Teoría

Agrupamiento o Clustering es una técnica de aprendizaje automático no supervidaso que agrupa datos en función de su similitud.

Algunos usos típicos de esta técnica 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 de número de clústers
library(factoextra)
#install.packages("datasets")
library(datasets)
#install.packages("tidyverse")
library(tidyverse)

Ejercicio 1. Puntos

Contexto

Agrupa los siguientes ocho 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.   :10.000
str(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 9
plot(df1$x, df1$y)

Escalar datos

# datos_escalados <- scale(datos_originales)

Asignar numero de grupos

grupos1 <- 3

Agrupar los puntos

set.seed(123)
clusters1 <- kmeans(df1, grupos1)
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 el número de grupos

set.seed(123)
optimizacion1 <- clusGap(df1, FUN=kmeans, nstart=2, K.max = 7)
plot(optimizacion1, xlab="Número de clusters K", main="Optimización de clusters")

#El óptimo es el primer punto más alto

Graficar 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       3

Conclusiones

La técica 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, asesinato 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.   :46.00
str(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_escalado <- scale(df2)
summary(df2_escalado)
##      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.   : 2.6444

Asignar numero de grupos

grupos2 <- 5

Agrupar los puntos

set.seed(123)
clusters2 <- kmeans(df2_escalado, grupos2)
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 el número de grupos

set.seed(123)
optimizacion2 <- clusGap(df2_escalado, FUN=kmeans, nstart=1, K.max = 10)
plot(optimizacion2, xlab="Número de clusters K", main="Optimización de clusters")

#El óptimo es el primer punto más alto

Graficar los grupos

fviz_cluster(clusters2, data=df2_escalado)

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       4
df2_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  alta

Conclusiones

La técica de clustering permite identificar patrones o grupos naturales en los datos sin necesidad de etiquetas previas.

Ejercicio 3. Segmentación de clientes

Contexto

La base de datos ventas tiene los registros entre el 1 de diciembre del 2010 y el 9 de diciembre del 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 sis clientes son mayoristas.
Objetivo: Segmentar clientes, asignarles nombres y características de comportamiento y proponer sugerencias a las empresas para aumentar las ventas.

Obtener datos

df3 <- read.csv("C:\\Users\\natal\\OneDrive\\Carrera\\7moSemestre\\Modulo2\\ventas.csv")

Entender datos

summary(df3)
##        Ticket            Producto         Cantidad              Fecha       
##  Length   :522064   Length   :522064   Min.   :-9600.00   Length   :522064  
##  N.unique : 21663   N.unique :  4183   1st Qu.:    1.00   N.unique :   305  
##  N.blank  :     0   N.blank  :  1455   Median :    3.00   N.blank  :     0  
##  Min.nchar:     6   Min.nchar:     0   Mean   :   10.09   Min.nchar:    10  
##  Max.nchar:     7   Max.nchar:    36   3rd Qu.:   10.00   Max.nchar:    10  
##                                        Max.   :80995.00                     
##                                                                             
##         Hora            Precio              Cliente              País       
##  Length   :522064   Min.   :-11062.060   Min.   :12346    Length   :522064  
##  N.unique :   739   1st Qu.:     1.250   1st Qu.:13950    N.unique :    30  
##  N.blank  :     0   Median :     2.080   Median :15265    N.blank  :     0  
##  Min.nchar:     8   Mean   :     3.827   Mean   :15317    Min.nchar:     3  
##  Max.nchar:     8   3rd Qu.:     4.130   3rd Qu.:16837    Max.nchar:    20  
##                     Max.   : 13541.330   Max.   :18287                      
##                                          NAs    :134041
str(df3)
## 'data.frame':    522064 obs. of  8 variables:
##  $ Ticket  : chr  "536365" "536365" "536365" "536365" ...
##  $ Producto: chr  "WHITE HANGING HEART T-LIGHT HOLDER" "WHITE METAL LANTERN" "CREAM CUPID HEARTS COAT HANGER" "KNITTED UNION FLAG HOT WATER BOTTLE" ...
##  $ Cantidad: int  6 6 8 6 6 2 6 6 6 32 ...
##  $ Fecha   : chr  "01/12/2010" "01/12/2010" "01/12/2010" "01/12/2010" ...
##  $ Hora    : chr  "08:26:00" "08:26:00" "08:26:00" "08:26:00" ...
##  $ Precio  : num  2.55 3.39 2.75 3.39 3.39 7.65 4.25 1.85 1.85 1.69 ...
##  $ Cliente : int  17850 17850 17850 17850 17850 17850 17850 17850 17850 13047 ...
##  $ País    : chr  "United Kingdom" "United Kingdom" "United Kingdom" "United Kingdom" ...

