] 1 2 1 1 1 2 1 1 2 2 1 1 1 1 1 1 2 1 2 2 1 2 1 1 1 1 1 1 1 2 1 2 1 2 1 1 2
## [778] 2 1 2 1 1 2 2 2 2 1 1 1 1 2 2 1 1 1 2 1 2 2 1 1 2 1 1 2 1 2 2 1 2 2 2 1 1
## [815] 1 1 2 1 2 1 1 1 1 1 2 1 1 2 2 1 1 1 1 1 2 2 2 2 2 1 2 1 2 2 2 1 1 2 1 2 1
## [852] 1 1 1 2 1 2 2 1 2 1 2 2 2 2 1 1 1 1 1 1 2 1 1 2 1 2 1 1 1 1 2 1 1 2 1 2 2
## [889] 2 2 2 2 1 1 2 2 2 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 2 2 2 1 2 2 1 2 1 2 1 2 1
## [926] 2 2 1 1 1 1 2 2 1 2 1 2 1 2 1 1 2 1 1 2 1 1 1 1 2 2 2 2 1 1 1 1 1 1 1 2 1
## [963] 1 2 2 2 2 2 1 1 2 2 1 2 1 2 2 1 1 1 1 2 2 1 1 2 1 1 2 1 2 2 1 2 2 1 2 1 2
## [1000] 2 1 1 1 1 1 2 2 1 2 1 2 1 1 1 1 2 1 1 2 2 1 1 2 2 1 2 1 1 1 1 1 2 1 2 1 1
## [1037] 1 1 2 1 1 1 1 2 1 2 1 2 1 1 1 1 2 2 2 2 2 2 2 2 1 2 2 1 1 1 1 1 1 1 1 2 1
## [1074] 1 1 1 1 1 1 2 1 2 1 1 2 1 1 2 1 1 1 1 1 1 1 2 1 1 2 1 1 2 2 2 1 1 1 1 1 1
## [1111] 1 2 1 1 1 1 2 1 2 1 1 1 1 1 1 2 2 1 2 1 1 1 1 1 1 2 1 2 2 2 1 1 2 1 1 1 1
## [1148] 1 2 2 2 2 2 2 1 1 2 1 2 2 2 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 2 2 1 1 1 1 1 2
## [1185] 2 2 1 2 1 1 2 1 1 2 1 1 2 2 2 2 1 2 2 1 1 2 2 1 1 1 1 1 2 2 1 1 2 1 2 1 2
## [1222] 2 1 1 2 1 2 1 1 1 2 1 2 1 2 1 1 1 1 1 2 2 2 1 1 1 1 2 2 1 2 1 1 1 1 2 2 2
## [1259] 2 1 1 1 1 2 2 2 1 1 2 2 2 2 1 1 1 2 1 2 1 2 1 2 1 1 1 2 2 2 2 1 2 1 2 2 1
## [1296] 1 2 2 1 1 2 2 2 1 2 2 2 1 2 1 1 2 1 1 2 1 1 1 2 1 1 2 2 1 1 2 2 1 1 2 1 2
## [1333] 1 1 1 2 1 1 2 2 2 1 2 2 1 1 2 1 1 2 2 2 2 1 1 1 1 2 2 1 2 2 2 1 1 1 2 2 2
## [1370] 2 2 1 1 2 2 1 1 2 1 1 2 2 2 1 2 1 1 1 1 1 2 1 1 1 1 2 2 1 2 2 1 2 1 2 2 1
## [1407] 2 1 1 2 1 2 2 1 1 2 2 1 1 1 2 1 2 2 2 1 1 2 1 1 1 2 2 2 2 1 2 2 2 2 1 1 1
## [1444] 2 2 1 2 2 2 1 1 1 2 1 2 2 1 2 1 2 2 1 1 2 1 2 2 1 2 1 1 2 1 1 2 1 1 2 2 2
## [1481] 1 1 2 2 2 1 1 1 1 1 2 1 1 1 2 1 2 2 2 2 1 2 2 2 1 1 1 2 1 1 2 1 1 1 2 1 1
## [1518] 1 1 2 2 1 2 2 2 1 2 2 1 1 1 1 2 2 2 1 1 1 1 2 1 2 1 1 1 2 1 1 1 2 1 1 2 2
## [1555] 2 1 2 2 1 2 2 1 1 1 1 1 2 2 2 2 1 1 2 1 1 2 1 1 1 1 1 1 2 1 1 2 2 1 2 1 2
## [1592] 2 2 2 1 2 2 2 2 1 1 2 1 2 2 2 2 2 1 2 2 1 1 1 2 2 2 2 2 2 1 1 1 2 2 1 1 1
## [1629] 2 1 1 2 1 1 2 1 1 1 2 2 1 2 2 1 2 1 1 2 1 2 2 1 1 2 2 1 2 2 2 1 1 2 1 2 2
## [1666] 1 2 2 1 2 2 1 2 2 2 1 1 2 2 1 1 2 1 1 2 2 1 2 1 1 2 1 1 1 1 1 1 2 1 1 1 1
## [1703] 2 2 2 1 1 2 2 2 1 2 1 1 2 2 2 2 1 2 2 2 1 2 1 1 1 2 2 2 1 1 1 1 2 1 1 1 2
## [1740] 2 1 2 2 1 2 2 2 2 1 2 1 2 1 2 2 2 2 1 2 2 1 1 2 2 2 2 1 2 2 1 2 2 2 2 1 2
## [1777] 1 1 1 1 1 2 2 1 2 1 1 1 2 1 2 2 1 1 1 1 2 2 1 1 1 1 1 2 1 2 2 1 1 1 1 1 1
## [1814] 2 2 2 1 2 1 1 1 2 2 2 2 1 2 2 2 2 1 1 1 1 2 2 2 2 2 1 2 2 2 2 2 2 1 1 2 1
## [1851] 1 2 1 1 1 2 1 2 1 1 2 2 2 1 2 2 1 2 1 1 2 2 1 2 1 2 2 1 2 1 2 2 1 1 2 1 1
## [1888] 1 1 1 1 2 1 2 1 1 1 1 2 1 1 1 2 2 1 1 2 1 2 1 2 1 2 1 2 2 1 1 2 1 1 2 1 1
## [1925] 1 1 2 1 1 2 2 2 1 1 1 1 2 1 1 1 1 1 1 2 2 1 2 2 2 2 1 1 2 2 2 1 2 2 1 2 1
## [1962] 2 1 2 2 1 1 2 2 1 1 1 1 2 1 2 1 2 1 2 1 1 1 2 1 2 2 1 1 2 2 2 1 2 1 1 2 2
## [1999] 1 2 1 1 1 1 2 1 1 2 1 2 1 1 2 1 1 2 2 1 2 1 1 1 2 2 2 2 1 1 1 2 2 2 2 2 1
## [2036] 1 1 2 1 1 2 1 2 1 1 1 2 2 1 1 1 2 1 1 2 2 1 1 1 2 1 1 1 1 1 1 1 2 2 2 1 2
## [2073] 1 1 2 1 2 2 1 2 1 2 2 1 2 1 2 1 2 1 1 1 2 2 2 2 1 1 1 1 1 1 2 1 1 1 1 2 1
## [2110] 2 2 1 2 1 1 2 2 1 1 1 1 1 2 1 2 2 2 1 2 2 1 1 2 1 2 1 2 1 2 1 2 1 1 2 1 1
## [2147] 2 2 1 1 2 1 2 2 2 1 1 2 2 1 1 2 2 1 2 2 1 1 2 1 1 1 2 1 1 2 2 2 2 1 1 1 2
## [2184] 2 1 2 1 2 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 2 2 1 2 2 2 1 1 2 1 2 1 2 2 2 1
## [2221] 2 1 2 1 1 2 1 1 1 1 2 1 2 2 1 2 2 1 2 2 1 2 1 1 2 2 1 1 1 1 2 2 1 2 1 2 2
## [2258] 2 1 2 1 2 2 1 1 2 1 1 1 1 1 1 2 1 2 1 2 2 1 2 1 1 1 1 1 2 2 2 2 1 2 2 1 2
## [2295] 1 1 2 1 1 1 1 2 1 2 1 1 1 1 2 2 2 2 2 1 2 1 1 2 2 1 1 1 1 1 1 2 1 2 1 1 1
## [2332] 2 2 1 2 1 2 2 1 2 1 2 1 1 1 2 2 2 1 1 1 2 1 1 2 2 1 2 1 2 2 2 2 2 1 1 1 1
## [2369] 2 2 1 1 2 2 2 1 2 1 1 2 2 2 2 1 2 1 1 1 2 1 1 2 2 1 1 2 1 1 2 1 2 1 1 1 2
## [2406] 2 2 1 1 2 1 2 1 1 1 2 2 2 2 1 2 2 1 1 1 1 1 1 1 1 1 2 1 2 2 2 2 1 2 1 2 2
## [2443] 1 2 2 2 2 1 1 1 1 1 2 2 1 1 1 2 1 1 1 1 1 1 2 1 1 2 2 2 1 2 1 2 1 1 2 2 1
## [2480] 2 2 1 1 1 2 2 1 1 1 1 1 2 2 1 1 1 1 1 2 2 2 2 1 2 1 1 2 1 2 2 1 1 1 1 1 2
## [2517] 1 1 2 1 1 1 2 2 2 1 1 2 2 1 2 1 1 1 2 1 2 1 1 2 1 1 1 1 2 2 1 1 1 2 2 2 1
## [2554] 2 1 1 1 1 2 1 2 1 1 1 1 1 1 2 2 1 1 1 1 2 2 1 1 1 2 1 1 1 2 2 1 1 2 1 2 1
## [2591] 2 2 1 1 2 1 1 1 1 1 2 2 1 1 1 1 1 1 1 2 1 1 1 2 1 1 2 1 2 1 2 1 2 1 2 1 1
## [2628] 2 1 2 1 1 2 1 1 2 1 1 1 1 2 2 1 1 1 1 2 2 1 2 1 1 1 2 1 2 2 1 1 1 1 1 2 1
## [2665] 2 2 2 1 2 1 1 2 1 1 1 1 1 1 2 2 1 1 1 2 1 1 2 2 2 1 1 1 1 1 1 1 2 2 2 1 1
## [2702] 1 2 1 1 1 1 2 1 2 1 1 2 1 1 2 1 2 2 2 1 2 1 2 2 1 1 1 2 1 1 2 2 1 2 1 1 2
## [2739] 1 1 1 1 1 2 2 2 1 1 2 2 2 2 2 1 1 1 1 2 2 2 2 2 1 2 1 2 1 2 2 1 1 1 1 1 1
## [2776] 1 2 1 2 1 1 2 2 2 2 1 2 1 1 1 1 1 1 2 1 1 2 1 1 2 2 2 1 2 1 1 2 1 1 2 2 2
## [2813] 1 2 1 1 2 1 1 1 1 1 2 2 1 1 1 2 1 1 1 1 2 2 2 1 1 2 1 1 1 1 2 2 1 1 1 2 2
## [2850] 2 1 1 2 2 2 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 2 2 2 2 1 2 1 2 1 1 1 1 1 1 1 2
## [2887] 1 1 1 1 1 2 2 1 1 1 1 2 1 2 2 2 1 2 2 2 2 1 1 1 1 1 1 2 2 1 2 2 2 1 1 1 1
## [2924] 1 1 1 1 2 1 1 2 2 2 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1 1 2 2
## [2961] 1 2 1 1 1 1 1 1 1 1 2 1 2 1 1 2 2 2 2 1 1 2 1 1 1 2 1 2 2 1 2 1 1 2 1 1 1
## [2998] 2 2 1 2 1 1 1 2 1 2 2 2 1 2 2 1 2 1 2 2 1 2 2 2 1 2 2 1 2 2 1 2 1 2 1 1 1
## [3035] 1 1 1 1 1 1 1 2 2 1 1 1 1 2 1 1 1 1 2 1 2 2 2 2 2 2 1 1 1 1 2 1 1 1 1 2 1
## [3072] 1 2 2 2 1 1 1 1 1 2 2 1 1 1 2 1 1 2 1 1 1 1 2 1 1 1 1 1 1 2 2 1 1 1 2 1 1
## [3109] 2 1 1 2 2 1 1 1 2 1 2 1 1 2 2 2 2 1 2 1 2 1 2 1 2 1 2 1 1 1 2 2 2 1 1 1 1
## [3146] 2 2 1 1 2 2 2 1 1 2 1 2 2 2 2 2 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 2 2 1 1 2 2
## [3183] 1 1 1 2 1 1 2 1 1 2 1 1 1 2 2 1 1 1 2 1 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1
## [3220] 1 1 1 1 1 2 1 1 1 2 1 2 2 1 2 2 1 1 1 2 1 2 2 1 1 1 1 2 1 1 2 1 2 1 1 1 2
## [3257] 2 1 2 1 1 1 1 1 1 1 1 2 1 2 2 1 1 1 1 2 2 2 2 1 1 2 2 1 2 1 2 2 2 1 1 1 2
## [3294] 1 1 1 1 1 1 2 1 2 1 1 2 1 1 1 1 1 2 1 2 2 2 2 1 1 1 1 2 1 1 1 2 2 1 2 1 1
## [3331] 2 1 2 1 1 2 2 1 1 1 1 1 1 1 1 1 1 2 2 1 2 1 1 2 2 1 2 1 2 1 1 1 2 1 1 1 1
## [3368] 1 2 2 2 2 1 1 2 1 1 2 2 2 1 1 2 1 1 1 1 2 2 1 1 2 2 1 2 1 2 1 2 2 1 1 2 2
## [3405] 2 1 1 2 2 1 2 2 1 1 1 1 1 2 1 2 1 2 1 2 1 2 1 2 2 1 1 1 1 2 2 2 2 2 2 2 1
## [3442] 1 2 1 1 1 2 2 1 2 1 2 2 1 2 1 2 1 1 1 2 1 2 2 1 2 1 2 1 1 1 1 1 1 1 2 2 1
## [3479] 1 2 1 1 1 1 1 2 1 1 2 2 1 2 2 2 1 2 1 1 2 2 1 1 1 2 1 1 2 1 1 2 2 2 1 2 1
## [3516] 1 1 1 2 1 2 2 2 1 1 2 2 2 1 1 2 2 1 1 1 1 2 2 2 1 2 1 1 2 2 1 1 1 1 1 2 1
## [3553] 1 2 2 1 1 2 1 1 1 2 2 1 1 1 1 1 2 2 1 1 1 1 1 1 2 1 2 1 1 2 2 1 2 2 1 2 1
## [3590] 2 1 1 1 1 1 2 1 2 1 1 1 2 1 1 1 1 1 2 2 2 1 2 1 2 1 1 1 1 1 1 2 1 1 1 1 1
## [3627] 1 2 1 1 2 2 2 2 1 1 2 2 2 1 1 1 1 2 2 1 2 1 1 1 2 1 2 1 1 1 1 1 2 2 2 2 1
## [3664] 2 2 1 1 1 2 2 2 2 1 2 2 1 2 1 1 1 2 1 2 1 1 1 1 2 2 2 2 2 2 2 2 2 1 2 2 1
## [3701] 1 1 2 1 1 2 1 2 2 2 2 2 2 2 2 1 1 2 2 2 1 2 1 1 1 2 2 1 1 2 2 1 1 2 2 1 1
## [3738] 1 2 1 2 1 2 2 2 2 1 1 2 1 2 1 1 2 2 1 2 2 2 1 1 2 1 2 2 2 1 1 2 1 2 1 1 1
## [3775] 2 1 1 2 2 1 1 1 2 2 1 2 2 1 2 1 1 2 1 1 2 2 2 1 1 1 2 2 1 2 1 1 2 2 2 2 1
## [3812] 1 1 2 1 2 2 1 1 1 1 1 1 2 1 1 1 1 2 1 2 1 2 2 1 2 2 1 2 1 1 1 1 2 1 1 2 2
## [3849] 2 2 1 2 1 1 2 2 2 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 2 1 1 2 1 1 2 1 1 1 1 2 2
## [3886] 2 2 2 2 1 2 1 2 1 1 1 1 2 1 2 1 2 1 1 1 2 1 1 1 1 2 1 1 1 2 2 2 2 1 1 1 1
## [3923] 1 1 1 1 2 2 1 2 1 1 2 1 1 2 1 2 2 2 1 1 1 2 2 1 2 2 2 1 1 1 1 1 2 2 2 2 1
## [3960] 1 2 1 1 1 1 2 1 1 1 2 1 2 1 1 1 1 2 2 1 1 2 2 1 1 2 1 1 2 2 1 1 2 1 1 1 1
## [3997] 1 2 2 1 1 1 2 1 2 1 2 2 1 1 2 2 2 2 2 1 1 1 1 2 1 1 1 2 1 2 1 2 1 1 2 2 2
## [4034] 2 1 1 2 2 1 2 1 1 1 1 1 1 1 1 1 1 2 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4071] 1 1 2 2 1 2 2 1 1 1 1 2 1 1 1 2 2 2 2 1 1 1 2 1 1 1 2 1 1 2 1 1 2 1 1 