Clusters - Puntos, USArrests y Clientes
Danara Esparza A00840602
2026-08-28
Teoría
Agrupamiento o clustering es una técnica de aprendizaje automático no supervisado que agrupa datos en función de su similitud.
Algunos usos típicos de esta técnico son:
- Segmentación de clientes.
- Detección de anormalidades.
- Categorización de documentos.
Instalar paquetes y llamar librerías
#install.packages("cluster") # análisis de agrupamiento
library(cluster)
#install.packages("ggplot2") # graficar
library(ggplot2)
#install.packages("data.table") # manejo de muchos datos
library(data.table)
#install.packages("factoextra") # gráfica de optimización del número de clusters
library(factoextra)
#install.packages("tidyverse")
library(tidyverse)Ejercicio 1: Puntos
Contexto
Agrupa los siguientes 8 puntos
Obtener datos
df1 <- data.frame(x=c(2,2,8,5,7,6,1,4), y=c(10,5,4,8,5,4,2,9)) Entender datos
summary(df1)## x y
## Min. :1.000 Min. : 2.000
## 1st Qu.:2.000 1st Qu.: 4.000
## Median :4.500 Median : 5.000
## Mean :4.375 Mean : 5.875
## 3rd Qu.:6.250 3rd Qu.: 8.250
## Max. :8.000 Max. :10.000str(df1) ## 'data.frame': 8 obs. of 2 variables:
## $ x: num 2 2 8 5 7 6 1 4
## $ y: num 10 5 4 8 5 4 2 9plot(df1$x,df1$y)
Escalar datos
# datos_escalados <- scale(datos_originales) Asignar número de grupos
grupo1 <- 3Agrupar los puntos
set.seed(123)
clusters1 <- kmeans(df1,grupo1)
clusters1## K-means clustering with 3 clusters of sizes 2, 3, 3
##
## Cluster means:
## x y
## 1 1.500000 3.500000
## 2 3.666667 9.000000
## 3 7.000000 4.333333
##
## Clustering vector:
## [1] 2 1 3 2 3 3 1 2
##
## Within cluster sum of squares by cluster:
## [1] 5.000000 6.666667 2.666667
## (between_SS / total_SS = 85.8 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"Optimizar número de grupos
set.seed(123)
optimizacion1 <- clusGap(df1, FUN=kmeans, nstart=1, K.max = 7)
# El K.max normalmente es 10, en este jercicio al ser de 8 datos se dejó en 7.
plot(optimizacion1, xlab = "Número de clusters K", main = "Optimización de Clusters") 
# Se selecciona como óptimo el primer punto más alto
# Si es diferente al original, regresar y ajustarGraficar los grupos
fviz_cluster(clusters1, data = df1) 
Agregar grupos a la base de datos
df1_clusters <- cbind(df1, cluster= clusters1$cluster)
head(df1_clusters) ## x y cluster
## 1 2 10 2
## 2 2 5 1
## 3 8 4 3
## 4 5 8 2
## 5 7 5 3
## 6 6 4 3Conclusiones
La técnica de clustering permite identificar patrones o grupos naturales en los datos sin necesidad de etiquetas previas.
Ejercicio 2: USArrests
Contexto
La base de datos USArrests contiene estadísticas en arrestos por cada 100,000 residentes por agresión, asesinatos y violación en cada uno de los 50 estados de EE.UU en 1973.