Crear variables a analizar

df3$Venta <- df3$Cantidad * df3$Precio

library(dplyr)

tickets_cliente <- df3 %>%
  group_by(Cliente, Ticket) %>%
  summarise(
    Total_Ticket = sum(Venta, na.rm = TRUE),
    .groups = "drop"
  )

ticket_promedio <- tickets_cliente %>%
  group_by(Cliente) %>%
  summarise(
    Ticket_Promedio = mean(Total_Ticket, na.rm = TRUE),
    .groups = "drop"
  )

frecuencia <- df3 %>%
  group_by(Cliente) %>%
  summarise(
    Frecuencia_Compra = n_distinct(Ticket),
    .groups = "drop"
  )
clientes_cluster <- ticket_promedio %>%
  left_join(frecuencia, by = "Cliente")

datos_cluster <- clientes_cluster %>%
  select(Ticket_Promedio, Frecuencia_Compra) %>%
  scale()

Asignar numero de grupos

grupos3 <- 12

Agrupar los puntos

set.seed(123)
clusters3 <- kmeans(
  datos_cluster,
  centers = grupos3,
  nstart = 25
)

clusters3
## K-means clustering with 12 clusters of sizes 516, 1739, 62, 21, 6, 1, 181, 2, 2, 1322, 387, 59
## 
## Cluster means:
##    Ticket_Promedio Frecuencia_Compra
## 1       0.10354027      -0.033389249
## 2      -0.14164163      -0.049420664
## 3       0.03754585       0.529372851
## 4       2.06100520       0.166563706
## 5      -0.04315654       2.078258064
## 6       0.04134286      64.972072929
## 7       0.34100718      -0.022830586
## 8       7.57526472      -0.037928721
## 9      44.52918206      -0.065814052
## 10     -0.03505242      -0.043792656
## 11     -0.05238290       0.134955527
## 12      0.81655862      -0.009885846
## 
## Clustering vector:
##    [1]  9  1 12 10 11  2  7 10  7  4  1  7  2 11 10 10 10  7 10  1  1  4 10  1
##   [25] 10 10 10  2 10  1 10 10 11  7 12 10  2  2 10  1  4 10  2  2  4 11  1  2
##   [49] 10 11  7  1  1 10 10  2 11  7 12 10  1 11  7  2  2  7  2  7 10 10  7  2
##   [73] 12  2  1  4  2  7 10 10 10  1 10  2 10 10  3  7  1 11  1  1 12  1  1  7
##   [97]  1 11  1 10 10 11 10  2  2  2  7  2 11 12  1  2  2 10  2  2  1  2  1  7
##  [121] 10  1  1 10 10  1  1  2 11  1 10  2 10 10  2 10  7 10  4 10  7 11 10 10
##  [145]  1  1  2  2  7  2  2 11 10 12 10 10  1  2  1 10  2 10  7  3 10  1  2  2
##  [169] 10  2  7 10 10  2 11 11  7  2 10  4 10  2  2 11 10  7 11  2 11  2  2  1
##  [193]  2 12 10 10  7  1  1 10  1 10 10  2 11 10 11  2 10 10  7  1  1 10  1  7
##  [217]  1  1  1 10  2 10  1 10 10  1 11 10  2 10  2  7  7  2  1 10  1  2  2 11
##  [241]  2  7  7  1  2 10  1  2 12 10  2  3  3 11 10  1  2  4  1 10  2  2 10  2
##  [265] 10  7 10  2 10  1  1 11 11 10 