2 1
## [4108] 2 1 2 1 1 2 1 1 1 1 1 1 2 1 1 2 1 2 1 2 2 1 1 1 1 1 2 1 2 2 1 2 1 2 2 2 1
## [4145] 1 1 2 2 1 1 2 1 1 2 1 2 2 1 1 1 2 2 1 1 2 1 1 2 1 2 1 1 1 1 1 1 2 1 1 2 1
## [4182] 1 2 1 2 2 2 1 2 1 2 1 1 1 1 1 2 1 1 1 2 1 2 1 2 1 2 2 2 1 2 2 2 2 1 1 2 1
## [4219] 1 1 2 1 1 1 2 1 1 1 1 2 1 1 2 1 1 2 1 1 1 1 2 1 1 1 2 2 1 2 2 1 2 1 1 1 1
## [4256] 1 1 2 2 2 2 1 1 1 2 1 2 2 1 2 1 2 2 1 1 1 2 2 1 1 2 1 2 2 2 2 1 2 2 2 1 2
## [4293] 1 1 1 1 2 2 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 2 1 1
## [4330] 2 1 1 1 2 2 1 2 1 1 2 1 1 1 2 1 1 1 1 2 2 2 1 1 2 2 1 2 1 2 1 2 1 1 1 2 1
## [4367] 2 2 1 2 2 2 1 2 1 2 2 1 2 2 1 2 2 2 1 1 2 2 1 2 1 1 2 2 1 2 1 2 1 1 1 1 1
## [4404] 2 1 1 1 2 1 2 1 1 1 1 1 2 1 1 1 1 1 1 2 1 2 1 1 2 2 1 2 1 2 1 2 1 2 2 1 1
## [4441] 2 2 1 1 1 1 2 1 2 1 1 2 1 1 1 1 2 2 1 1 1 1 2 2 2 1 2 2 1 1 2 1 2 2 1 2 2
## [4478] 1 2 1 2 2 2 1 1 1 2 2 2 1 1 1 1 1 1 2 1 2 1 1 1 2 1 2 1 2 1 1 2 1 2 1 2 1
## [4515] 1 2 2 2 2 2 1 1 2 1 1 1 1 1 1 1 1 2 2 1 2 2 2 2 1 1 2 2 2 1 1 1 2 2 1 1 2
## [4552] 2 2 2 1 2 1 2 1 2 1 2 1 1 1 1 1 2 1 1 1 1 2 2 1 2 1 2 1 1 1 2 1 1 2 2 2 1
## [4589] 2 1 2 1 1 2 1 1 1 1 2 1 1 2 1 1 1 1 2 1 1 1 2 1 1 2 2 1 2 1 2 1 1 1 1 1 1
## [4626] 2 1 1 1 1 2 1 1 2 1 1 2 1 2 2 1 2 1 2 1 2 1 1 2 1 1 2 2 1 1 2 1 2 1 2 1 2
## [4663] 2 1 1 1 2 1 2 1 2 1 2 1 2 1 1 2 1 1 2 1 1 2 1 1 1 1 1 1 1 1 2 1 1 1 2 1 1
## [4700] 1 1 1 1 2 1 1 2 2 2 2 1 1 2 1 1 1 2 1 1 1 1 1 1 1 1 2 2 2 1 2 1 1 2 2 1 1
## [4737] 2 1 1 1 1 2 1 1 2 1 1 1 1 2 1 2 1 2 1 1 2 1 2 2 2 1 2 2 1 1 1 1 2 1 1 1 1
## [4774] 2 2 1 1 1 1 1 1 1 1 1 2 1 1 2 1 1 2 1 2 1 1 2 1 2 1 1 1 1 2 1 1 1 1 1 2 1
## [4811] 1 1 1 2 1 2 1 2 1 1 2 1 2 2 2 1 2 1 2 2 2 1 2 1 2 1 1 1 1 1 1 2 2 1 2 2 1
## [4848] 1 1 2 1 1 1 2 1 1 2 2 2 2 2 1 2 1 1 2 1 2 2 2 1 1 1 1 1 2 2 1 1 2 1 2 2 1
## [4885] 1 2 1 1 2 2 1 2 1 2 1 1 2 2 1 1 2 2 1 2 2 2 2 1 1 1 1 2 1 2 1 1 1 2 1 2 2
## [4922] 2 1 1 2 2 1 2 1 1 1 1 1 1 1 1 1 2 1 2 2 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1
## [4959] 2 2 1 1 1 1 2 2 1 1 1 1 2 1 1 1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 1 2 1 2 2 1
## [4996] 1 1 1 1 1 2 2 1 1 1 1 1 1 2 2 2 1 1 2 2 1 2 1 2 1 2 2 2 2 1 1 1 2 2 1 1 1
## [5033] 1 1 1 1 1 2 1 2 1 1 1 1 2 1 2 1 2 2 2 2 1 1 2 2 2 1 2 1 1 1 1 2 2 2 1 1 1
## [5070] 1 2 1 1 1 2 2 2 1 2 1 2 2 1 1 1 1 2 2 2 2 1 2 1 2 2 2 1 1 2 1 1 1 1 1 1 2
## [5107] 1 1 2 1 2 2 1 1 1 1 1 1 2 1 2 1 1 1 1 1 1 2 2 2 1 1 1 2 1 2 2 2 1 1 1 1 2
## [5144] 2 1 1 1 1 2 2 1 1 1 2 1 1 2 2 1 2 2 1 1 1 2 2 1 2 2 1 1 1 1 1 2 2 2 2 1 1
## [5181] 1 1 1 1 1 1 1 1 1 2 2 1 1 1 2 1 2 2 1 2 2 1 2 1 1 1 2 2 2 1 1 1 2 1 1 1 1
## [5218] 2 2 1 1 2 2 1 1 1 2 1 1 2 1 2 1 2 1 1 2 1 2 2 2 1 1 1 1 1 1 1 1 2 2 2 1 1
## [5255] 1 2 2 1 2 1 2 1 2 1 2 1 1 2 2 1 1 1 2 2 1 2 2 1 2 1 2 2 1 1 1 1 2 1 2 1 2
## [5292] 2 1 1 2 1 1 1 2 2 1 1 2 2 2 1 2 1 2 2 2 1 1 1 1 1 1 1 2 1 1 1 2 1 1 2 1 2
## [5329] 1 2 1 2 1 1 2 1 1 2 2 1 2 1 2 2 2 1 1 2 2 1 2 2 1 1 2 2 1 2 2 2 1 2 1 1 2
## [5366] 2 1 2 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 2 1 2 1 2 1 1 2 2
## [5403] 1 1 2 1 1 2 1 2 1 1 1 1 1 1 2 1 2 2 2 2 1 1 2 2 2 2 1 1 2 2 2 1 1 1 1 1 2
## [5440] 1 1 1 1 1 2 1 1 2 1 1 2 1 1 2 2 2 2 1 1 2 2 1 2 1 1 1 1 1 1 1 1 2 2 1 2 2
## [5477] 2 1 2 2 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 2 2 1 1 1 2 2 1 1 1 1 2 1 1 2 1 1 2
## [5514] 1 2 2 2 1 1 1 1 2 1 2 2 2 1 2 1 1 1 2 1 2 1 1 1 1 1 2 2 1 2 1 2 2 1 2 1 2
## [5551] 1 2 1 1 2 2 2 1 2 2 2 1 1 2 1 1 1 2 1 1 2 2 1 2 1 2 1 2 2 2 1 1 2 2 2 1 2
## [5588] 1 1 2 1 1 1 1 1 1 1 2 1 2 1 1 1 2 1 1 2 1 2 1 1 1 1 1 2 2 1 1 1 1 2 1 1 1
## [5625] 2 1 1 2 1 2 1 1 1 1 2 1 1 2 1 1 1 1 1 1 1 2 1 1 1 2 1 2 2 1 2 1 2 2 1 1 2
## [5662] 1 1 1 2 1 2 1 1 1 2 1 2 2 2 1 1 1 2 2 1 1 1 2 1 1 1 2 1 2 1 1 1 1 2 2 1 1
## [5699] 2 2 1 1 1 1 1 1 2 2 2 1 1 1 1 2 1 1 2 1 2 2 1 1 1 1 2 1 1 1 2 2 2 1 2 1 2
## [5736] 1 1 1 2 1 1 1 2 1 2 1 1 2 1 1 2 2 1 1 1 2 1 2 1 1 1 1 2 2 1 1 1 1 1 1 2 2
## [5773] 1 1 1 1 2 1 2 1 1 2 1 2 1 1 2 2 2 1 1 1 1 1 2 2 1 1 2 1 1 1 1 1 2 2 2 2 1
## [5810] 2 1 1 2 1 1 2 2 1 1 2 1 2 1 1 2 1 2 1 1 1 1 2 2 1 2 1 2 1 1 2 1 2 1 1 2 1
## [5847] 1 2 1 2 1 1 2 1 1 2 2 2 2 1 2 2 2 1 1 1 2 1 1 2 1 1 2 2 1 2 1 1 1 2 1 2 1
## [5884] 2 1 1 2 1 1 1 2 1 2 1 2 1 1 2 1 1 1 2 1 1 2 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1
## [5921] 1 1 2 1 1 2 1 2 1 2 2 1 2 1 1 2 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 2 2 1 1 2 1
## [5958] 2 1 2 2 2 2 2 2 2 1 1 1 1 1 1 2 1 1 2 2 1 2 1 1 2 1 1 1 1 2 1 1 1 1 1 1 1
## [5995] 1 1 1 2 1 1 2 1 2 1 1 1 1 2 1 2 1 1 2 1 1 1 1 1 2 2 1 2 1 1 1 2 2 2 2 1 2
## [6032] 1 2 2 2 2 2 1 2 1 2 2 1 2 1 1 2 1 2 2 2 1 1 1 1 2 1 2 2 1 2 1 1 2 1 2 1 1
## [6069] 1 2 1 1 2 1 1 1 2 2 2 1 2 2 1 1 2 1 2 1 1 1 2 2 1 2 2 2 2 2 1 2 2 1 1 2 1
## [6106] 2 1 1 2 2 1 1 1 2 2 1 1 1 1 1 1 2 1 1 1 1 1 2 2 1 1 2 1 2 2 1 1 1 1 2 1 2
## [6143] 1 1 1 2 1 2 2 2 1 2 1 2 1 2 2 2 1 1 2 1 1 1 1 2 1 1 1 1 1 2 1 2 2 1 2 1 1
## [6180] 1 1 1 1 2 2 2 1 1 1 1 2 2 1 2 1 1 1 1 2 2 1 1 1 1 1 1 2 1 1 1 2 1 1 2 1 1
## [6217] 2 1 2 2 1 1 2 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 2 2 1 1 2 1 1 1 1 1 2 2 1 1 1
## [6254] 2 2 1 2 1 2 1 1 1 1 1 2 1 1 2 2 1 1 2 1 2 1 2 2 1 1 2 2 2 1 2 2 1 1 2 1 1
## [6291] 2 1 2 1 1 1 2 2 2 1 1 1 2 2 2 2 2 1 1 1 1 2 1 1 1 2 2 2 1 2 2 1 1 2 1 2 1
## [6328] 1 1 2 1 2 2 1 2 1 2 1 1 1 1 1 1 1 1 2 1 2 1 2 1 1 2 2 1 1 1 1 2 1 1 1 2 1
## [6365] 1 1 1 1 2 2 1 1 2 1 2 2 1 1 1 1 2 2 2 2 1 1 1 1 2 1 2 1 2 1 1 2 1 1 1 1 2
## [6402] 1 1 2 2 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 2 1 1 2 2 1 2 1 2 2 1 2 2 1 1 2 1 1
## [6439] 2 1 2 2 1 2 2 1 1 1 1 1 2 2 1 2 1 1 1 1 2 2 2 1 1 1 1 1 1 2 1 1 2 1 1 1 1
## [6476] 1 1 1 1 1 2 1 2 2 2 1 1 2 1 2 2 1 1 2 1 2 2 1 1 2 2 1 1 2 1 2 1 2 2 1 2 2
## [6513] 2 1 1 1 2 1 2 2 2 1 1 2 1 1 1 2 2 2 1 1 1 2 1 2 2 1 1 2 1 2 1 2 1 1 1 2 1
## [6550] 1 1 1 1 2 2 1 2 1 1 2 2 1 1 2 1 1 1 1 1 2 2 1 1 1 2 2 1 2 2 1 1 2 1 2 1 1
## [6587] 1 2 2 1 1 1 2 1 1 1 1 1 1 1 2 1 2 2 1 1 1 1 2 2 2 2 1 2 1 1 2 2 1 1 1 1 1
## [6624] 2 2 2 2 2 1 2 1 1 2 2 2 2 2 1 2 1 2 1 1 1 1 1 1 2 2 1 2 2 1 1 1 1 2 1 1 1
## [6661] 2 2 1 1 2 1 2 1 1 1 2 1 1 2 1 1 1 1 2 1 1 1 2 1 1 1 2 2 2 2 1 2 1 2 1 1 1
## [6698] 2 2 1 1 1 1 1 2 2 2 1 2 2 1 1 1 2 1 2 1 2 1 1 1 1 2 1 2 1 1 1 1 1 2 1 2 1
## [6735] 1 2 1 2 1 1 2 1 1 1 1 2 2 2 1 2 2 2 2 2 1 1 1 2 1 1 1 1 1 2 2 1 1 1 1 2 1
## [6772] 1 1 1 1 1 1 2 2 2 1 2 2 1 2 1 1 1 2 1 1 1 1 1 1 2 1 2 2 2 1 1 1 1 2 2 1 2
## [6809] 1 2 1 1 1 1 2 1 1 1 2 1 2 2 1 1 1 2 1 2 2 1 2 2 1 2 1 2 1 2 2 1 1 1 1 1 1
## [6846] 1 2 2 1 1 2 1 1 1 1 1 2 2 1 1 2 2 1 1 1 2 1 1 1 2 1 2 1 2 1 2 1 1 1 2 1 1
## [6883] 1 2 1 1 1 2 2 1 2 1 1 2 1 2 2 2 1 1 1 1 2 2 2 1 2 1 1 1 1 2 1 1 1 1 2 1 2
## [6920] 1 1 2 2 1 2 2 1 1 2 2 1 1 1 2 1 1 1 2 2 1 2 1 1 1 2 1 1 1 2 1 2 1 2 1 2 1
## [6957] 1 2 1 1 1 2 1 1 1 1 1 2 1 1 2 1 2 1 1 2 1 2 2 1 2 1 2 2 1 1 2 2 2 1 2 1 2
## [6994] 1 1 1 1 1 2 2 2 1 1 1 2 1 1 1 2 2 1 1 1 2 2 1 2 1 2 2 1 1 2 1 1 2 1 1 2 2
## [7031] 2 2 1 1 1 2 1 2 2 2 1 1 1 1 1 1 2 2 2 2 1 2 1 1 1 2 1 1 2 1 2 1 2 1 1 1 1
## [7068] 2 1 1 1 2 2 1 1 1 1 1 2 2 1 2 2 1 2 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 2 1 1 1
## [7105] 1 1 2 1 1 1 1 2 1 1 2 2 1 1 2 1 2 2 2 1 2 2 2 2 2 1 1 1 1 1 2 1 2 2 2 1 1
## [7142] 2 1 1 1 2 1 1 2 2 2 2 2 1 2 1 1 1 1 2 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2
## [7179] 1 1 1 1 2 1 2 1 1 2 2 1 2 1 1 1 1 2 2 1 1 1 1 2 1 1 1 1 2 1 2 2 1 1 1 1 1
## [7216] 1 1 1 1 1 2 1 1 2 2 1 2 1 1 2 2 1 2 1 1 2 1 1 1 1 1 1 2 1 1 2 2 1 2 1 1 1
## [7253] 2 1 2 1 1 1 1 1 1 1 2 2 1 2 1 1 1 2 2 2 1 1 1 1 1 2 1 2 1 2 2 1 2 1 2 1 1
## [7290] 2 1 1 1 1 2 1 1 1 2 1 1 2 1 1 1 1 2 1 2 2 1 2 2 1 1 1 2 2 1 2 2 2 2 1 1 1
## [7327] 1 1 2 1 2 2 1 1 2 1 2 2 1 1 2 2 2 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 2 2
## [7364] 1 1 2 2 1 2 2 2 2 2 2 1 1 2 2 2 1 1 1 2 1 1 2 1 2 2 1 1 1 1 1 1 1 1 1 1 1
## [7401] 1 1 1 1 2 1 1 1 2 2 1 2 1 1 1 1 2 2 1 2 1 1 1 1 1 1 1 2 1 2 1 2 1 2 1 1 2
## [7438] 1 2 1 