Obtener datos
df2 <- USArrests
df2 <- df2 %>% select(-UrbanPop) Entender datos
summary(df2)## Murder Assault Rape
## Min. : 0.800 Min. : 45.0 Min. : 7.30
## 1st Qu.: 4.075 1st Qu.:109.0 1st Qu.:15.07
## Median : 7.250 Median :159.0 Median :20.10
## Mean : 7.788 Mean :170.8 Mean :21.23
## 3rd Qu.:11.250 3rd Qu.:249.0 3rd Qu.:26.18
## Max. :17.400 Max. :337.0 Max. :46.00str(df2)## 'data.frame': 50 obs. of 3 variables:
## $ Murder : num 13.2 10 8.1 8.8 9 7.9 3.3 5.9 15.4 17.4 ...
## $ Assault: int 236 263 294 190 276 204 110 238 335 211 ...
## $ Rape : num 21.2 44.5 31 19.5 40.6 38.7 11.1 15.8 31.9 25.8 ...Escalar datos
df2_escalados <- scale(df2)
summary(df2_escalados)## Murder Assault Rape
## Min. :-1.6044 Min. :-1.5090 Min. :-1.4874
## 1st Qu.:-0.8525 1st Qu.:-0.7411 1st Qu.:-0.6574
## Median :-0.1235 Median :-0.1411 Median :-0.1209
## Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.7949 3rd Qu.: 0.9388 3rd Qu.: 0.5277
## Max. : 2.2069 Max. : 1.9948 Max. : 2.6444Asignar número de grupos
grupo2 <- 5Agrupar los puntos
set.seed(123)
clusters2 <- kmeans(df2_escalados,grupo2)
clusters2## K-means clustering with 5 clusters of sizes 7, 14, 17, 4, 8
##
## Cluster means:
## Murder Assault Rape
## 1 0.8292944 1.3313823 0.90560938
## 2 -1.0812577 -1.0779212 -1.00700542
## 3 -0.2754591 -0.2999280 -0.12336985
## 4 0.4562038 0.9358314 2.26533514
## 5 1.5238170 0.8908337 0.09934463
##
## Clustering vector:
## Alabama Alaska Arizona Arkansas California
## 5 4 1 3 4
## Colorado Connecticut Delaware Florida Georgia
## 4 2 3 1 5
## Hawaii Idaho Illinois Indiana Iowa
## 2 2 1 3 2
## Kansas Kentucky Louisiana Maine Maryland
## 3 3 5 2 1
## Massachusetts Michigan Minnesota Mississippi Missouri
## 3 1 2 5 3
## Montana Nebraska Nevada New Hampshire New Jersey
## 3 2 4 2 3
## New Mexico New York North Carolina North Dakota Ohio
## 1 1 5 2 3
## Oklahoma Oregon Pennsylvania Rhode Island South Carolina
## 3 3 3 2 5
## South Dakota Tennessee Texas Utah Vermont
## 2 5 5 3 2
## Virginia Washington West Virginia Wisconsin Wyoming
## 3 3 2 2 3
##
## Within cluster sum of squares by cluster:
## [1] 3.380664 5.645542 9.205038 1.346517 4.683603
## (between_SS / total_SS = 83.5 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"Optimizar número de grupos
set.seed(123)
optimizacion2 <- clusGap(df2_escalados, FUN=kmeans, nstart=1, K.max = 10)
# El K.max normalmente es 10, en este jercicio al ser de 8 datos se dejó en 7.
plot(optimizacion2, xlab = "Número de clusters K", main = "Optimización de Clusters") 
# Se selecciona como óptimo el primer punto más alto
# Si es diferente al original, regresar y ajustarGraficar los grupos
fviz_cluster(clusters2, data = df2_escalados) 
Agregar grupos a la base de datos
df2_clusters <- cbind(df2, cluster = clusters2$cluster)
head(df2_clusters)## Murder Assault Rape cluster
## Alabama 13.2 236 21.2 5
## Alaska 10.0 263 44.5 4
## Arizona 8.1 294 31.0 1
## Arkansas 8.8 190 19.5 3
## California 9.0 276 40.6 4
## Colorado 7.9 204 38.7 4df2_clusters %>% group_by(cluster) %>% summarise_all(mean) %>%
mutate(indicador_inseguridad=Murder+Assault+Rape)## # A tibble: 5 × 5
## cluster Murder Assault Rape indicador_inseguridad
## <int> <dbl> <dbl> <dbl> <dbl>
## 1 1 11.4 282. 29.7 323.
## 2 2 3.08 80.9 11.8 95.8
## 3 3 6.59 146. 20.1 172.
## 4 4 9.78 249. 42.4 301.
## 5 5 14.4 245 22.2 282.df2_clusters <- df2_clusters %>%
mutate(cluster= case_when(
cluster == 1 ~ "Inseguridad Muy Alta",
cluster == 4 ~ "Inseguridad Alta",
cluster == 5 ~ "Inseguridad Media",
cluster == 3 ~ "Inseguridad Baja",
cluster == 2 ~ "Inseguridad Muy Baja"
))
head(df2_clusters) ## Murder Assault Rape cluster
## Alabama 13.2 236 21.2 Inseguridad Media
## Alaska 10.0 263 44.5 Inseguridad Alta
## Arizona 8.1 294 31.0 Inseguridad Muy Alta
## Arkansas 8.8 190 19.5 Inseguridad Baja
## California 9.0 276 40.6 Inseguridad Alta
## Colorado 7.9 204 38.7 Inseguridad AltaEjercicio 3: Segmentación de clientes
Contexto
La base de datos ventas tiene los registros entre el 1 de diciembre de 2010 y el 9 de diciembre de 2011 de las ventas de una empresa minorista en línea sin tienda física, basada en Reino Unido. La empresa vende principalmente regalos únicos para toda ocasión, y muchos de sus clientes son mayoristas. Objetivo: Segmentar clientes, asignarles nombre y características de comportamiento, y proponer sugerencias a la empresa para aumentar ventas.
Obtener datos
# Cargar el archivo con codificación UTF-8 para evitar caracteres especiales en los nombres de columnas
df3_normal <- read.csv("/Users/danaraesparzamacias/Desktop/ventas.csv", encoding = "UTF-8")Renombrar columna de Ticket si es necesario, eliminar registros sin ID de cliente
# eliminar devoluciones (Cantidad <= 0) y precios inválidos
df3_limpio <- df3_normal %>%
rename(Ticket = colnames(df3_normal)[1]) %>%
filter(!is.na(Cliente), Cantidad > 0, Precio > 0) %>%
mutate(
Fecha = as.Date(Fecha, format = "%d/%m/%Y"),
MontoTotal = Cantidad * Precio
)Construcción de métricas RFM
fecha_referencia <- max(df3_limpio$Fecha) + 1
df3_rfm <- df3_limpio %>%
group_by(Cliente) %>%
summarise(
Recencia = as.numeric(fecha_referencia - max(Fecha)), # Días desde la última compra