1 1 1 1 2 1 2 2 1 1 1 1 1 1 1 2 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 2
## [7475] 1 1 1 2 1 2 1 2 1 1 2 2 1 1 1 1 2 2 2 1 2 1 1 2 2 1 1 1 1 1 2 2 1 2 2 1 2
## [7512] 2 2 2 2 1 2 2 1 1 1 2 2 2 1 1 2 2 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 2
## [7549] 1 1 1 2 1 2 2 1 2 1 1 1 1 2 1 2 2 2 1 2 2 2 2 2 1 1 1 2 1 2 1 2 2 2 1 1 1
## [7586] 1 2 2 1 2 2 1 1 1 2 2 1 2 2 1 1 1 2 1 2 1 2 1 1 2 2 2 1 2 1 2 1 1 1 2 1 1
## [7623] 1 1 1 1 1 2 2 2 2 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 2 1 1 1 1 2 1 2 2 2 1 2 1
## [7660] 2 2 2 2 1 1 2 1 1 1 1 2 1 1 1 1 1 2 1 2 1 2 1 1 1 1 1 1 2 1 2 1 2 2 1 2 1
## [7697] 1 2 1 1 2 1 1 1 2 1 2 2 1 1 1 2 1 2 1 2 1 1 2 1 2 2 1 1 1 1 1 2 1 2 2 1 1
## [7734] 2 1 2 2 1 1 2 1 1 2 1 2 1 1 1 1 1 1 2 2 1 1 1 1 1 2 2 1 2 2 1 1 2 2 1 2 1
## [7771] 2 2 1 1 1 1 1 1 2 1 2 1 1 1 2 1 2 1 1 1 1 1 2 2 2 2 2 2 1 1 2 2 1 1 2 1 2
## [7808] 1 1 2 1 1 1 2 1 1 2 2 2 2 2 1 2 1 1 2 1 2 1 2 1 2 2 1 2 1 1 2 1 1 1 1 1 2
## [7845] 1 1 1 2 1 1 2 1 2 1 1 2 1 1 1 1 1 1 1 1 2 1 1 1 2 1 1 2 1 2 1 1 2 2 1 2 2
## [7882] 1 2 1 2 1 2 1 2 2 2 1 2 2 1 2 2 1 2 2 2 1 1 1 1 2 1 2 1 1 2 2 2 1 2 2 2 2
## [7919] 1 1 1 2 1 2 1 1 2 1 1 2 2 1 2 2 1 2 1 2 1 1 1 2 2 2 1 1 1 1 2 1 2 1 1 1 1
## [7956] 2 1 1 1 1 1 2 2 1 1 2 1 1 2 2 1 1 2 1 1 2 2 2 1 1 2 2 1 1 2 1 2 1 2 2 1 1
## [7993] 1 1 1 1 1 1 2 1 1 1 1 2 2 2 2 1 2 1 1 1 1 1 1 2 2 2 1 1 1 2 2 2 2 1 2 2 1
## [8030] 1 1 1 1 2 1 2 1 1 1 2 2 1 2 1 2 2 1 2 1 1 2 1 1 1 2 1 2 2 2 2 1 2 2 2 1 2
## [8067] 2 1 2 1 1 2 1 2 2 1 1 1 2 2 2 1 1 1 1 1 1 1 1 2 2 1 2 1 2 1 2 1 2 2 2 1 1
## [8104] 2 2 1 2 1 2 1 2 1 2 1 1 1 2 2 2 1 1 1 1 2 2 2 1 1 2 2 2 1 1 1 1 2 1 1 1 1
## [8141] 1 2 1 1 2 1 1 1 1 1 1 1 2 1 1 2 1 1 1 2 1 2 1 1 1 1 2 1 2 1 1 1 2 1 2 2 2
## [8178] 2 1 2 1 2 2 2 1 2 2 1 1 2 1 1 1 1 1 1 2 1 1 2 1 2 2 1 1 2 1 1 1 2 1 1 1 1
## [8215] 2 2 1 1 1 1 1 2 1 1 2 1 1 1 1 1 1 1 1 1 2 1 2 1 1 2 1 1 1 1 1 2 2 2 2 1 1
## [8252] 1 2 2 1 2 2 1 1 2 1 2 2 2 1 1 1 1 1 1 2 2 1 2 2 2 1 1 1 2 1 1 1 1 1 2 2 1
## [8289] 1 2 2 2 2 1 1 2 1 1 1 2 2 1 1 2 1 1 1 1 1 1 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1
## [8326] 2 2 1 1 1 2 2 1 1 2 2 1 2 1 2 1 2 1 1 1 2 1 1 2 2 1 1 2 1 1 2 2 2 2 1 1 2
## [8363] 2 2 1 1 1 2 1 2 1 1 2 2 1 2 1 1 2 2 2 2 2 2 1 2 1 1 2 2 1 1 2 1 2 1 2 1 1
## [8400] 2 1 1 1 1 1 1 2 2 1 1 1 1 1 2 2 2 1 2 1 1 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1
## [8437] 2 2 1 2 1 1 1 2 1 1 2 1 1 1 1 1 2 1 2 2 2 1 1 1 2 1 2 1 1 2 2 1 1 2 2 1 1
## [8474] 1 1 2 1 1 1 1 1 1 2 1 1 1 2 1 2 2 1 1 2 2 1 2 2 1 2 1 1 1 1 1 1 1 1 1 1 2
## [8511] 1 2 1 2 2 1 1 2 1 1 2 1 2 1 1 1 2 2 1 1 1 1 1 2 2 2 1 2 2 1 1 2 1 2 1 1 1
## [8548] 2 2 1 1 1 2 2 1 2 1 2 2 1 1 1 2 2 1 1 1 1 1 1 2 2 2 2 1 1 2 1 1 1 1 1 1 1
## [8585] 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 2 2 1 2 2 1 2 1 2 1 1 2 1 2 1 1 1 2 2 1 2
## [8622] 1 1 1 2 1 1 1 1 2 2 2 2 1 1 1 2 1 1 1 2 1 1 2 2 1 1 1 1 1 2 1 2 1 2 1 1 2
## [8659] 1 2 1 2 2 1 2 1 2 2 1 2 1 1 1 1 1 1 1 2 1 1 1 2 2 1 1 1 1 1 1 2 1 1 1 2 1
## [8696] 2 2 1 2 1 1 1 2 1 2 1 2 2 1 1 1 2 2 1 2 2 2 2 1 1 1 2 1 1 1 2 1 1 2 1 1 2
## [8733] 1 1 1 2 1 2 1 1 1 2 2 1 1 1 1 2 1 2 2 2 1 2 2 1 2 1 1 1 1 2 2 1 2 1 2 2 2
## [8770] 2 2 1 1 2 1 2 2 1 1 1 1 2 1 2 1 1 2 1 2 1 1 1 1 1 2 1 1 2 2 1 2 2 1 2 1 1
## [8807] 2 1 2 2 2 1 1 1 2 1 1 2 2 1 2 1 2 2 2 2 2 2 1 1 1 1 1 1 1 1 2 2 1 2 1 1 1
## [8844] 1 1 1 2 2 1 2 2 1 1 1 1 1 2 1 1 1 2 2 1 2 1 1 2 1 1 1 2 1 1 2 2 2 1 2 1 1
## [8881] 1 2 1 2 1 1 1 2 2 2 2 2 1 2 2 1 2 2 1 1 1 1 2 2 2 1 1 2 2 1 1 1 1 2 1 1 1
## [8918] 1 1 1 1 1 2 2 1 2 2 2 2 1 1 2 2 2 1 2 2 1 1 1 2 1 2 1 1 2 2 1 1 1
##
## Within cluster sum of squares by cluster:
## [1] 57621.41 70148.61
## (between_SS / total_SS = 16.0 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault" "crit"
## [11] "bestk"Numero de clustering: k =7
# Usando la funcion kmeans() con 7 clusters
# ntart=25, significa que se probarón 100 puntos iniciales
# aleatorios y luego elegir? aquel donde la variación
# dentro de cluster sea minima. El valor por defecto es 1
set.seed(123)
agrupacion2_km <- kmeans(credito_st,
centers=7, # Número de Cluster
nstart = 100, # Número de puntos iniciales
iter.max = 1000) # Número de iteraciones máxima# Mostrar resumen de los clusters
print(agrupacion2_km)## K-means clustering with 7 clusters of sizes 629, 1186, 2049, 81, 894, 2846, 1265
##
## Cluster means:
## BALANCE BALANCE_FREQUENCY PURCHASES ONEOFF_PURCHASES
## 1 -0.33548683 -0.3480563 -0.28450959 -0.2089610
## 2 -0.70185522 -2.1353744 -0.30707758 -0.2305684
## 3 -0.37010983 0.3307223 -0.04044644 -0.2323855
## 4 1.41086703 0.4133560 7.12740831 6.3006262
## 5 1.66342130 0.3925068 -0.20165682 -0.1483789
## 6 0.00758072 0.4020436 -0.34246008 -0.2232139
## 7 0.14136201 0.4310136 0.95148444 0.9000910
## INSTALLMENTS_PURCHASES CASH_ADVANCE PURCHASES_FREQUENCY
## 1 -0.2884590 0.06553502 -0.1987235
## 2 -0.3023702 -0.32293895 -0.5473794
## 3 0.3311265 -0.36881520 0.9795992
## 4 5.2746145 0.01008892 1.0847069
## 5 -0.2043053 1.99345930 -0.4546730
## 6 -0.3995501 -0.10446911 -0.8093484
## 7 0.5961252 -0.30684927 1.0980333
## ONEOFF_PURCHASES_FREQUENCY PURCHASES_INSTALLMENTS_FREQUENCY
## 1 -0.2725572 -0.2307420
## 2 -0.4288460 -0.4410267
## 3 -0.3520883 1.1708958
## 4 1.8853550 1.0387160
## 5 -0.1877592 -0.4026141
## 6 -0.3343386 -0.7528907
## 7 1.8720547 0.5435232
## CASH_ADVANCE_FREQUENCY CASH_ADVANCE_TRX PURCHASES_TRX CREDIT_LIMIT PAYMENTS
## 1 0.3040953 -0.002215869 -0.3855649 -0.5574688 -0.3906787
## 2 -0.5220910 -0.376710762 -0.4166341 -0.1720637 -0.2016367
## 3 -0.4784524 -0.363126048 0.1695659 -0.2778674 -0.2228754
## 4 -0.2948836 -0.112437370 4.7418167 2.1659223 4.9049000
## 5 1.9103036 1.925602011 -0.2378460 1.0086432 0.8370880
## 6 0.0840972 -0.042020463 -0.4641917 -0.2998682 -0.2478932
## 7 -0.4071095 -0.316658116 1.2164780 0.7117184 0.3963639
## MINIMUM_PAYMENTS PRC_FULL_PAYMENT TENURE
## 1 -0.21632053 0.01289805 -3.19358659
## 2 -0.28507804 0.29568550 0.20189526
## 3 -0.02276624 0.30594224 0.25235377
## 4 1.10764506 0.84746214 0.33298534
## 5 0.55724342 -0.39082062 0.06980324
## 6 -0.01231509 -0.45234587 0.27191962
## 7 -0.02532010 0.46043795 0.30749896
##
## Clustering vector:
## [1] 6 5 7 6 6 3 7 3 6 2 3 6 3 3 6 5 1 2 3 3 3 7 3 5 6 3 6 3 5 6 5 3 6 7 3 6 5
## [38] 7 5 5 6 6 6 6 3 6 1 6 7 6 5 7 6 1 3 6 6 7 6 6 6 6 6 2 3 6 1 6 3 6 3 5 1 6
## [75] 6 3 7 3 6 5 3 2 2 2 7 7 5 5 6 5 7 5 6 6 6 6 6 6 2 1 1 3 7 2 6 6 3 5 3 5 3
## [112] 6 7 5 3 3 3 6 2 6 7 6 7 6 5 4 1 3 5 2 2 3 2 5 3 6 7 3 4 7 6 6 5 7 7 6 3 6
## [149] 3 3 5 7 3 4 7 2 5 6 7 6 6 6 3 6 1 6 3 7 3 3 1 4 2 1 7 6 6 5 7 2 3 2 5 2 3
## [186] 3 6 3 6 6 6 6 2 3 6 7 3 7 6 5 2 6 3 5 4 2 6 5 5 2 5 6 6 6 6 2 3 2 5 7 4 7
## [223] 1 7 7 6 3 7 2 4 3 3 7 6 7 7 5 6 2 6 5 2 7 6 7 2 7 3 5 7 6 3 6 7 6 2 6 7 7
## [260] 6 6 7 7 5 3 7 7 7 6 7 7 6 7 4 5 2 6 2 3 3 7 3 6 3 6 5 6 6 2 6 7 6 6 6 3 7
## [297] 6 6 7 7 6 7 6 6 5 3 7 3 6 3 7 7 7 6 6 6 1 6 3 2 5 5 5 6 6 3 7 7 6 7 6 7 7
## [334] 7 5 5 2 7 2 3 6 5 6 2 7 2 7 3 5 3 6 7 5 2 2 7 7 5 2 6 6 6 1 5 6 3 6 3 5 5
## [371] 7 5 2 7 3 2 7 3 6 6 5 6 6 2 7 2 6 5 3 3 6 7 6 4 3 6 3 1 5 3 3 3 5 7 6 6 2
## [408] 6 6 2 6 7 2 5 3 7 6 7 2 3 3 6 6 7 3 6 6 6 5 5 6 5 2 6 6 5 3 7 6 7 2 5 6 3
## [445] 7 3 3 2 6 2 7 7 3 5 1 3 3 3 6 7 7 3 3 3 6 5 7 3 7 2 5 6 3 6 6 6 3 7 6 6 2
## [482] 7 5 6 7 7 6 7 5 7 7 5 7 6 7 5 6 6 2 7 3 4 7 3 3 3 3 4 6 7 3 4 5 3 7 7 6 2
## [519] 3 3 5 3 2 3 7 6 5 5 3 3 3 3 6 6 7 2 7 5 2 5 3 2 5 1 7 7 7 3 7 1 4 7 5 7 5
## [556] 3 6 5 5 6 4 6 6 4 6 7 7 3 2 5 6 6 6 2 4 6 6 5 6 6 6 7 6 6 4 7 2 4 2 7 3 4
## [593] 6 6 6 2 2 7 7 6 5 6 5 3 6 2 5 3 5 7 5 6 7 7 6 5 7 3 2 7 4 2 7 3 4 6 3 6 7
## [630] 7 3 6 2 3 5 2 6 5 6 7 7 6 7 7 7 4 5 7 5 6 1 3 4 2 2 7 7 2 5 2 6 7 7 6 7 3
## [667] 3 2 7 4 6 6 3 3 6 3 6 7 6 5 2 5 3 7 3 6 3 1 6 7 7 6 1 7 6 3 5 3 7 3 6 1 6
## [704] 6 7 6 6 6 4 7 5 6 7 3 1 7 5 6 6 6 6 6 6 5 2 7 7 6 3 7 6 6 6 7 3 5 2 2 6 5
## [741] 1 3 6 5 1 3 6 6 3 7 