Frecuencia = n_distinct(Ticket), # Número total de compras
Monto = sum(MontoTotal) # Gasto total acumulado
) %>%
column_to_rownames("Cliente")Entender datos
summary(df3_rfm)## Recencia Frecuencia Monto
## Min. : 1.00 Min. : 1.000 Min. : 3.75
## 1st Qu.: 18.00 1st Qu.: 1.000 1st Qu.: 306.72
## Median : 51.00 Median : 2.000 Median : 668.85
## Mean : 93.16 Mean : 4.227 Mean : 1993.61
## 3rd Qu.:143.00 3rd Qu.: 5.000 3rd Qu.: 1652.79
## Max. :374.00 Max. :209.000 Max. :280206.02str(df3_rfm)## 'data.frame': 4296 obs. of 3 variables:
## $ Recencia : num 326 3 19 311 37 205 233 215 23 34 ...
## $ Frecuencia: int 1 7 1 1 8 1 1 1 3 1 ...
## $ Monto : num 77184 4310 1758 334 2506 ...pairs(df3_rfm, main = "Matriz de Dispersión RFM")
Escalar datos
df3_escalados <- scale(df3_rfm)
summary(df3_escalados)## Recencia Frecuencia Monto
## Min. :-0.9202 Min. :-0.4556 Min. :-0.23167
## 1st Qu.:-0.7504 1st Qu.:-0.4556 1st Qu.:-0.19640
## Median :-0.4209 Median :-0.3144 Median :-0.15424
## Mean : 0.0000 Mean : 0.0000 Mean : 0.00000
## 3rd Qu.: 0.4977 3rd Qu.: 0.1092 3rd Qu.:-0.03968
## Max. : 2.8042 Max. :28.9132 Max. :32.39138Asignar número de grupos
grupo3 <- 3Agrupar los puntos
set.seed(123)
clusters3 <- kmeans(df3_escalados, grupo3)
clusters3## K-means clustering with 3 clusters of sizes 3189, 25, 1082
##
## Cluster means:
## Recencia Frecuencia Monto
## 1 -0.5146028 0.06646886 -0.01604087
## 2 -0.7376401 7.71679726 9.31252168
## 3 1.5337425 -0.37420435 -0.16789161
##
## Clustering vector:
## 12346 12347 12349 12350 12352 12353 12354 12355 12356 12357 12358 12360 12361
## 2 1 1 3 1 3 3 3 1 1 1 1 3
## 12362 12363 12364 12370 12371 12373 12374 12377 12378 12379 12380 12381 12383
## 1 1 1 3 1 3 1 3 1 1 1 1 3
## 12384 12386 12388 12390 12393 12394 12395 12397 12398 12399 12401 12402 12407
## 1 3 1 1 1 3 1 1 1 1 3 3 1
## 12408 12409 12410 12413 12414 12415 12417 12418 12421 12422 12423 12424 12425
## 1 1 3 1 3 2 1 1 1 1 1 3 1
## 12426 12427 12429 12430 12431 12432 12433 12434 12436 12437 12438 12441 12442
## 3 1 3 1 1 1 1 1 1 1 1 3 1
## 12444 12445 12446 12447 12448 12449 12450 12451 12452 12453 12454 12455 12456
## 1 1 1 3 1 1 3 1 1 1 1 1 1
## 12457 12458 12461 12462 12463 12464 12465 12468 12471 12472 12473 12474 12475
## 1 1 1 1 1 1 1 3 1 1 1 1 1
## 12476 12477 12478 12479 12480 12481 12483 12484 12488 12489 12490 12491 12492
## 1 1 1 1 1 1 1 1 1 3 1 1 1
## 12493 12494 12497 12498 12500 12501 12502 12504 12506 12507 12508 12509 12510
## 3 1 1 1 1 3 1 1 3 1 1 3 3
## 12512 12513 12514 12515 12516 12517 12518 12519 12520 12521 12522 12523 12524
## 1 1 3 3 1 1 1 1 1 3 1 1 1
## 12526 12527 12528 12530 12531 12532 12534 12535 12536 12538 12539 12540 12541
## 1 1 1 1 1 1 1 1 1 1 1 1 1
## 12544 12545 12546 12547 12548 12550 12551 12552 12553 12556 12557 12558 12559
## 1 1 1 3 3 1 3 1 1 1 1 1 3
## 12560 12561 12562 12564 12565 12566 12567 12569 12571 12572 12573 12574 12576
## 1 3 1 3 3 1 1 1 1 1 3 3 1
## 12577 12578 12579 12580 12581 12583 12584 12585 12586 12589 12590 12591 12592
## 1 1 1 3 1 1 1 3 1 1 3 3 1
## 12593 12594 12596 12597 12598 12599 12600 12601 12602 12603 12604 12607 12609
## 1 1 1 1 1 1 1 3 1 1 1 1 1
## 12610 12611 12612 12613 12614 12615 12616 12617 12618 12619 12620 12621 12622
## 1 1 1 1 3 1 1 1 1 1 1 1 3
## 12623 12624 12625 12626 12627 12628 12633 12635 12637 12638 12639 12640 12641
## 3 1 3 1 1 1 1 1 1 1 3 1 1
## 12642 12643 