1 3 6 1 6 5 3 6 3 7 6 3 5 5 2 6 6 6 5 7 6 7 6 7 6 1 7
## [778] 7 6 7 5 2 7 7 2 3 5 1 6 5 3 3 6 6 2 3 6 3 3 2 6 7 2 5 3 6 7 3 6 3 5 7 5 6
## [815] 2 6 3 6 3 6 2 6 6 6 7 6 5 3 3 5 6 6 6 6 3 3 3 3 3 6 7 5 5 5 5 5 6 3 6 6 6
## [852] 5 6 5 4 6 7 7 6 3 2 7 3 3 3 6 5 6 6 6 6 7 6 6 3 6 3 6 5 1 6 3 5 5 7 6 7 7
## [889] 3 7 7 7 6 5 7 7 3 2 5 3 6 6 5 5 6 7 6 6 6 5 5 2 2 3 2 6 7 7 2 7 2 7 5 3 5
## [926] 3 7 6 5 6 6 3 6 6 3 6 3 6 7 5 2 4 6 6 3 6 2 2 6 3 7 3 7 6 6 2 2 6 6 6 7 6
## [963] 5 3 3 3 3 7 6 6 4 7 6 5 6 3 7 5 6 6 6 7 7 6 5 3 6 6 3 5 7 7 6 6 3 6 3 6 3
## [1000] 3 6 6 6 6 6 7 3 5 3 1 7 6 5 6 6 7 6 1 6 7 6 2 3 3 6 7 6 6 2 5 5 7 5 3 2 5
## [1037] 6 5 3 6 1 2 6 3 1 7 2 7 6 6 6 6 2 7 3 3 3 7 3 5 6 7 7 5 6 6 2 6 6 6 6 3 1
## [1074] 6 2 2 5 2 6 7 2 6 6 2 7 2 5 3 6 5 2 5 2 6 6 3 5 2 7 6 5 3 3 3 6 6 6 3 6 6
## [1111] 5 3 6 6 5 6 3 6 7 6 6 6 1 2 6 7 7 2 3 6 5 2 6 6 6 3 6 7 3 3 6 6 7 6 2 5 6
## [1148] 5 3 7 7 7 3 3 6 2 7 2 3 3 3 7 6 5 2 2 2 1 6 3 6 6 6 6 2 6 7 3 6 6 6 6 2 7
## [1185] 3 3 6 3 2 2 4 1 6 7 6 5 3 3 3 7 6 3 7 2 2 3 3 6 5 2 2 5 7 7 3 2 7 5 7 2 7
## [1222] 7 2 2 1 5 7 6 2 5 3 6 3 6 3 2 5 2 6 6 7 7 7 1 6 6 2 3 3 5 3 1 6 2 2 7 4 3
## [1259] 3 6 1 6 6 7 5 3 2 6 7 7 3 7 2 6 6 7 2 3 6 2 6 3 5 6 2 3 7 7 7 6 7 6 7 7 6
## [1296] 2 3 7 6 2 5 1 7 6 7 7 3 5 7 2 6 7 2 6 7 5 6 6 3 6 6 7 7 6 2 7 3 6 6 7 6 3
## [1333] 5 5 1 5 6 2 7 3 3 5 7 7 6 5 3 6 5 7 5 7 3 2 2 1 1 7 7 5 7 7 3 2 6 5 3 5 3
## [1370] 7 7 6 6 7 3 2 2 2 6 6 3 3 3 6 7 1 2 5 6 6 3 6 6 6 6 7 3 6 7 7 6 3 6 7 3 2
## [1407] 7 6 2 3 5 7 4 6 6 3 7 2 6 2 7 2 7 7 5 2 6 7 6 2 3 7 7 4 5 5 3 7 1 7 6 2 5
## [1444] 7 7 3 3 4 7 6 5 5 3 5 7 3 6 3 2 3 7 6 5 7 6 7 7 6 7 6 2 7 2 3 7 5 6 7 7 7
## [1481] 2 6 7 7 3 6 5 5 6 5 7 5 6 6 7 6 3 7 7 3 2 3 3 7 6 5 6 3 6 2 7 6 6 6 7 6 6
## [1518] 5 5 7 3 1 7 7 7 1 3 3 6 6 2 6 7 7 3 6 5 6 2 3 6 3 6 2 2 3 6 5 6 7 6 6 3 3
## [1555] 3 6 3 3 6 3 4 6 5 6 2 2 3 7 3 4 6 6 7 3 2 7 6 6 5 6 2 2 4 6 3 4 7 2 7 6 3
## [1592] 2 2 3 6 6 3 3 3 6 6 3 6 7 4 7 3 3 6 7 3 2 6 6 3 7 7 7 7 7 3 2 6 3 7 6 5 6
## [1629] 3 5 6 5 2 5 3 6 6 6 7 7 6 4 3 6 7 6 5 7 6 7 7 2 5 7 7 6 7 3 3 6 5 7 6 7 3
## [1666] 6 3 7 6 1 6 6 1 3 3 5 5 3 7 6 5 7 2 6 3 3 6 3 6 5 5 2 2 6 2 6 6 7 6 6 6 6
## [1703] 7 3 7 6 5 7 7 4 5 3 6 6 7 3 7 7 5 7 7 7 3 3 6 2 2 7 7 7 6 6 6 2 3 6 6 6 7
## [1740] 7 6 5 3 2 3 3 3 7 2 3 2 3 2 7 4 3 7 2 3 4 5 2 3 7 3 4 6 7 3 5 3 3 7 3 5 7
## [1777] 6 6 5 2 6 5 7 6 7 6 6 6 7 6 3 7 6 2 6 5 3 3 6 6 6 5 6 3 2 7 3 6 1 6 5 5 6
## [1814] 6 7 3 6 7 6 2 6 3 3 6 7 2 7 7 3 3 2 6 5 2 3 5 7 2 2 6 6 3 7 2 3 7 2 6 7 6
## [1851] 6 7 6 6 6 3 5 7 5 6 3 3 3 2 7 3 2 7 2 6 6 7 6 3 6 3 3 6 3 2 3 3 6 5 7 6 2
## [1888] 2 6 2 1 3 6 7 6 6 1 6 3 6 2 1 7 7 5 6 7 5 3 5 3 6 7 5 3 7 6 5 3 5 5 3 6 5
## [1925] 5 5 3 3 6 3 3 3 6 5 6 6 5 1 2 6 1 6 1 5 5 6 3 3 3 3 5 6 3 7 7 6 3 5 3 7 6
## [1962] 7 5 3 7 6 6 3 3 2 2 1 6 3 6 7 6 3 2 7 6 6 2 5 6 3 7 6 5 3 6 4 6 1 6 2 1 7
## [1999] 6 3 2 5 6 5 3 6 6 3 1 3 6 6 3 6 6 4 7 2 3 6 5 3 7 3 7 7 2 6 6 7 2 3 3 3 5
## [2036] 6 6 3 6 1 7 6 3 6 6 6 7 7 5 6 6 7 2 6 7 7 2 6 6 7 1 6 1 6 6 1 6 7 7 3 5 7
## [2073] 6 2 7 5 3 7 6 5 5 7 7 6 3 6 5 2 7 6 6 1 5 3 7 7 6 1 6 2 6 5 2 6 6 6 6 7 6
## [2110] 7 3 6 3 6 6 7 7 1 6 6 6 6 3 6 3 3 3 6 3 7 6 5 7 6 3 6 3 6 7 6 7 2 2 7 3 6
## [2147] 7 3 6 6 7 3 1 3 7 6 6 7 7 5 2 3 3 6 7 3 6 6 3 6 2 5 3 6 1 3 3 7 2 6 6 6 7
## [2184] 3 6 3 2 6 7 6 6 6 6 6 6 6 5 3 6 2 6 2 6 7 7 7 5 3 7 3 5 6 5 6 7 5 2 7 7 6
## [2221] 7 6 3 2 6 7 6 6 2 6 3 2 7 3 6 7 7 1 3 3 5 7 6 2 3 3 6 6 6 5 7 7 6 3 6 3 7
## [2258] 7 5 7 1 4 3 5 6 7 1 5 1 1 2 5 7 6 3 2 5 6 6 7 3 2 6 6 6 3 7 3 5 2 3 7 6 3
## [2295] 6 6 7 2 5 6 6 3 6 3 6 2 5 2 2 7 7 7 3 6 3 6 1 3 3 6 6 2 6 2 5 3 2 3 6 5 3
## [2332] 7 7 1 3 6 3 5 6 7 5 6 5 5 1 7 3 3 6 5 6 6 6 6 6 3 6 3 6 3 7 5 7 7 3 6 5 3
## [2369] 3 6 6 1 3 7 3 6 3 1 6 3 2 3 7 6 7 5 6 5 3 5 6 7 5 6 6 7 6 5 7 6 7 2 6 5 3
## [2406] 3 7 1 5 2 3 3 2 6 2 3 7 3 3 3 3 7 5 6 6 6 6 6 2 6 6 7 5 3 3 3 3 5 1 6 7 5
## [2443] 5 3 7 3 5 6 5 6 6 6 2 7 5 1 6 7 2 2 6 6 1 5 3 6 6 5 7 3 6 3 6 7 6 5 7 7 3
## [2480] 1 3 6 6 2 3 5 6 1 6 6 5 1 3 6 6 5 2 6 7 7 7 3 6 7 6 2 7 6 3 2 2 6 6 6 2 7
## [2517] 5 6 3 6 2 2 7 4 3 6 6 7 7 1 3 5 6 6 7 2 3 6 6 7 2 6 6 6 1 7 6 6 5 3 7 7 6
## [2554] 3 2 5 6 2 3 6 7 5 6 6 6 6 6 3 3 2 6 5 6 3 5 6 5 6 3 5 2 6 3 3 6 6 3 6 2 6
## [2591] 3 7 6 5 3 6 5 6 5 6 3 3 6 6 3 6 5 6 5 3 6 6 5 7 6 6 3 6 3 6 3 1 3 3 3 1 6
## [2628] 3 2 7 2 5 5 5 6 7 6 6 6 6 3 3 5 5 6 5 3 3 6 3 6 6 2 3 6 3 7 5 6 2 5 6 7 6
## [2665] 7 3 3 6 7 5 3 7 6 6 6 2 6 5 7 3 5 5 5 3 6 5 3 7 7 3 5 6 6 5 6 6 5 7 7 6 6
## [2702] 6 3 2 2 6 6 3 6 7 6 2 7 1 6 3 1 7 6 3 2 7 6 7 3 2 5 6 7 6 6 3 3 6 3 2 6 5
## [2739] 2 2 2 6 5 7 3 7 5 6 3 1 7 3 3 6 2 5 6 7 7 7 7 7 6 5 2 3 2 3 3 2 3 6 6 6 6
## [2776] 6 7 6 7 5 5 3 6 7 3 6 7 2 3 2 2 6 5 7 6 6 5 2 6 7 7 7 2 7 6 2 7 6 6 3 7 7
## [2813] 6 3 6 5 7 6 1 6 6 2 7 4 6 1 6 7 6 6 6 6 3 7 7 6 6 7 6 5 5 2 3 7 6 6 5 7 3
## [2850] 3 2 6 3 3 3 2 2 6 6 6 6 6 5 2 6 6 6 5 7 5 7 3 3 7 6 3 6 7 5 6 6 6 2 6 6 3
## [2887] 5 6 5 1 6 3 3 6 5 2 1 6 6 3 3 3 2 7 3 3 1 6 6 6 2 6 2 7 3 5 3 3 5 2 6 6 6
## [2924] 5 2 2 6 7 6 6 3 7 3 6 3 6 6 5 6 6 3 5 6 6 2 6 6 5 3 1 6 7 2 6 6 6 6 6 3 3
## [2961] 6 5 5 6 5 6 5 2 6 2 4 6 3 5 1 7 7 3 3 5 6 2 6 6 6 7 6 7 7 6 3 1 6 3 6 5 3
## [2998] 3 3 2 7 2 2 6 3 6 7 7 7 2 7 1 6 3 6 3 3 6 3 7 3 2 7 3 5 3 7 6 3 2 7 6 5 6
## [3035] 6 6 5 6 5 5 6 3 3 6 6 5 6 6 6 1 6 6 3 3 3 7 3 7 7 7 6 6 5 5 3 6 2 6 2 7 2
## [3072] 6 3 7 3 6 2 6 6 2 3 7 5 5 6 2 6 6 7 5 6 6 2 4 6 1 3 6 6 5 3 3 6 5 6 7 5 5
## [3109] 3 5 2 3 3 1 2 6 3 6 5 2 5 3 3 4 3 5 3 5 7 6 3 6 3 2 3 5 6 2 3 3 7 5 3 6 6
## [3146] 3 7 6 6 3 2 7 6 5 7 5 3 3 5 3 7 6 6 6 6 5 6 6 2 6 3 7 3 6 6 2 3 7 5 6 7 4
## [3183] 6 2 1 3 6 2 7 2 5 3 6 6 6 7 3 5 6 6 7 6 6 7 5 3 6 6 2 2 5 6 5 6 6 6 6 6 6
## [3220] 5 6 5 6 2 7 2 6 6 7 6 3 3 5 3 7 2 2 3 7 3 7 3 6 6 3 6 3 6 3 3 6 7 6 5 2 3
## [3257] 3 6 3 5 2 5 5 2 5 6 2 7 6 5 5 5 2 5 5 7 3 5 3 6 5 6 4 5 3 6 3 7 3 6 6 5 3
## [3294] 6 6 6 2 1 6 6 6 3 5 2 3 6 2 2 5 3 3 1 3 1 7 3 6 2 2 1 7 5 6 6 7 3 6 6 6 6
## [3331] 3 5 3 6 6 3 7 6 6 6 6 6 6 6 2 6 5 7 5 2 7 5 7 3 7 6 7 6 3 6 5 6 1 6 5 6 6
## [3368] 6 7 3 3 3 6 5 1 6 2 3 3 7 6 6 7 6 1 6 6 7 7 2 6 3 6 5 3 6 3 6 7 3 5 6 3 3
## [3405] 7 6 2 3 7 5 7 3 1 6 5 6 2 6 6 3 6 3 6 7 2 7 6 3 3 2 6 6 6 2 7 3 3 3 3 3 5
## [3442] 6 7 6 2 6 7 3 5 3 6 1 7 6 7 6 3 6 2 1 7 6 3 3 6 3 3 3 6 6 1 2 6 6 6 7 7 6
## [3479] 6 7 2 5 6 6 5 7 6 6 3 3 5 7 3 3 6 7 5 6 3 5 6 5 6 7 6 6 7 1 6 3 7 3 6 7 5
## [3516] 2 6 6 3 6 7 7 7 6 2 7 3 7 6 6 7 7 6 6 1 5 7 7 3 6 3 6 6 3 7 5 2 5 6 6 7 6
## [3553] 5 7 3 5 6 6 6 6 5 3 5 1 6 6 6 6 3 5 5 5 6 6 5 6 7 2 7 6 2 3 7 2 7 3 6 3 6
## [3590] 3 2 5 6 5 1 3 2 7 1 1 2 6 6 2 3 6 6 7 3 7 6 3 6 2 5 6 6 6 6 6 3 2 5 5 5 1
## [3627] 3 1 6 5 2 7 3 7 6 6 3 7 5 6 2 5 6 7 5 5 3 6 6 1 7 6 4 6 6 6 5 6 7 7 2 3 6
## [3664] 3 3 2 5 6 3 7 3 7 6 3 7 6 7 5 6 6 3 6 7 1 6 6 6 7 7 6 3 7 7 3 6 7 1 3 4 2
## [3701] 6 1 7 6 6 7 6 7 3 3 3 1 5 3 3 6 6 3 3 4 6 5 6 6 6 7 3 2 2 7 3 6 6 5 7 6 6
## [3738] 6 3 6 3 2 3 3 7 7 6 6 2 5 3 1 6 5 3 1 7 3 5 1 1 3 6 7 3 3 6 6 7 6 7 5 6 6
## [3775] 6 5 5 3 7 6 6 5 7 7 6 7 3 2 4 6 5 7 6 2 7 7 7 6 2 1 5 3 6 3 6 2 5 7 2 7 6
## [3812] 6 6 3 6 3 3 6 6 6 6 5 5 7 2 6 6 2 3 6 7 6 7 3 6 3 7 5 3 6 5 2 6 3 2 6 7 3
## [3849] 3 3 6 2 2 3 3 7 3 7 5 7 6 2 7 6 3 6 3 6 7 6 3 6 7 2 1 7 6 6 7 2 6 3 6 7 1
## [3886] 7 3 7 3 6 3 6 7 2 2 6 6 3 6 3 6 3 2 6 6 7 5 2 5 6 7 6 6 2 3 3 1 3 6 1 6 6
## [3923] 5 6 3 5 3 3 6 3 5 6 7 1 6 7 6 4 3 7 6 6 6 3 5 6 7 3 7 6 2 2 2 2 7 7 7 2 6
## [3960] 2 3 6 2 6 2 3 6 6 6 7 6 7 2 6 6 6 3 3 6 2 3 3 2 6 5 6 1 3 7 5 6 7 2 6 6 2
## [3997] 6 7 3 5 6 6 7 6 3 6 7 7 5 6 7 2 7 7 3 6 5 5 5 7 6 2 5 3 6 7 2 3 5 2 4 3 3
## [4034] 7 6 2 3 3 6 1 5 1 6 6 2 6 6 2 6 6 3 7 6 7 2 6 1 2 2 6 6 6 5 6 6 5 6 6 2 5
## [4071] 2 6 3 3 5 3 3 6 6 5 6 7 2 6 6 3 7 3 7 5 3 5 7 6 6 5 7 6 6 1 5 6 7 5 6 7 6
## [4108] 3 6 7 6 6 7 6 6 6 6 2 2 7 1 2 7 6 7 6 7 3 2 6 2 6 5 7 1 7 3 5 7 6 7 3 7 6
## [4145] 5 6 7 3 5 6 3 6 3 3 6 7 3 2 1 2 3 3 6 6 3 2 6 7 6 7 6 6 6 2 6 6 3 2 5 1 2
## [4182] 6 2 6 7 3 3 3 1 2 3 2 6 6 5 5 5 6 6 1 7 2 3 6 7 6 4 7 3 6 3 3 7 7 1 5 7 6
## [4219] 6 1 4 3 2 6 1 6 6 6 6 3 6 2 7 6 6 7 6 1 6 5 7 5 6 6 3 3 2 3 3 5 3 2 5 6 2
## [4256] 2 5 3 2 3 7 2 6 5 7 6 7 3 6 3 6 7 7 5 6 2 3 3 6 6 3 2 4 3 7 7 6 7 3 3 6 7
## [4293] 6 6 6 6 7 7 6 7 3 5 6 6 6 1 2 6 2 2 2 2 5 1 6 6 5 5 6 6 2 6 3 3 3 6 7 2 6
## [4330] 3 6 6 2 7 1 2 7 6 6 7 5 2 2 3 2 2 6 6 5 5 3 6 6 3 3 3 7 6 2 6 3 6 6 5 3 6
## [4367] 3 3 5 3 3 7 6 3 2 3 4 6 7 3 1 3 5 3 6 6 3 7 6 7 6 2 3 3 6 3 5 7 6 6 6 2 6
## [4404] 7 6 2 6 1 6 7 6 5 6 5 2 7 2 6 6 5 6 6 7 6 3 6 5 7 7 6 3 6 3 2 3 6 7 5 3 6
## [4441] 7 7 1 6 3 6 7 6 3 6 6 2 6 6 5 1 7 7 1 6 6 1 7 3 7 6 7 3 1 1 3 3 3 3 6 3 3
## [4478] 6 7 6 7 5 3 6 6 5 3 1 3 5 6 6 6 6 6 3 6 3 6 6 6 7 6 1 6 7 5 6 7 5 3 6 3 6
## [4515] 5 4 2 7 7 3 6 2 3 2 6 3 6 6 6 6 6 3 7 2 2 7 3 3 2 1 4 7 4 2 2 2 3 3 6 6 7
## [4552] 1 7 7 6 3 6 7 5 5 6 1 5 2 1 5 6 2 6 5 6 6 3 7 6 7 6 7 2 5 6 5 5 6 7 5 7 6
## [4589] 3 2 7 6 2 3 6 6 3 5 5 6 2 3 5 6 6 2 3 6 1 6 7 6 6 7 7 6 3 5 7 5 2 3 6 6 6
## [4626] 3 5 2 2 2 7 3 5 3 2 6 7 2 3 7 5 3 6 7 6 7 5 6 3 2 6 3 3 2 6 3 6 7 5 3 6 3
## [4663] 1 6 6 6 3 2 5 6 3 6 7 3 3 6 1 3 2 6 3 6 6 3 6 6 6 6 6 2 6 2 7 2 6 6 7 2 1
## [4700] 3 1 6 1 3 6 2 7 7 5 7 6 6 7 6 5 5 6 5 2 6 5 6 6 1 5 3 3 1 6 7 2 6 3 7 6 6
## [4737] 3 5 6 6 6 3 2 6 5 6 6 6 2 5 6 3 6 5 5 6 7 6 3 3 7 2 3 3 6 6 2 6 7 6 6 6 6
## [4774] 7 3 6 6 2 2 6 1 2 6 6 7 6 2 3 6 6 7 6 7 6 2 3 5 7 6 2 1 6 3 6 1 6 2 6 7 2
## [4811] 6 2 6 3 6 3 6 3 6 6 3 6 3 1 3 6 7 6 7 3 4 2 3 6 1 6 5 1 6 2 6 7 3 2 3 7 5
## [4848] 2 3 3 6 6 6 3 6 2 6 3 7 2 7 3 7 6 6 7 6 7 7 3 5 3 2 6 6 2 7 5 2 7 6 7 7 2
## [4885] 2 3 2 2 3 3 6 7 2 3 2 6 3 3 5 1 7 7 6 7 7 7 7 5 6 6 1 7 6 3 6 6 1 3 2 7 7
## [4922] 3 1 6 3 3 6 6 6 2 2 2 2 2 5 6 6 2 6 1 1 2 6 6 6 5 2 6 6 6 7 3 1 6 2 6 6 6
## [4959] 3 7 5 6 5 2 3 7 5 2 2 2 3 2 5 6 2 6 6 5 6 7 3 7 3 3 7 1 6 6 2 6 3 6 7 3 6
## [4996] 5 6 6 7 6 3 7 2 6 5 6 6 2 3 2 7 6 6 7 3 6 7 6 7 6 3 1 7 7 2 6 6 7 7 2 6 6
## [5033] 5 6 1 6 6 1 5 7 6 6 3 6 7 6 7 6 4 3 7 7 6 1 7 1 3 6 3 5 2 5 6 3 3 7 6 1 5
## [5070] 5 3 6 6 2 3 3 3 2 7 6 3 3 2 6 6 6 4 7 7 7 3 7 6 3 7 3 2 6 3 2 2 5 6 2 6 6
## [5107] 6 2 6 6 3 7 6 2 2 6 5 2 3 6 3 6 6 6 6 6 6 3 7 7 6 3 5 3 5 7 7 7 2 5 5 6 3
## [5144] 3 6 6 6 2 3 1 6 6 6 7 5 6 7 1 1 3 2 6 2 6 3 3 1 3 7 6 1 5 6 2 1 3 3 3 5 2
## [5181] 2 6 1 3 6 2 6 3 6 3 3 6 2 6 7 6 3 7 5 7 3 6 1 1 6 6 2 3 7 6 1 6 7 6 5 6 6
## [5218] 7 7 2 1 7 3 3 2 6 7 6 1 7 6 3 6 3 6 6 3 6 3 3 7 6 2 5 1 6 1 6 6 3 3 3 6 1
## [5255] 6 5 7 6 3 6 4 1 3 3 7 2 6 7 3 6 6 6 1 7 6 3 7 2 1 2 7 5 5 6 6 6 3 5 3 2 3
## [5292] 1 2 6 7 5 5 6 3 3 1 6 3 3 3 2 1 6 3 3 7 5 5 6 2 6 6 6 2 5 6 2 3 6 6 3 6 3
## [5329] 1 3 6 7 6 6 7 6 6 3 7 2 7 5 6 3 1 5 2 7 3 5 3 3 6 2 6 3 5 6 4 3 5 3 6 5 3
## [5366] 3 6 3 6 6 5 6 6 6 5 2 2 3 2 6 6 6 6 6 6 5 6 5 3 5 2 6 3 3 6 5 2 7 2 6 7 7
## [5403] 6 2 7 6 2 3 5 7 5 6 2 1 6 6 3 2 7 3 3 7 5 5 3 3 3 3 2 6 2 3 3 6 6 1 6 6 3
## [5440] 6 5 2 2 2 7 5 5 7 6 6 7 6 6 7 7 3 3 6 6 2 7 6 3 2 2 3 1 2 6 6 6 3 4 2 3 7
## [5477] 3 6 3 3 6 6 6 6 6 1 5 2 5 6 3 7 7 6 2 4 3 5 6 5 3 7 6 2 5 6 3 2 6 7 6 2 3
## [5514] 3 7 7 7 2 6 6 1 7 6 1 3 7 2 3 6 6 2 3 6 7 6 1 6 2 1 3 7 2 3 5 7 5 6 7 7 7
## [5551] 6 3 6 6 3 3 1 6 3 3 3 6 6 7 6 6 5 7 5 6 3 1 5 7 6 4 6 3 3 3 5 5 3 3 3 5 7
## [5588] 6 6 7 6 6 6 6 2 6 6 7 6 7 6 6 2 3 2 6 7 5 7 2 5 6 6 2 7 2 2 6 6 6 3 2 5 6
## [5625] 3 2 3 3 2 3 6 6 6 2 3 1 6 7 6 2 6 6 6 6 6 7 5 2 2 5 1 7 1 6 6 6 3 5 6 3 7
## [5662] 1 5 6 3 5 3 3 1 6 7 6 3 7 7 6 1 6 3 3 6 6 6 7 6 1 2 3 6 3 6 6 6 2 7 7 6 2
## [5699] 3 3 6 6 6 6 5 6 7 3 3 2 6 6 1 7 2 6 5 6 3 7 6 5 6 6 3 6 6 6 3 3 3 6 7 5 3
## [5736] 6 5 5 3 6 5 6 7 6 3 6 6 3 6 6 3 7 1 6 5 3 6 3 6 6 6 2 7 2 6 6 2 6 6 6 3 4
## [5773] 5 2 6 6 3 6 3 5 5 3 2 3 6 6 3 2 7 5 2 6 2 2 7 3 5 6 3 2 6 6 6 6 7 3 3 7 2
## [5810] 3 6 6 7 2 6 7 3 5 6 3 2 3 6 5 3 6 7 6 1 2 5 7 7 6 3 6 3 6 6 7 5 3 5 1 3 6
## [5847] 6 7 6 1 5 6 7 6 6 3 5 1 7 2 4 7 3 6 2 1 3 2 6 3 6 1 3 7 2 3 2 1 2 3 5 3 2
## [5884] 7 6 2 2 5 6 2 7 6 3 6 3 6 2 3 1 3 6 1 6 5 1 1 1 3 6 1 2 6 6 5 1 6 6 6 6 5
## [5921] 6 6 3 2 6 3 6 3 2 7 3 1 6 6 6 7 7 7 6 2 3 3 5 6 3 7 6 6 5 3 6 3 5 1 6 3 1
## [5958] 7 6 3 7 3 3 7 7 7 6 3 5 6 5 6 7 6 6 6 3 6 3 6 2 7 5 6 3 6 3 6 5 5 5 6 6 6
## [5995] 6 6 6 3 6 5 7 6 3 6 6 6 6 3 6 3 6 6 3 1 2 6 6 6 1 3 2 7 1 6 2 3 3 7 5 6 7
## [6032] 2 3 3 1 7 3 6 7 6 7 3 2 7 2 6 5 6 2 7 3 6 2 6 6 7 6 7 3 6 7 6 1 7 2 7 6 5
## [6069] 3 3 2 2 3 1 5 6 7 3 5 1 3 3 6 2 7 2 3 6 6 2 7 3 1 7 3 3 7 3 6 3 3 1 5 3 2
## [6106] 3 5 1 3 3 6 6 1 3 3 6 6 6 6 1 5 7 6 6 6 6 5 7 7 6 6 7 5 3 3 6 2 2 5 1 6 7
## [6143] 6 6 1 3 5 3 3 3 2 7 6 7 2 7 3 6 5 6 3 5 6 2 6 5 5 6 1 3 3 3 5 3 3 6 7 2 2
## [6180] 6 6 5 6 3 7 6 6 6 6 6 3 3 6 3 2 6 6 6 3 3 6 6 1 6 3 6 7 6 1 3 3 6 6 3 2 2
## [6217] 7 6 3 7 1 6 2 5 6 2 3 2 5 2 7 1 2 3 6 6 1 6 3 7 6 6 3 2 5 6 2 5 7 3 2 6 6
## [6254] 3 3 5 3 1 7 6 6 6 6 2 7 6 6 3 3 6 6 2 1 7 1 7 3 6 6 7 3 2 5 3 7 6 6 7 5 3
## [6291] 7 1 7 5 6 2 7 7 3 2 2 6 3 3 3 7 3 6 6 6 6 2 6 6 6 3 3 3 5 7 7 2 6 7 5 3 5
## [6328] 2 6 7 6 7 7 6 7 6 3 2 6 6 2 5 3 2 5 3 5 3 6 3 6 6 7 3 6 1 2 6 3 6 6 6 3 2
## [6365] 6 1 6 6 3 3 1 5 3 2 3 3 6 6 6 6 7 3 5 3 6 6 2 6 3 2 4 6 2 5 6 3 2 6 6 6 7
## [6402] 6 6 3 7 6 5 3 5 6 2 6 1 6 2 3 6 5 6 5 3 6 6 7 7 6 7 2 7 7 6 3 1 5 1 7 1 6
## [6439] 3 6 3 7 2 7 3 5 2 2 3 6 6 5 6 6 1 5 1 6 3 7 3 6 2 2 6 6 3 3 6 6 3 2 6 6 5
## [6476] 6 3 6 6 5 7 6 3 3 3 5 6 3 5 3 3 6 6 3 6 3 7 6 1 7 3 1 6 3 6 3 2 3 3 6 1 3
## [6513] 7 6 2 2 7 1 1 3 3 5 2 3 2 6 2 3 3 3 1 2 6 6 6 1 3 6 5 3 6 3 6 1 2 2 6 3 2
## [6550] 6 5 2 6 6 3 3 3 1 2 3 7 6 6 6 5 6 5 6 5 3 3 2 1 6 3 3 5 7 3 6 6 7 6 3 6 2
## [6587] 5 7 3 6 2 6 3 6 2 6 6 2 5 6 7 6 3 7 6 2 6 6 3 3 3 3 1 6 6 6 3 1 3 6 6 6 5
## [6624] 3 7 3 7 3 6 7 2 6 7 5 3 3 3 2 7 6 4 6 1 6 6 6 6 7 7 2 3 3 2 5 1 2 3 6 6 6
## [6661] 7 3 1 1 3 2 3 6 6 6 3 6 6 2 6 6 1 6 7 5 2 5 5 6 6 6 7 3 3 7 2 3 6 7 2 6 1
## [6698] 3 3 6 6 1 6 2 3 2 3 5 3 7 6 2 6 7 1 3 6 3 5 2 6 2 7 6 3 1 5 6 3 6 3 2 3 3
## [6735] 6 3 6 3 6 6 1 2 6 6 3 3 7 7 2 7 7 3 3 3 6 3 3 3 6 1 6 6 6 3 3 6 6 6 6 3 6
## [6772] 6 2 6 6 2 2 3 3 3 6 5 3 6 3 1 1 6 7 1 2 3 6 1 6 3 2 3 7 3 6 2 6 6 3 3 5 6
## [6809] 6 3 2 2 3 2 3 6 2 6 7 2 3 3 5 6 2 6 5 3 3 5 3 3 2 3 6 3 2 3 5 6 2 1 1 1 6
## [6846] 2 3 3 6 3 3 5 2 2 2 6 3 7 5 6 3 7 6 5 5 3 6 1 6 7 2 3 6 1 6 3 2 6 2 6 6 2
## [6883] 6 5 5 3 2 7 3 6 3 6 1 3 2 7 3 3 6 2 5 6 3 3 3 5 3 6 6 5 6 3 6 3 6 2 7 6 3
## [6920] 2 2 3 2 2 3 6 5 6 3 3 3 2 6 3 6 6 1 7 1 6 1 2 6 5 7 6 6 2 3 6 6 5 3 6 3 6
## [6957] 5 3 6 6 6 3 6 6 6 6 6 3 1 5 3 2 2 6 1 2 6 3 3 2 7 3 3 3 2 2 1 3 3 2 7 1 7
## [6994] 6 6 6 2 1 3 2 3 2 2 6 3 2 2 6 7 3 6 6 6 7 7 6 2 2 3 7 6 6 3 3 6 3 6 5 3 3
## [7031] 3 3 3 6 6 3 2 2 3 2 5 6 1 1 1 6 4 2 3 7 5 3 2 6 6 1 6 6 3 6 3 2 3 6 1 6 2
## [7068] 3 3 3 2 3 3 6 6 2 6 6 7 3 6 3 2 2 3 3 6 2 6 2 6 6 3 6 3 1 3 1 7 6 7 2 1 3
## [7105] 2 6 3 2 6 6 6 7 6 3 3 3 6 3 7 6 2 3 7 6 7 1 3 7 2 2 6 6 5 5 3 2 2 3 3 2 6
## [7142] 3 2 6 6 3 2 2 3 3 3 3 7 2 3 3 5 5 6 3 2 6 3 6 2 6 2 1 6 6 6 6 2 6 6 7 2 6
## [7179] 6 6 6 6 5 6 3 6 2 7 3 6 7 2 6 5 3 5 3 2 5 5 5 3 5 2 6 6 3 2 3 7 6 6 5 6 6
## [7216] 6 6 6 6 5 3 6 5 3 3 6 3 6 6 3 3 5 3 6 5 1 1 2 1 5 6 6 3 6 3 5 3 6 2 6 6 2
## [7253] 7 2 5 2 6 2 6 3 2 2 3 7 6 7 6 2 2 3 3 3 6 1 6 2 5 4 1 5 6 3 3 6 3 2 3 3 6
## [7290] 2 1 6 6 6 3 1 6 6 3 6 2 3 1 5 6 6 2 6 7 3 2 3 7 2 1 6 3 1 2 7 3 3 3 6 6 3
## [7327] 6 2 3 6 7 7 2 5 7 6 7 7 1 6 3 3 7 2 1 3 3 3 3 3 7 1 3 3 3 3 3 2 6 6 6 7 2
## [7364] 6 2 7 3 5 3 3 3 3 7 3 2 5 3 3 7 6 2 1 3 2 5 2 6 3 3 6 6 2 3 6 6 2 5 6 6 2
## [7401] 6 6 6 6 1 6 6 6 3 3 6 2 6 1 6 1 3 7 6 3 6 6 6 2 6 6 2 5 5 7 2 3 5 3 1 2 3
## [7438] 1 3 2 2 6 6 5 3 6 3 3 6 6 2 6 2 6 6 3 2 6 3 2 6 1 3 6 2 6 3 5 6 6 3 6 6 7
## [7475] 5 6 6 3 6 3 6 6 2 5 7 3 6 5 1 1 7 3 3 6 3 6 6 3 7 6 6 2 6 5 3 3 3 3 7 2 3
## [7512] 3 3 7 7 2 3 3 6 6 2 7 3 3 2 6 3 3 6 2 3 6 2 6 6 6 3 2 5 6 2 6 6 6 3 6 6 1
## [7549] 1 3 6 3 2 4 3 6 3 2 6 2 1 3 6 3 3 7 6 3 7 7 3 3 6 2 2 3 6 3 6 3 7 7 1 6 6
## [7586] 6 3 7 6 5 1 2 1 6 3 3 5 3 7 1 6 6 3 6 3 2 3 2 6 3 3 3 6 3 6 3 6 6 2 1 5 5
## [7623] 6 6 6 2 6 3 3 7 3 