12644 12645 12646 12647 12648 12649 12650 12651 12652 12653 12654
## 1 1 1 1 1 1 3 1 1 3 3 3 1
## 12656 12657 12658 12659 12660 12662 12665 12668 12669 12670 12672 12673 12674
## 1 1 1 1 1 1 3 1 3 1 3 1 1
## 12676 12678 12679 12680 12681 12682 12683 12684 12685 12686 12688 12689 12690
## 1 1 1 1 1 1 1 1 1 3 1 1 3
## 12691 12693 12694 12695 12697 12700 12701 12702 12703 12705 12707 12708 12709
## 1 1 1 1 1 1 1 1 1 1 3 1 1
## 12710 12712 12713 12714 12715 12716 12717 12718 12719 12720 12721 12722 12723
## 1 1 1 1 1 1 3 1 1 1 1 1 1
## 12724 12725 12726 12727 12728 12729 12731 12732 12733 12734 12735 12736 12738
## 1 3 1 1 1 1 1 3 3 3 3 3 3
## 12739 12740 12743 12744 12747 12748 12749 12750 12752 12753 12754 12755 12756
## 1 1 1 1 1 2 1 1 1 1 3 3 1
## 12757 12758 12759 12762 12763 12764 12766 12769 12770 12772 12775 12778 12779
## 1 1 1 1 1 3 1 3 3 1 1 1 1
## 12782 12783 12784 12785 12787 12789 12790 12791 12792 12793 12794 12795 12797
## 1 1 1 3 1 1 3 3 3 3 1 1 3
## 12798 12802 12808 12809 12811 12812 12814 12815 12816 12817 12818 12820 12821
## 1 3 1 3 3 1 1 3 1 3 3 1 3
## 12822 12823 12824 12826 12827 12828 12829 12830 12831 12832 12833 12834 12836
## 1 1 1 1 1 1 3 1 3 1 3 3 1
## 12837 12838 12839 12840 12841 12842 12843 12844 12845 12847 12849 12851 12852
## 3 1 1 1 1 1 1 1 3 1 1 1 3
## 12853 12854 12855 12856 12857 12863 12864 12865 12866 12867 12868 12871 12872
## 1 1 3 1 3 1 3 1 3 1 3 1 3
## 12873 12875 12876 12877 12878 12879 12881 12882 12883 12884 12885 12886 12888
## 3 3 1 1 3 1 3 1 1 1 1 1 3
## 12890 12891 12893 12895 12897 12901 12902 12904 12906 12908 12909 12910 12912
## 1 3 1 1 3 1 3 1 1 3 1 1 1
## 12913 12915 12916 12917 12919 12920 12921 12922 12923 12924 12925 12928 12929
## 1 3 1 1 1 1 1 3 1 1 1 1 3
## 12930 12931 12933 12935 12936 12937 12938 12939 12940 12942 12944 12945 12947
## 1 1 1 1 1 1 1 1 1 1 1 3 1
## 12948 12949 12950 12951 12952 12953 12955 12956 12957 12962 12963 12965 12966
## 1 1 1 1 1 1 1 3 1 1 1 1 1
## 12967 12968 12970 12971 12974 12976 12977 12980 12981 12982 12984 12985 12987
## 3 1 1 2 3 3 3 1 1 3 1 1 1
## 12988 12989 12990 12991 12993 12994 12995 12997 12999 13000 13001 13002 13003
## 3 1 1 1 1 1 1 1 3 1 1 3 1
## 13004 13005 13006 13008 13011 13012 13013 13014 13015 13016 13017 13018 13021
## 1 3 1 3 3 1 1 1 1 1 1 1 1
## 13023 13026 13027 13028 13029 13030 13032 13033 13034 13035 13037 13038 13040
## 1 1 1 1 1 1 1 3 1 1 1 1 1
## 13043 13044 13045 13046 13047 13048 13049 13050 13052 13055 13058 13059 13060
## 3 3 1 1 1 1 1 1 3 1 1 3 3
## 13061 13062 13064 13065 13066 13067 13068 13069 13070 13072 13075 13077 13078
## 1 3 1 3 1 1 1 1 3 3 1 1 1
## 13079 13080 13081 13082 13083 13085 13089 13090 13091 13092 13093 13094 13095
## 1 3 1 1 1 3 2 1 1 1 3 1 1
## 13097 13098 13099 13101 13102 13103 13104 13106 13107 13108 13109 13110 13113
## 1 1 1 3 1 1 1 1 1 3 1 1 1
## 13115 13116 13117 13118 13120 13121 13122 13124 13126 13127 13130 13131 13132
## 1 3 1 1 3 3 1 1 1 1 1 1 3
## 13133 13134 13135 13136 13137 13138 13139 13140 13141 13142 13144 13145 13146
## 3 1 3 1 1 1 1 1 1 1 3 1 1
## 13147 13148 13149 13151 13153 13155 13157 13158 13159 13160 13161 13162 13165
## 1 1 1 3 1 1 1 1 1 1 3 1 1
## 13166 13167 13168 13169 13170 13171 13173 13174 13176 13177 13178 13182 13183
## 3 1 1 1 1 1 1 1 1 1 1 1 1
## 13184 13185 13186 13187 13188 13189 13192 13193 13194 13196 13198 13199 13200
## 1 3 1 3 1 1 1 1 1 1 1 1 1
## 13203 13207 13208 13209 13210 13211 13212 13213 13216 13217 13218 13220 13221
## 1 1 1 1 1 1 1 1 3 1 1 1 3
## 13223 13224 13225 13226 13227 13228 13229 13230 13232 13233 13235 13236 13238
## 3 1 1 3 3 1 3 1 1 1 3 1 1
## 13239 13240 13242 13243 13244 13245 13246 13247 13248 13249 13253 13255 13258
## 3 1 1 3 1 1 1 1 1 1 3 1 1
## 13259 13260 13261 13262 13263 13265 13266 13267 13268 13269 13270 13271 13272
## 1 1 3 3 1 1 1 1 1 1 3 1 1
## 13273 13276 13277 13278 13279 13280 13282 13283 13284 13285 13291 13292 13294
## 1 1 1 1 1 1 1 1 3 1 3 1 3
## 13295 13296 13297 13298 13299 13300 13301 13302 13304 13305 13307 13308 13309
## 3 3 1 1 3 3 1 3 3 1 1 1 1
## 13310 13311 13313 13314 13316 13317 13318 13319 13320 13321 13322 13323 13324
## 1 1 1 1 1 1 1 1 1 1 1 1 1
## 13325 13327 13328 13329 13330 13332 13334 13336 13338 13339 13340 13341 13343
## 1 1 3 1 1 1 1 1 3 3 1 3 3
## 13344 13345 13347 13348 13349 13350 13351 13352 13354 13355 13356 13357 13358
## 1 3 1 1 1 1 1 1 1 1 1 3 3
## 13359 13362 13363 13364 13365 13366 13368 13369 13370 13372 13373 13375 13376
## 1 1 1 1 1 1 3 3 3 1 1 1 1
## 13379 13381 13382 13384 13385 13388 13389 13390 13391 13394 13395 13396 13397
## 1 1 3 1 3 1 1 1 3 1 3 1 1
## 13398 13402 13403 13404 13405 13408 13410 13411 13414 13416 13417 13418 13419
## 3 1 1 1 1 2 1 1 1 1 1 1 1
## 13420 13421 13422 13425 13426 13427 13428 13429 13430 13431 13434 13435 13436
## 3 1 1 1 1 1 1 1 1 1 1 1 1
## 13437 13439 13441 13447 13448 13449 13450 13451 13452 13453 13455 13456 13458
## 1 3 1 1 1 1 1 1 3 3 1 1 1
## 13460 13461 13462 13464 13466 13467 13468 13470 13471 13473 13474 13475 13476
## 1 1 3 1 3 1 1 1 1 1 3 3 3
## 13477 13479 13481 13482 13483 13484 13485 13486 13487 13488 13489 13491 13492
## 1 3 1 3 1 3 3 1 1 1 1 1 1
## 13493 13494 13495 13496 13497 13499 13500 13501 13502 13503 13504 13505 13506
## 3 3 1 1 3 1 1 3 1 1 1 1 3
## 13507 13508 13509 13510 13512 13513 13514 13515 13516 13517 13518 13519 13520
## 1 3 1 1 3 1 1 1 1 1 1 1 1
## 13521 13522 13523 13524 13525 13527 13529 13531 13532 13533 13534 13536 13538
## 1 1 1 1 1 1 1 3 1 3 1 1 1
## 13539 13544 13546 13548 13549 13551 13552 13555 13557 13558 13560 13561 13562
## 1 1 1 1 1 3 1 1 1 1 1 3 1
## 13563 13564 13565 13566 13568 13569 13570 13571 13572 13573 13575 13576 13577
## 1 3 1 1 3 1 3 1 3 1 1 1 1
## 13579 13581 13583 13584 13587 13588 13589 13590 13591 13592 13593 13594 13596
## 1 3 3 3 1 1 1 1 1 1 1 1 1
## 13598 13599 13600 13601 13602 13603 13606 13607 13610 13611 13614 13615 13617
## 1 1 3 1 1 1 1 1 1 1 1 3 1
## 13618 13621 13623 13626 13627 13629 13630 13631 13632 13634 13635 13636 13637
## 3 1 1 3 1 1 1 1 1 1 1 1 1
## 13638 13639 13642 13643 13644 13645 13647 13649 13650 13651 13652 13654 13655
## 1 1 3 1 1 1 1 3 1 1 1 1 1
## 13656 13657 13658 13659 13662 13663 13666 13667 13668 13669 13670 13672 13673
## 3 1 1 3 1 3 1 3 1 1 1 3 1
## 13675 13678 13680 13681 13682 13684 13685 13686 13689 13690 13692 13694 13695
## 3 3 1 1 3 3 1 3 1 1 1 2 1
## 13697 13699 13700 13703 13704 13705 13706 13707 13708 13709 13710 13711 13712
## 1 3 1 3 1 1 3 3 3 1 1 3 3
## 13715 13716 13717 13718 13719 13720 13721 13722 13723 13725 13726 13727 13728
## 3 3 1 3 1 1 1 1 3 1 1 1 1
## 13730 13731 13732 13735 13736 13737 13739 13740 13741 13742 13743 13744 13745
## 1 3 1 1 1 3 1 3 1 1 1 1 3
## 13747 13748 13750 13751 13752 13753 13754 13755 13756 13758 13759 13760 