6 3 6 6 6 2 6 3 2 6 2 6 2 3 5 3 2 6 5 6 3 2 3 7 7 6 3 1
## [7660] 3 3 7 3 6 2 3 6 1 5 2 1 6 5 2 6 6 3 6 2 6 7 1 6 6 6 5 6 3 5 3 3 3 3 6 2 6
## [7697] 6 3 2 6 7 2 2 6 3 1 7 3 6 6 6 7 6 1 6 3 2 6 3 6 3 3 1 5 6 3 6 3 1 7 3 6 5
## [7734] 2 6 3 3 6 6 3 2 6 7 6 3 2 6 2 6 6 6 1 2 1 6 6 6 2 3 7 6 7 3 6 5 3 3 6 3 2
## [7771] 3 5 1 6 1 6 6 2 2 6 3 2 6 6 3 5 7 2 2 2 6 6 3 3 7 3 3 3 6 6 3 3 6 1 3 6 1
## [7808] 6 6 1 2 6 6 3 2 6 7 3 7 7 3 6 3 2 6 3 6 3 6 3 1 2 3 2 2 6 6 3 5 6 6 6 6 3
## [7845] 2 2 2 7 6 6 3 6 7 2 6 2 6 6 6 1 6 6 2 5 3 2 2 6 3 6 5 3 6 3 6 6 2 3 2 3 3
## [7882] 1 7 6 3 3 3 6 6 3 3 6 3 2 6 3 3 6 3 7 3 1 6 2 6 3 1 3 2 6 3 7 3 1 3 3 3 3
## [7919] 6 2 6 7 6 7 6 6 3 2 2 3 7 6 3 2 3 3 6 3 2 2 3 7 3 3 2 6 2 6 3 6 3 1 2 6 2
## [7956] 3 2 6 6 2 6 2 5 5 1 3 6 2 3 2 6 2 3 2 2 1 3 3 3 6 3 3 6 2 3 1 3 1 3 2 2 1
## [7993] 3 6 6 5 3 6 3 6 2 1 6 3 3 7 3 6 3 6 2 2 6 6 2 3 3 3 1 1 6 7 3 2 3 2 3 3 1
## [8030] 6 2 2 2 3 6 1 6 6 6 3 3 6 3 3 3 3 1 3 6 6 2 6 6 6 3 5 3 3 3 3 6 7 3 1 6 3
## [8067] 3 2 3 1 6 3 6 7 7 2 6 6 3 3 3 1 6 2 1 6 6 2 6 5 3 2 2 2 3 6 3 2 7 3 1 1 1
## [8104] 3 2 6 3 2 3 2 3 6 3 6 2 2 3 3 3 6 5 6 6 3 3 3 2 5 3 3 3 6 2 6 2 3 2 1 1 1
## [8141] 6 3 2 6 3 6 3 6 5 6 5 1 2 2 1 3 2 2 2 7 6 3 6 6 6 6 3 6 1 2 2 3 3 2 3 3 3
## [8178] 3 2 3 5 3 5 3 2 3 3 6 1 3 2 2 6 6 2 1 3 6 6 3 6 3 3 6 6 3 6 6 5 3 6 2 2 2
## [8215] 3 7 6 5 6 2 6 3 1 5 3 2 2 5 6 1 2 6 6 2 1 6 3 5 6 7 1 1 6 1 6 3 3 2 3 2 6
## [8252] 6 3 3 6 7 7 2 5 3 2 3 3 3 1 5 6 6 1 6 3 3 6 2 3 1 6 2 3 3 1 1 6 5 1 3 3 6
## [8289] 6 3 3 3 7 2 2 3 5 2 6 3 3 6 1 3 6 6 6 1 5 5 3 1 3 3 1 5 1 6 1 6 6 2 1 1 1
## [8326] 3 3 2 3 2 1 3 2 2 3 3 1 3 6 3 6 3 6 2 6 3 6 6 3 3 5 2 7 6 1 3 3 3 3 1 6 3
## [8363] 3 3 2 5 1 3 2 3 2 6 3 3 6 6 2 1 3 3 3 3 3 3 2 7 2 1 3 3 2 5 7 2 3 6 7 6 6
## [8400] 3 2 2 6 2 2 2 3 1 6 6 6 6 2 3 3 3 2 3 6 6 3 6 5 6 6 6 2 2 1 3 1 2 3 2 6 2
## [8437] 5 3 5 3 1 6 2 3 2 2 3 1 2 2 6 6 7 6 3 3 3 1 2 1 3 6 3 1 2 7 3 6 2 7 3 6 2
## [8474] 6 6 3 6 2 2 1 2 2 3 1 2 2 3 2 3 7 2 2 3 3 2 3 3 2 3 2 2 6 1 6 1 2 1 6 6 3
## [8511] 2 3 2 3 3 1 2 3 6 2 3 6 3 2 2 6 3 3 2 5 2 6 2 3 7 1 2 2 3 3 6 7 2 3 6 5 1
## [8548] 3 3 5 6 3 7 3 1 3 1 2 3 6 6 2 1 7 2 2 2 1 2 1 6 3 3 1 6 6 3 6 2 1 2 1 5 6
## [8585] 5 6 6 2 1 1 3 6 6 2 2 6 1 6 6 6 3 3 6 3 3 2 3 2 3 1 6 7 2 7 3 6 6 3 3 2 3
## [8622] 2 2 3 3 6 5 3 2 3 3 3 2 1 6 2 3 2 1 6 3 2 2 3 3 6 6 1 6 1 3 1 3 6 3 6 2 3
## [8659] 6 1 6 7 7 1 3 6 3 3 6 3 2 2 1 2 2 6 6 2 1 6 6 3 3 2 5 6 6 2 6 7 6 6 1 3 6
## [8696] 1 3 2 3 2 1 1 3 1 3 5 3 7 6 2 2 3 3 2 3 3 7 3 1 2 3 2 6 6 6 3 3 1 3 6 2 3
## [8733] 1 2 6 3 1 7 6 6 6 3 3 2 1 1 6 3 1 3 2 2 2 2 3 2 3 1 1 3 3 3 3 6 3 1 3 3 3
## [8770] 3 3 2 2 3 6 3 3 1 2 1 6 3 6 3 2 6 3 2 3 6 1 6 1 2 3 5 1 1 3 2 3 6 6 3 6 1
## [8807] 3 6 3 3 3 1 2 5 3 1 1 3 3 1 1 1 3 1 3 3 3 3 1 2 1 1 2 1 1 1 3 1 1 1 1 1 1
## [8844] 2 1 1 1 3 1 3 1 1 1 1 2 1 7 5 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1
## [8881] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8918] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 1 1 1 1 1 1 1 1
##
## Within cluster sum of squares by cluster:
## [1] 5135.407 6404.103 11284.113 9851.827 19408.272 10652.610 16755.565
## (between_SS / total_SS = 47.7 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"# Sumas de cuadrados
agrupacion2_km$withinss # Suma de cuadrados dentro de cada cluster## [1] 5135.407 6404.103 11284.113 9851.827 19408.272 10652.610 16755.565agrupacion2_km$tot.withinss # Suma de cuadrados Total dentro de cada cluster## [1] 79491.9agrupacion2_km$totss # Suma de cuadrados total suma(cuadrado(x - media))## [1] 152133agrupacion2_km$betweenss # Suma de cuadrados entre cluster. ## [1] 72641.1Se obtiene por diferencia
# Tamaño de cada cluster
agrupacion2_km$size## [1] 629 1186 2049 81 894 2846 1265# Proporciones de cada grupo
prop.table(agrupacion2_km$size)*100## [1] 7.0279330 13.2513966 22.8938547 0.9050279 9.9888268 31.7988827 14.1340782# Promedios de cada cluster
agrupacion2_km$centers## BALANCE BALANCE_FREQUENCY PURCHASES ONEOFF_PURCHASES
## 1 -0.33548683 -0.3480563 -0.28450959 -0.2089610
## 2 -0.70185522 -2.1353744 -0.30707758 -0.2305684
## 3 -0.37010983 0.3307223 -0.04044644 -0.2323855
## 4 1.41086703 0.4133560 7.12740831 6.3006262
## 5 1.66342130 0.3925068 -0.20165682 -0.1483789
## 6 0.00758072 0.4020436 -0.34246008 -0.2232139
## 7 0.14136201 0.4310136 0.95148444 0.9000910
## INSTALLMENTS_PURCHASES CASH_ADVANCE PURCHASES_FREQUENCY
## 1 -0.2884590 0.06553502 -0.1987235
## 2 -0.3023702 -0.32293895 -0.5473794
## 3 0.3311265 -0.36881520 0.9795992
## 4 5.2746145 0.01008892 1.0847069
## 5 -0.2043053 1.99345930 -0.4546730
## 6 -0.3995501 -0.10446911 -0.8093484
## 7 0.5961252 -0.30684927 1.0980333
## ONEOFF_PURCHASES_FREQUENCY PURCHASES_INSTALLMENTS_FREQUENCY
## 1 -0.2725572 -0.2307420
## 2 -0.4288460 -0.4410267
## 3 -0.3520883 1.1708958
## 4 1.8853550 1.0387160
## 5 -0.1877592 -0.4026141
## 6 -0.3343386 -0.7528907
## 7 1.8720547 0.5435232
## CASH_ADVANCE_FREQUENCY CASH_ADVANCE_TRX PURCHASES_TRX CREDIT_LIMIT PAYMENTS
## 1 0.3040953 -0.002215869 -0.3855649 -0.5574688 -0.3906787
## 2 -0.5220910 -0.376710762 -0.4166341 -0.1720637 -0.2016367
## 3 -0.4784524 -0.363126048 0.1695659 -0.2778674 -0.2228754
## 4 -0.2948836 -0.112437370 4.7418167 2.1659223 4.9049000
## 5 1.9103036 1.925602011 -0.2378460 1.0086432 0.8370880
## 6 0.0840972 -0.042020463 -0.4641917 -0.2998682 -0.2478932
## 7 -0.4071095 -0.316658116 1.2164780 0.7117184 0.3963639
## MINIMUM_PAYMENTS PRC_FULL_PAYMENT TENURE
## 1 -0.21632053 0.01289805 -3.19358659
## 2 -0.28507804 0.29568550 0.20189526
## 3 -0.02276624 0.30594224 0.25235377
## 4 1.10764506 0.84746214 0.33298534
## 5 0.55724342 -0.39082062 0.06980324
## 6 -0.01231509 -0.45234587 0.27191962
## 7 -0.02532010 0.46043795 0.30749896# promedios de cada cluster - opción 2
aggregate(credito_st, by=list(cluster=agrupacion2_km$cluster), mean)## cluster BALANCE BALANCE_FREQUENCY PURCHASES ONEOFF_PURCHASES
## 1 1 -0.33548683 -0.3480563 -0.28450959 -0.2089610
## 2 2 -0.70185522 -2.1353744 -0.30707758 -0.2305684
## 3 3 -0.37010983 0.3307223 -0.04044644 -0.2323855
## 4 4 1.41086703 0.4133560 7.12740831 6.3006262
## 5 5 1.66342130 0.3925068 -0.20165682 -0.1483789
## 6 6 0.00758072 0.4020436 -0.34246008 -0.2232139
## 7 7 0.14136201 0.4310136 0.95148444 0.9000910
## INSTALLMENTS_PURCHASES CASH_ADVANCE PURCHASES_FREQUENCY
## 1 -0.2884590 0.06553502 -0.1987235
## 2 -0.3023702 -0.32293895 -0.5473794
## 3 0.3311265 -0.36881520 0.9795992
## 4 5.2746145 0.01008892 1.0847069
## 5 -0.2043053 1.99345930 -0.4546730
## 6 -0.3995501 -0.10446911 -0.8093484
## 7 0.5961252 -0.30684927 1.0980333
## ONEOFF_PURCHASES_FREQUENCY PURCHASES_INSTALLMENTS_FREQUENCY
## 1 -0.2725572 -0.2307420
## 2 -0.4288460 -0.4410267
## 3 -0.3520883 1.1708958
## 4 1.8853550 1.0387160
## 5 -0.1877592 -0.4026141
## 6 -0.3343386 -0.7528907
## 7 1.8720547 0.5435232
## CASH_ADVANCE_FREQUENCY CASH_ADVANCE_TRX PURCHASES_TRX CREDIT_LIMIT PAYMENTS
## 1 0.3040953 -0.002215869 -0.3855649 -0.5574688 -0.3906787
## 2 -0.5220910 -0.376710762 -0.4166341 -0.1720637 -0.2016367
## 3 -0.4784524 -0.363126048 0.1695659 -0.2778674 -0.2228754
## 4 -0.2948836 -0.112437370 4.7418167 2.1659223 4.9049000
## 5 1.9103036 1.925602011 -0.2378460 1.0086432 0.8370880
## 6 0.0840972 -0.042020463 -0.4641917 -0.2998682 -0.2478932
## 7 -0.4071095 -0.316658116 1.2164780 0.7117184 0.3963639
## MINIMUM_PAYMENTS PRC_FULL_PAYMENT TENURE
## 1 -0.21632053 0.01289805 -3.19358659
## 2 -0.28507804 0.29568550 0.20189526
## 3 -0.02276624 0.30594224 0.25235377
## 4 1.10764506 0.84746214 0.33298534
## 5 0.55724342 -0.39082062 0.06980324
## 6 -0.01231509 -0.45234587 0.27191962
## 7 -0.02532010 0.46043795 0.30749896# Junta el archivo de datos con la columna de cluster
library(dplyr)
credito_st %>% mutate(grp=agrupacion2_km$cluster) -> credito_finalhead(credito_final)## BALANCE BALANCE_FREQUENCY PURCHASES ONEOFF_PURCHASES
## 1 -0.7319485 -0.2494205 -0.4248760 -0.3569141
## 2 0.7869169 0.1343172 -0.4695256 -0.3569141
## 3 0.4471102 0.5180549 -0.1076622 0.1088824
## 4 0.0490964 -1.0168960 0.2320449 0.5461589
## 5 -0.3587553 0.5180549 -0.4620372 -0.3472749
## 6 0.1178718 0.5180549 0.1544837 -0.3569141
## INSTALLMENTS_PURCHASES CASH_ADVANCE PURCHASES_FREQUENCY
## 1 -0.3490593 -0.4667595 -0.8064453
## 2 -0.4545508 2.6054589 -1.2216898
## 3 -0.4545508 -0.4667595 1.2697723
## 4 -0.4545508 -0.3686327 -1.0140688
## 5 -0.4545508 -0.4667595 -1.0140688
## 6 1.0197650 -0.4667595 0.4392858
## ONEOFF_PURCHASES_FREQUENCY PURCHASES_INSTALLMENTS_FREQUENCY
## 1 -0.6786229 -0.7072736
## 2 -0.6786229 -0.9169440
## 3 2.6733017 -0.9169440
## 4 -0.3992970 -0.9169440
## 5 -0.3992970 -0.9169440
## 6 -0.6786229 0.5507533
## CASH_ADVANCE_FREQUENCY CASH_ADVANCE_TRX PURCHASES_TRX CREDIT_LIMIT PAYMENTS
## 1 -0.6753111 -0.4760432 -0.5113047 -0.9603247 -0.5289492
## 2 0.5739307 0.1100677 -0.5917628 0.6886400 0.8185964
## 3 -0.6753111 -0.4760432 -0.1090140 0.8260537 -0.3837833
## 4 -0.2588989 -0.3295155 -0.5515337 0.8260537 -0.5986548
## 5 -0.6753111 -0.4760432 -0.5515337 -0.9053593 -0.3643474
## 6 -0.6753111 -0.4760432 -0.2699303 -0.7404628 -0.1150531
## MINIMUM_PAYMENTS PRC_FULL_PAYMENT TENURE grp
## 1 -0.30238310 -0.5255216 0.3606594 6
## 2 0.09749408 0.2342138 0.3606594 5
## 3 -0.09328819 -0.5255216 0.3606594 7
## 4 -0.22829414 -0.5255216 0.3606594 6
## 5 -0.25725202 -0.5255216 0.3606594 6
## 6 0.66972926 -0.5255216 0.3606594 3str(credito_final)## 'data.frame': 8950 obs. of 18 variables:
## $ BALANCE : num -0.7319 0.7869 0.4471 0.0491 -0.3588 ...
## $ BALANCE_FREQUENCY : num -0.249 0.134 0.518 -1.017 0.518 ...
## $ PURCHASES : num -0.425 -0.47 -0.108 0.232 -0.462 ...
## $ ONEOFF_PURCHASES : num -0.357 -0.357 0.109 0.546 -0.347 ...
## $ INSTALLMENTS_PURCHASES : num -0.349 -0.455 -0.455 -0.455 -0.455 ...
## $ CASH_ADVANCE : num -0.467 2.605 -0.467 -0.369 -0.467 ...
## $ PURCHASES_FREQUENCY : num -0.806 -1.222 1.27 -1.014 -1.014 ...
## $ ONEOFF_PURCHASES_FREQUENCY : num -0.679 -0.679 2.673 -0.399 -0.399 ...
## $ PURCHASES_INSTALLMENTS_FREQUENCY: num -0.707 -0.917 -0.917 -0.917 -0.917 ...
## $ CASH_ADVANCE_FREQUENCY : num -0.675 0.574 -0.675 -0.259 -0.675 ...
## $ CASH_ADVANCE_TRX : num -0.476 0.11 -0.476 -0.33 -0.476 ...
## $ PURCHASES_TRX : num -0.511 -0.592 -0.109 -0.552 -0.552 ...
## $ CREDIT_LIMIT : num -0.96 0.689 0.826 0.826 -0.905 ...
## $ PAYMENTS : num -0.529 0.819 -0.384 -0.599 -0.364 ...
## $ MINIMUM_PAYMENTS : num -0.3024 0.0975 -0.0933 -0.2283 -0.2573 ...
## $ PRC_FULL_PAYMENT : num -0.526 0.234 -0.526 -0.526 -0.526 ...
## $ TENURE : num 0.361 0.361 0.361 0.361 0.361 ...
## $ grp : int 6 5 7 6 6 3 7 3 6 2 ...credito_final$grp <- factor(credito_final$grp)
write.csv(credito_final,"credito_final_agrup_km.csv") #--- guardamos el clusteringValidación de resultados
# 1. índice de Validación de Davies-Bouldin (más pequeño)
cluster<-as.integer(credito_final$grp)library(clusterSim)# validación
indice<-index.DB(credito_st, cluster, centrotypes = "centroids")
indice$DB## [1] 1.565359# 2. Indice de Dunn (Más grande)
library(clValid)
dunn(Data=credito_st, clusters=cluster, distance = NULL)## [1] 0.004236815library(clv)
indices2<-cls.scatt.data(credito_st,cluster)
indices2## $intracls.complete
## c1 c2 c3 c4 c5 c6 c7
## [1,] 8.484273 11.50156 17.50348 47.27644 39.31679 13.15602 23.94542
##
## $intracls.average
## c1 c2 c3 c4 c5 c6 c7
## [1,] 3.847108 3.027454 3.014267 13.84299 5.707176 2.495759 4.769001
##
## $intracls.centroid
## c1 c2 c3 c4 c5 c6 c7
## [1,] 2.737592 2.127577 2.111381 9.610287 3.930929 1.745521 3.351321
##
## $intercls.single
## c1 c2 c3 c4 c5 c6 c7
## c1 0.0000000 0.4133254 0.6106389 8.140120 0.9904837 0.7532141 1.3749800
## c2 0.4133254 0.0000000 0.3271081 7.449947 1.2165143 0.2478713 0.5441095
## c3 0.6106389 0.3271081 0.0000000 4.749696 0.9790090 0.2003015 0.5144203
## c4 8.1401198 7.4499466 4.7496960 0.000000 5.1298704 7.3906286 1.8943831
## c5 0.9904837 1.2165143 0.9790090 5.129870 0.0000000 0.4530279 1.0627473
## c6 0.7532141 0.2478713 0.2003015 7.390629 0.4530279 0.0000000 0.3992235
## c7 1.3749800 0.5441095 0.5144203 1.894383 1.0627473 0.3992235 0.0000000
##
## $intercls.complete
## c1 c2 c3 c4 c5 c6 c7
## c1 0.00000 13.25043 18.51670 40.22090 33.60927 14.18016 23.93314
## c2 13.25043 0.00000 20.31798 40.01684 33.51233 16.45171 25.28403
## c3 18.51670 20.31798 0.00000 41.05209 35.82458 17.69370 22.98288
## c4 40.22090 40.01684 41.05209 0.00000 46.35467 40.77111 43.58798
## c5 33.60927 33.51233 35.82458 46.35467 0.00000 34.22501 38.27701
## c6 14.18016 16.45171 17.69370 40.77111 34.22501 0.00000 23.26053
## c7 23.93314 25.28403 22.98288 43.58798 38.27701 23.26053 0.00000
##
## $intercls.average
## c1 c2 c3 c4 c5 c6 c7
## c1 0.000000 5.337188 5.456850 17.34245 7.274408 4.942644 6.932803
## c2 5.337188 0.000000 4.611060 17.06413 7.241794 4.018687 6.292408
## c3 5.456850 4.611060 0.000000 16.11246 7.029049 4.115103 5.118805
## c4 17.342450 17.064125 16.112457 0.00000 17.026995 16.889592 14.526420
## c5 7.274408 7.241794 7.029049 17.02699 0.000000 5.928891 7.747875
## c6 4.942644 4.018687 4.115103 16.88959 5.928891 0.000000 5.780941
## c7 6.932803 6.292408 5.118805 14.52642 7.747875 5.780941 0.000000
##
## $intercls.centroid
## c1 c2 c3 c4 c5 c6 c7
## c1 0.000000 4.036469 4.196301 14.72460 5.483634 3.712840 5.411975
## c2 4.036469 0.000000 3.468556 14.52052 5.689157 2.883428 4.885333
## c3 4.196301 3.468556 0.000000 13.47958 5.416962 3.023611 3.234118
## c4 14.724605 14.520521 13.479584 0.00000 13.844557 14.390706 11.292122
## c5 5.483634 5.689157 5.416962 13.84456 0.000000 4.241809 5.669594
## c6 3.712840 2.883428 3.023611 14.39071 4.241809 0.000000 4.425887
## c7 5.411975 4.885333 3.234118 11.29212 5.669594 4.425887 0.000000
##
## $intercls.ave_to_cent
## c1 c2 c3 c4 c5 c6 c7
## c1 0.000000 4.687493 4.793385 15.22618 6.465095 4.225525 6.255069
## c2 4.687493 0.000000 4.072511 14.83631 6.433683 3.448815 5.625459
## c3 4.793385 4.072511 0.000000 13.75025 6.087183 3.583187 4.167871
## c4 15.226184 14.836309 13.750246 0.00000 14.679512 14.574157 11.901827
## c5 6.465095 6.433683 6.087183 14.67951 0.000000 4.837984 6.734635
## c6 4.225525 3.448815 3.583187 14.57416 4.837984 0.000000 4.988281
## c7 6.255069 5.625459 4.167871 11.90183 6.734635 4.988281 0.000000
##
## $intercls.hausdorff
## c1 c2 c3 c4 c5 c6 c7
## c1 0.000000 6.067932 6.407900 12.21986 6.664294 5.578556 6.716782
## c2 8.821189 0.000000 8.034756 11.66558 5.965738 7.779734 7.206007
## c3 14.453641 15.752449 0.000000 14.86964 6.254283 6.160095 9.220192
## c4 36.281246 34.973599 36.419443 0.00000 33.415484 35.721406 30.527737
## c5 28.930554 29.214105 29.392232 24.37168 0.000000 29.295505 28.551525
## c6 9.677054 11.245608 4.313352 13.46892 4.167078 0.000000 10.285113
## c7 20.207960 21.505820 9.735826 14.96926 9.326078 11.279921 0.000000
##
## $cluster.center
## [,1] [,2] [,3] [,4] [,5] [,6]
## c1 -0.33548683 -0.3480563 -0.28450959 -0.2089610 -0.2884590 0.06553502
## c2 -0.70185522 -2.1353744 -0.30707758 -0.2305684 -0.3023702 -0.32293895
## c3 -0.37010983 0.3307223 -0.04044644 -0.2323855 0.3311265 -0.36881520
## c4 1.41086703 0.4133560 7.12740831 6.3006262 5.2746145 0.01008892
## c5 1.66342130 0.3925068 -0.20165682 -0.1483789 -0.2043053 1.99345930
## c6 0.00758072 0.4020436 -0.34246008 -0.2232139 -0.3995501 -0.10446911
## c7 0.14136201 0.4310136 0.95148444 0.9000910 0.5961252 -0.30684927
## [,7] [,8] [,9] [,10] [,11] [,12]
## c1 -0.1987235 -0.2725572 -0.2307420 0.3040953 -0.002215869 -0.3855649
## c2 -0.5473794 -0.4288460 -0.4410267 -0.5220910 -0.376710762 -0.4166341
## c3 0.9795992 -0.3520883 1.1708958 -0.4784524 -0.363126048 0.1695659
## c4 1.0847069 1.8853550 1.0387160 -0.2948836 -0.112437370 4.7418167
## c5 -0.4546730 -0.1877592 -0.4026141 1.9103036 1.925602011 -0.2378460
## c6 -0.8093484 -0.3343386 -0.7528907 0.0840972 -0.042020463 -0.4641917
## c7 1.0980333 1.8720547 0.5435232 -0.4071095 -0.316658116 1.2164780
## [,13] [,14] [,15] [,16] [,17]
## c1 -0.5574688 -0.3906787 -0.21632053 0.01289805 -3.19358659
## c2 -0.1720637 -0.2016367 -0.28507804 0.29568550 0.20189526
## c3 -0.2778674 -0.2228754 -0.02276624 0.30594224 0.25235377
## c4 2.1659223 4.9049000 1.10764506 0.84746214 0.33298534
## c5 1.0086432 0.8370880 0.55724342 -0.39082062 0.06980324
## c6 -0.2998682 -0.2478932 -0.01231509 -0.45234587 0.27191962
## c7 0.7117184 0.3963639 -0.02532010 0.46043795 0.30749896
##
## $cluster.size
## [1] 629 1186 2049 81 894 2846 1265
##
## attr(,"class")
## [1] "cls.list"#Creando un for y comparando
set.seed(123)