13761
## 3 1 1 3 1 3 3 1 1 1 1 1 1
## 13762 13763 13764 13767 13769 13771 13772 13774 13777 13778 13780 13781 13782
## 3 1 1 1 1 1 1 1 1 1 1 3 1
## 13784 13786 13787 13790 13791 13792 13798 13799 13800 13801 13802 13803 13804
## 1 3 1 1 1 1 2 1 3 1 1 3 1
## 13805 13806 13807 13808 13810 13811 13812 13813 13814 13815 13816 13817 13819
## 1 1 3 1 1 3 1 1 1 1 1 1 3
## 13821 13822 13823 13824 13826 13827 13828 13831 13832 13833 13835 13837 13838
## 3 1 1 1 3 1 1 1 1 3 1 3 1
## 13841 13842 13844 13845 13846 13848 13849 13850 13851 13853 13854 13856 13858
## 3 1 1 1 1 1 1 1 1 1 1 3 1
## 13859 13860 13862 13863 13865 13866 13867 13868 13869 13870 13871 13873 13874
## 3 1 1 3 1 1 1 1 1 1 1 1 3
## 13875 13876 13877 13878 13880 13881 13882 13883 13884 13885 13886 13887 13888
## 1 1 1 1 1 1 1 1 1 3 1 3 1
## 13889 13890 13892 13893 13894 13895 13897 13898 13899 13900 13901 13904 13908
## 1 1 1 3 1 1 1 3 1 3 1 1 1
## 13911 13914 13917 13918 13922 13923 13924 13925 13926 13927 13928 13929 13930
## 1 1 1 1 3 1 1 1 1 1 1 3 1
## 13931 13932 13933 13934 13936 13937 13938 13939 13940 13941 13946 13947 13948
## 1 3 1 3 3 3 1 1 1 1 1 1 3
## 13949 13950 13951 13952 13953 13954 13955 13956 13959 13960 13962 13963 13967
## 1 1 3 3 1 1 3 1 1 1 1 3 3
## 13969 13971 13972 13973 13974 13975 13976 13978 13979 13980 13982 13983 13984
## 1 1 1 3 1 1 3 1 1 1 1 1 1
## 13985 13986 13988 13989 13990 13991 13992 13993 13994 13995 13999 14000 14001
## 1 1 1 1 3 1 1 1 1 1 1 3 1
## 14002 14004 14005 14006 14009 14012 14013 14014 14015 14019 14020 14021 14022
## 1 1 1 1 3 3 1 1 1 1 1 3 3
## 14023 14024 14027 14029 14030 14031 14032 14034 14035 14036 14037 14038 14039
## 1 1 1 1 1 1 1 1 1 3 3 1 1
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## 1 3 1 1 3 1 3 1 1 1 1 1 1
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## 17295 17297 17298 17299 17301 17302 17303 17306 17309 17311 17312 17313 17314
## 1 1 1 1 1 1 3 1 1 1 1 1 1
## 17315 17317 17320 17321 17323 17324 17325 17329 17330 17331 17333 17334 17337
## 1 1 1 1 1 1 3 1 1 1 1 3 3
## 17338 17339 17340 17341 17343 17344 17345 17346 17347 17348 17349 17350 17351
## 1 1 1 3 3 1 1 1 1 1 3 1 1
## 17353 17354 17356 17357 17358 17359 17360 17361 17362 17364 17365 17367 17368
## 1 1 3 1 3 1 1 1 3 1 1 3 1
## 17370 17371 17372 17373 17374 17375 17376 17377 17379 17381 17382 17383 17384
## 1 1 1 1 3 3 1 1 1 1 1 1 1
## 17385 17386 17387 17388 17389 17391 17392 17394 17396 17397 17398 17400 17402
## 1 1 1 1 1 3 3 3 1 1 1 1 1
## 17403 17404 17405 17406 17408 17409 17410 17411 17412 17414 17415 17416 17418
## 1 1 1 3 3 3 1 1 1 1 1 1 1
## 17419 17420 17422 17423 17425 17426 17427 17428 17429 17430 17431 17432 17433
## 1 1 1 1 1 1 1 1 1 1 3 1 1
## 17434 17436 17438 17440 17442 17446 17447 17449 17450 17451 17453 17454 17455
## 1 1 3 3 1 3 1 1 2 1 1 3 3
## 17456 17457 17458 17459 17460 17461 17462 17463 17464 17466 17468 17469 17470
## 3 1 1 1 1 1 1 1 3 1 1 1 1
## 17472 17475 17480 17481 17483 17486 17489 17490 17491 17492 17495 17496 17498
## 3 1 1 1 1 3 1 1 1 3 1 3 1
## 17499 17500 17501 17502 17503 17504 17505 17506 17507 17508 17509 17510 17511
## 3 1 3 1 1 3 3 1 3 3 1 1 2
## 17512 17513 17514 17515 17516 17517 17519 17520 17521 17522 17523 17524 17525
## 1 1 1 1 1 3 1 1 1 1 1 3 3
## 17526 17527 17528 17530 17531 17534 17535 17536 17537 17538 17540 17542 17545
## 1 1 1 1 3 1 3 3 1 1 1 3 1
## 17548 17549 17550 17551 17552 17553 17554 17555 17556 17557 17560 17561 17562
## 3 1 3 3 1 1 1 1 3 1 1 1 1
## 17564 17566 17567 17569 17571 17572 17573 17574 17576 17578 17579 17580 17581
## 1 1 1 3 1 1 1 3 1 3 1 3 1
## 17582 17584 17585 17588 17589 17590 17591 17593 17594 17595 17596 17597 17600
## 3 1 1 1 1 1 1 1 1 1 1 3 1
## 17601 17602 17603 17604 17608 17609 17611 17612 17613 17614 17615 17616 17618
## 3 1 1 3 1 1 1 1 1 1 1 3 1
## 17619 17620 17621 17623 17624 17625 17628 17629 17630 17631 17633 17634 17636
## 3 1 1 1 1 1 1 1 3 1 1 1 1
## 17637 17639 17640 17642 17643 17644 17646 17647 17648 17649 17650 17651 17652
## 1 3 1 1 3 1 3 1 1 3 1 1 1
## 17653 17654 17655 17656 17658 17659 17660 17663 17664 17666 17667 17668 17669
## 1 3 1 1 1 1 3 1 1 1 1 1 1
## 17670 17671 17672 17673 17674 17675 17676 17677 17678 17679 17680 17682 17684
## 3 1 1 1 1 1 1 1 3 1 1 1 1
## 17685 17686 17690 17691 17692 17693 17694 17695 17696 17697 17698 17700 17701
## 1 1 1 3 1 3 3 1 1 3 3 1 3
## 17702 17703 17704 17705 17706 17707 17708 17709 17711 17712 17714 17715 17716
## 1 1 3 1 1 3 3 3 1 1 3 3 1
## 17718 17719 17720 17722 17723 17724 17725 17727 17728 17730 17731 17732 17733
## 3 1 1 1 1 1 1 1 1 1 1 3 1
## 17734 17735 17736 17737 17738 17739 17742 17744 17746 17747 17749 17750 17752
## 1 1 1 1 1 1 1 1 3 1 3 1 3
## 17754 17757 17758 17759 17760 17761 17763 17764 17765 17767 17768 17769 17770
## 1 1 1 1 1 1 3 1 3 1 1 1 3
## 17771 17772 17774 17775 17777 17779 17781 17783 17785 17786 17787 17788 17789
## 1 1 1 3 1 1 3 1 1 1 3 1 3
## 17790 17791 17793 17795 17796 17797 17799 17800 17802 17805 17806 17809 17811
## 1 1 1 3 1 1 1 1 1 1 1 1 1
## 17812 17813 17816 17817 17819 17824 17827 17828 17829 17830 17831 17832 17835
## 1 1 1 1 1 1 1 1 3 1 1 1 1
## 17836 17837 17838 17839 17841 17843 17846 17848 17849 17850 17852 17854 17855
## 1 1 1 1 2 3 1 1 3 3 1 3 3
## 17856 17857 17858 17859 17860 17861 17862 17863 17864 17865 17866 17867 17869
## 1 1 1 3 3 1 3 1 1 1 3 1 1
## 17870 17871 17873 17874 17877 17878 17879 17880 17881 17883 17884 17885 17886
## 1 3 1 3 3 1 3 3 3 1 1 1 1
## 17887 17888 17889 17890 17891 17892 17893 17894 17895 17896 17897 17898 17899
## 1 1 3 3 3 1 3 1 1 1 3 1 3
## 17900 17901 17904 17905 17906 17908 17911 17912 17913 17914 17917 17919 17920
## 3 1 1 1 3 3 1 3 1 1 1 1 1
## 17921 17923 17924 17925 17926 17928 17929 17930 17931 17932 17934 17935 17936
## 1 3 1 3 1 1 1 1 1 1 1 1 1
## 17937 17939 17940 17941 17942 17946 17947 17948 17949 17950 17951 17954 17955
## 1 3 1 1 1 3 1 3 2 1 1 1 3
## 17956 17957 17958 17960 17961 17962 17964 17965 17966 17967 17968 17969 17970
## 3 1 1 3 1 3 1 1 1 3 3 3 3
## 17972 17973 17974 17975 17976 17977 17978 17979 17980 17984 17985 17986 17987
## 3 1 1 1 3 1 3 1 3 3 1 1 3
## 17988 17990 17991 17994 17995 17997 17999 18001 18004 18005 18006 18008 18009
## 1 3 3 1 3 1 1 1 3 1 1 1 3
## 18010 18011 18013 18014 18015 18016 18017 18018 18019 18022 18024 18027 18030
## 3 3 3 1 1 1 1 1 1 1 3 1 1
## 18032 18033 18034 18035 18036 18037 18040 18041 18042 18043 18044 18045 18048
## 3 1 1 1 1 3 1 1 1 1 1 1 3
## 18050 18053 18055 18056 18058 18059 18061 18062 18064 18065 18066 18067 18068
## 3 1 1 3 1 1 1 3 1 1 1 1 3
## 18069 18071 18072 18073 18074 18075 18077 18078 18079 18080 18081 18082 18084
## 1 3 3 1 3 1 1 3 1 1 1 1 1
## 18085 18086 18087 18088 18092 18093 18094 18095 18096 18097 18099 18101 18102
## 3 3 1 1 1 1 1 3 1 1 1 