db<-numeric()
dunn<-numeric()
for(k in 2:7){
resul<-kmeans(credito_st,k)
grupos<- resul$cluster
indice_db<-index.DB(credito_st,grupos,centrotypes = "centroids")
db[k]<-indice_db$DB
indiceDunn<- dunn(Data=credito_st, clusters=grupos, distance = NULL)
dunn[k]<- indiceDunn
}
indices_totales<-data.frame(cluster=c(2:7),
indice_db=db[2:7],
indiceDunn=dunn[2:7])
indices_totales## cluster indice_db indiceDunn
## 1 2 2.288551 0.003712166
## 2 3 1.990229 0.004787972
## 3 4 1.763470 0.003274795
## 4 5 1.658618 0.005243019
## 5 6 1.507591 0.004448280
## 6 7 1.565389 0.004236815Visualización de los resultados usando ACP
Si se tienen datos multidimensionales, una solución es realizar un ACP y plotear los individuos de acuerdo a los dos primeros componentes
library(factoextra)
fviz_cluster(agrupacion2_km, data = credito_st, ellipse.type = "convex") +
theme_classic()
### Validación de Resultados del k-means
# Bootstrap Evaluation of Clusters
library(fpc)
kclusters <- clusterboot(credito_st,
B=100,
clustermethod=kmeansCBI,
k=7,
seed=123)## boot 1
## boot 2
## boot 3
## boot 4
## boot 5
## boot 6
## boot 7
## boot 8
## boot 9
## boot 10
## boot 11
## boot 12
## boot 13
## boot 14
## boot 15
## boot 16
## boot 17
## boot 18
## boot 19
## boot 20
## boot 21
## boot 22
## boot 23
## boot 24
## boot 25
## boot 26
## boot 27
## boot 28
## boot 29
## boot 30
## boot 31
## boot 32
## boot 33
## boot 34
## boot 35
## boot 36
## boot 37
## boot 38
## boot 39
## boot 40
## boot 41
## boot 42
## boot 43
## boot 44
## boot 45
## boot 46
## boot 47
## boot 48
## boot 49
## boot 50
## boot 51
## boot 52
## boot 53
## boot 54
## boot 55
## boot 56
## boot 57
## boot 58
## boot 59
## boot 60
## boot 61
## boot 62
## boot 63
## boot 64
## boot 65
## boot 66
## boot 67
## boot 68
## boot 69
## boot 70
## boot 71
## boot 72
## boot 73
## boot 74
## boot 75
## boot 76
## boot 77
## boot 78
## boot 79
## boot 80
## boot 81
## boot 82
## boot 83
## boot 84
## boot 85
## boot 86
## boot 87
## boot 88
## boot 89
## boot 90
## boot 91
## boot 92
## boot 93
## boot 94
## boot 95
## boot 96
## boot 97
## boot 98
## boot 99
## boot 100# Los promedios deben salir lo más cercano a 1 posible.
# Un valor > 0.75 - 0.85 es muy bueno.
# Un valor < 0.6 es malo
kclusters$bootmean## [1] 0.4887709 0.7929662 0.7226087 0.5671568 0.7559132 0.8231856 0.6251651prop.table(table(credito_final$grp))*100##
## 1 2 3 4 5 6 7
## 7.0279330 13.2513966 22.8938547 0.9050279 9.9888268 31.7988827 14.1340782Importancia de las variables con el paquete FeatureImpCluster
library(FeatureImpCluster)
library(flexclust)
cl_km <- as.kcca(agrupacion2_km, credito_st)
str(cl_km)## Formal class 'kcca' [package "flexclust"] with 17 slots
## ..@ second : int [1:8950] 2 6 6 2 2 6 3 6 3 6 ...
## ..@ xrange : num [1:2, 1:17] -0.752 8.397 -3.703 0.518 -0.47 ...
## .. ..- attr(*, "dimnames")=List of 2
## .. .. ..$ : NULL
## .. .. ..$ : chr [1:17] "BALANCE" "BALANCE_FREQUENCY" "PURCHASES" "ONEOFF_PURCHASES" ...
## ..@ xcent : Named num [1:17] -2.68e-17 1.65e-16 -1.29e-18 4.65e-17 1.95e-17 ...
## .. ..- attr(*, "names")= chr [1:17] "BALANCE" "BALANCE_FREQUENCY" "PURCHASES" "ONEOFF_PURCHASES" ...
## ..@ totaldist: num 31547
## ..@ clsim : num [1:7, 1:7] 1 0.0483 0.0288 0 0.054 ...
## ..@ centers : num [1:7, 1:17] -0.335 -0.702 -0.37 1.411 1.663 ...
## .. ..- attr(*, "dimnames")=List of 2
## .. .. ..$ : chr [1:7] "1" "2" "3" "4" ...
## .. .. ..$ : chr [1:17] "BALANCE" "BALANCE_FREQUENCY" "PURCHASES" "ONEOFF_PURCHASES" ...
## ..@ family :Formal class 'kccaFamily' [package "flexclust"] with 9 slots
## .. .. ..@ name : chr "kmeans"
## .. .. ..@ dist :function (x, centers)
## .. .. ..@ cent :function (x)
## .. .. ..@ allcent :function (x, cluster, k = max(cluster, na.rm = TRUE))
## .. .. ..@ wcent :function (x, weights)
## .. .. ..@ weighted: logi TRUE
## .. .. ..@ cluster :function (x, centers, n = 1, distmat = NULL)
## .. .. ..@ preproc :function (x)
## .. .. ..@ groupFun:function (cluster, group, distmat)
## ..@ cldist : num [1:8950, 1:2] 1.62 2.91 3.04 2.18 1.27 ...
## ..@ k : int 7
## ..@ cluster : int [1:8950] 6 5 7 6 6 3 7 3 6 2 ...
## ..@ iter : int 1
## ..@ converged: logi TRUE
## ..@ clusinfo :'data.frame': 7 obs. of 4 variables:
## .. ..$ size : int [1:7] 629 1186 2049 81 894 2846 1265
## .. ..$ av_dist : num [1:7] 2.74 2.13 2.11 9.61 3.93 ...
## .. ..$ max_dist : num [1:7] 6.03 10.14 16.4 33.16 28.58 ...
## .. ..$ separation: num [1:7] 2.32 1.78 1.81 6.41 2.4 ...
## ..@ index : num(0)
## ..@ call : language as.kcca(object = agrupacion2_km, data = credito_st)
## ..@ control :Formal class 'flexclustControl' [package "flexclust"] with 10 slots
## .. .. ..@ iter.max : num 200
## .. .. ..@ tolerance : num 1e-06
## .. .. ..@ verbose : num 0
## .. .. ..@ classify : chr "auto"
## .. .. ..@ initcent : chr "randomcent"
## .. .. ..@ gamma : num 1
## .. .. ..@ simann : num [1:3] 0.3 0.95 10
## .. .. ..@ ntry : num 5
## .. .. ..@ min.size : num 2
## .. .. ..@ subsampling: num 1
## ..@ data :Formal class 'ModelEnv' [package "modeltools"] with 4 slots
## .. .. ..@ env :<environment: 0x000001b7e91ebe10>
## .. .. ..@ get :function (which)
## .. .. ..@ set :function (which, data)
## .. .. ..@ hooks: list()cl_km@xcent # Promedios de cada variable## BALANCE BALANCE_FREQUENCY
## -2.682290e-17 1.649061e-16
## PURCHASES ONEOFF_PURCHASES
## -1.293483e-18 4.648167e-17
## INSTALLMENTS_PURCHASES CASH_ADVANCE
## 1.952097e-17 -1.170153e-17
## PURCHASES_FREQUENCY ONEOFF_PURCHASES_FREQUENCY
## 2.607280e-17 -7.842888e-18
## PURCHASES_INSTALLMENTS_FREQUENCY CASH_ADVANCE_FREQUENCY
## 6.203449e-17 1.369869e-17
## CASH_ADVANCE_TRX PURCHASES_TRX
## -1.993440e-17 -1.768604e-17
## CREDIT_LIMIT PAYMENTS
## 8.552749e-17 -4.211017e-17
## MINIMUM_PAYMENTS PRC_FULL_PAYMENT
## 7.771367e-18 1.245822e-17
## TENURE
## 2.881370e-16cl_km@centers # Promedios de cada variable por cada cluster## BALANCE BALANCE_FREQUENCY PURCHASES ONEOFF_PURCHASES
## 1 -0.33548683 -0.3480563 -0.28450959 -0.2089610
## 2 -0.70185522 -2.1353744 -0.30707758 -0.2305684
## 3 -0.37010983 0.3307223 -0.04044644 -0.2323855
## 4 1.41086703 0.4133560 7.12740831 6.3006262
## 5 1.66342130 0.3925068 -0.20165682 -0.1483789
## 6 0.00758072 0.4020436 -0.34246008 -0.2232139
## 7 0.14136201 0.4310136 0.95148444 0.9000910
## INSTALLMENTS_PURCHASES CASH_ADVANCE PURCHASES_FREQUENCY
## 1 -0.2884590 0.06553502 -0.1987235
## 2 -0.3023702 -0.32293895 -0.5473794
## 3 0.3311265 -0.36881520 0.9795992
## 4 5.2746145 0.01008892 1.0847069
## 5 -0.2043053 1.99345930 -0.4546730
## 6 -0.3995501 -0.10446911 -0.8093484
## 7 0.5961252 -0.30684927 1.0980333
## ONEOFF_PURCHASES_FREQUENCY PURCHASES_INSTALLMENTS_FREQUENCY
## 1 -0.2725572 -0.2307420
## 2 -0.4288460 -0.4410267
## 3 -0.3520883 1.1708958
## 4 1.8853550 1.0387160
## 5 -0.1877592 -0.4026141
## 6 -0.3343386 -0.7528907
## 7 1.8720547 0.5435232
## CASH_ADVANCE_FREQUENCY CASH_ADVANCE_TRX PURCHASES_TRX CREDIT_LIMIT PAYMENTS
## 1 0.3040953 -0.002215869 -0.3855649 -0.5574688 -0.3906787
## 2 -0.5220910 -0.376710762 -0.4166341 -0.1720637 -0.2016367
## 3 -0.4784524 -0.363126048 0.1695659 -0.2778674 -0.2228754
## 4 -0.2948836 -0.112437370 4.7418167 2.1659223 4.9049000
## 5 1.9103036 1.925602011 -0.2378460 1.0086432 0.8370880
## 6 0.0840972 -0.042020463 -0.4641917 -0.2998682 -0.2478932
## 7 -0.4071095 -0.316658116 1.2164780 0.7117184 0.3963639
## MINIMUM_PAYMENTS PRC_FULL_PAYMENT TENURE
## 1 -0.21632053 0.01289805 -3.19358659
## 2 -0.28507804 0.29568550 0.20189526
## 3 -0.02276624 0.30594224 0.25235377
## 4 1.10764506 0.84746214 0.33298534
## 5 0.55724342 -0.39082062 0.06980324
## 6 -0.01231509 -0.45234587 0.27191962
## 7 -0.02532010 0.46043795 0.30749896barplot(cl_km)
data <- as.data.table(credito_st)
Importancia_km <- FeatureImpCluster(cl_km,data)
plot(Importancia_km)
#head(credito_final_agrup_km)library(MASS)
grupos = as.numeric(credito_final$grp)
parcoord(credito_final[,1:17],col =grupos)