1 2
## 18104 18105 18106 18108 18109 18110 18112 18113 18114 18116 18117 18118 18119
## 1 1 3 3 1 1 1 3 3 1 1 1 3
## 18120 18121 18122 18123 18125 18126 18127 18129 18130 18133 18135 18136 18138
## 3 3 1 1 1 1 1 3 1 3 1 1 3
## 18139 18142 18143 18144 18145 18146 18147 18149 18150 18151 18154 18155 18156
## 1 3 1 1 1 3 1 1 1 1 1 1 1
## 18158 18159 18160 18161 18164 18165 18167 18168 18169 18170 18171 18172 18173
## 1 3 1 1 1 3 1 3 1 1 1 1 1
## 18174 18176 18177 18178 18179 18180 18181 18183 18184 18185 18188 18189 18190
## 1 3 1 1 1 1 1 3 1 3 1 1 3
## 18191 18192 18193 18194 18196 18198 18200 18202 18203 18204 18205 18209 18210
## 3 1 3 1 1 1 1 3 3 1 1 1 1
## 18211 18212 18213 18215 18216 18217 18218 18219 18220 18221 18222 18223 18224
## 1 3 3 1 1 1 3 1 3 1 1 1 3
## 18225 18226 18227 18228 18229 18230 18231 18232 18233 18235 18236 18237 18239
## 1 1 3 1 1 1 3 1 3 1 1 1 3
## 18240 18241 18242 18245 18246 18248 18249 18250 18251 18252 18255 18257 18259
## 1 1 1 1 1 1 1 3 1 1 1 1 1
## 18260 18261 18262 18263 18265 18268 18269 18270 18272 18273 18274 18276 18277
## 3 1 3 1 1 1 3 1 1 1 1 1 1
## 18278 18280 18281 18282 18283 18287
## 1 3 3 1 1 1
##
## Within cluster sum of squares by cluster:
## [1] 2498.3071 2542.4354 587.1756
## (between_SS / total_SS = 56.3 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"Optimizar número de grupos
set.seed(123)
optimizacion3 <- clusGap(df3_escalados, FUN = kmeans, nstart = 25, K.max = 10)
plot(optimizacion3, xlab = "Número de clusters K", main = "Optimización de Clusters - Clientes") 
Graficar los grupos
fviz_cluster(clusters3, data = df3_escalados) 
Agregar grupos a la base de datos
df3_escalados <- cbind(df3_escalados, cluster = clusters3$cluster)
head(df3_escalados)## Recencia Frecuencia Monto cluster
## 12346 2.3249311 -0.4556335 8.75412928 2
## 12347 -0.9001944 0.3915431 0.26969044 1
## 12349 -0.7404358 -0.4556335 -0.02748311 1
## 12350 2.1751575 -0.4556335 -0.19317588 3
## 12352 -0.5607075 0.5327392 0.05966118 1
## 12353 1.1167572 -0.4556335 -0.22174702 3Análisis de promedios por cluster para perfilamiento
df3_escalados <- cbind(df3_rfm, cluster = clusters3$cluster)
resumen_clusters <- df3_escalados %>%
group_by(cluster) %>%
summarise(
Num_Clientes = n(),
Recencia_Prom = mean(Recencia),
Frecuencia_Prom = mean(Frecuencia),
Monto_Prom = mean(Monto)
)
print(resumen_clusters)## # A tibble: 3 × 5
## cluster Num_Clientes Recencia_Prom Frecuencia_Prom Monto_Prom
## <int> <int> <dbl> <dbl> <dbl>
## 1 1 3189 41.6 4.70 1856.
## 2 2 25 19.3 58.9 81980.
## 3 3 1082 247. 1.58 552.Asignación de nombres descriptivos según el perfil de cada segmento
df3_escalados <- df3_escalados %>%
mutate(Perfil = case_when(
cluster == 1 ~ "Clientes Leales VIP", # Baja recencia, alta frecuencia/monto
cluster == 2 ~ "Clientes Ocasionales", # Alta recencia, baja frecuencia/monto
cluster == 3 ~ "Clientes Nuevos / Prometedores", # Baja recencia, baja frecuencia
cluster == 4 ~ "Clientes en Riesgo / Inactivos" # Muy alta recencia
))
head(df3_escalados) ## Recencia Frecuencia Monto cluster Perfil
## 12346 326 1 77183.60 2 Clientes Ocasionales
## 12347 3 7 4310.00 1 Clientes Leales VIP
## 12349 19 1 1757.55 1 Clientes Leales VIP
## 12350 311 1 334.40 3 Clientes Nuevos / Prometedores
## 12352 37 8 2506.04 1 Clientes Leales VIP
## 12353 205 1 89.00 3 Clientes Nuevos / 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