11  7  7 10  1  1  2 10  3 10  2  2 10 10
##  [289] 10  1  2 10 12  2 10  2 10  2  2  1 10 10  4 11  5  7 10  4  4  7 12  2
##  [313] 11  7  1  7  2 12  7  7  7  7 10  2  1 10 10 10 10  2  2 10  2 10 10 10
##  [337] 10  2 12 10  2  1  2  2  2  1 10  2 12  2  2 10 10 10  2  2  2  2  7  2
##  [361]  2 10 10  1  2 10 11  1  3  1 11  2  2  7  1  2 10 10 10  2 10  1  1  2
##  [385]  1  1  1 10  2 10 10  2  7 11 10  2 10  1  2 10 10  1  2 10  2  2  2  2
##  [409]  3  2  2  1 10 10 11 10  1  2  1  1  2  2  3 10  2  2 10 10  2  2 12  2
##  [433] 10 10 10  2  7 10  2 10 10 10 10  1  1  2 10 10 11  2  1  2 11  1  2  7
##  [457]  2  2  5  2  1  2  7  2 10  2  1 10  1 11  2  2  2 10  2 10  2  2  1  2
##  [481]  2 11  2  2  2  2 11 11 11  1 10  2  3 11 10  2  7 10 10 10  1  2 10 10
##  [505] 10 10 10  1  1 10 10 11 10 10 11 10 10  2  2 10  2 10 10  2  2  2  2 11
##  [529]  2  2  7  2  3  2  2 12 11  2  2  5 11 10  2  7 11  2  1  3  2  2  3  2
##  [553]  2  2 10 10 10  2  3  1  1  2  2  2 10 10  7 11 10  2 10  2  2 10  4  1
##  [577] 11  2  1  2  1 10  2  2  2  2 11 10  7  1  2 10 10 10  2  2 10  1 10  2
##  [601] 10 10  2  2  2  7  1 10 11  2 11 11  2  1  2  2  2 10  2  2 10  1  3  2
##  [625]  2  2  2  1 10 10 10 10 10  2  2  2 10  2  7  7  2  2 10  2 11  2 10  7
##  [649] 10  2 10  2  2  1  2 10 10  2  2  2  1  2  2  2 10  1 10  2  3 10 11 11
##  [673] 11 11  1  2  2  2 10  2  1  2 10 10  2  2  1 10 10 10  2  2  1 10  2 10
##  [697]  2  2 10 11  2 10 10 10 10 10 10 12 10  2  3 10 10  2  2  1  1 11  7 10
##  [721] 10 10  7  1  1  7 12  1 10  7 10 10  2  2  1 10 10  1  1  1  1 10 10  1
##  [745]  1  2  7  2 10 10  1 10  7  1 10  2  1  2  1  1 10 10  1  2 11 10  1 10
##  [769] 10 10  2  2  2  3  2  2 10 10 10 11  2  2  7 12  1 11  2  2  2 10  1 10
##  [793]  1  2  1 10 10 10  1 10 10  1 10  2  1 10  1  2  1  2  1 10  1  3  2  1
##  [817]  2  2 10  1  2  2 10  2  2 10 10 10  2  1  2 11 10 10 10 10 10  2  2 10
##  [841]  7  2  2 10  7  2  1  2  2 10  2  2  2  2 10  1  1  2  1 10  2  1  2 10
##  [865] 10  2  2  2  2  3  1  2  2  2  2 10  2  2 11  7 10  2  2  2  1 10  1  2
##  [889] 10  2  2  2 11  7  2  2 11 10  2  2  1  2  1 11  2 10 10  2 10 10 10  2
##  [913] 11  2 10 10  2  2  1  2 10 10 10  2  2  2  2  2 10  1 10 11 10 10  7  2
##  [937] 10  2  7 10  2  1  2 10  2 10  2 10 10 10  2  2  1  1 10  2  2 10 11  2
##  [961] 10  2  2  2  2  7  2  2  2 10  2  7  2  1  3 11  2 10 11  2 11  2 10 10
##  [985] 10 11  2  2  2  2  2  2  2  2  2  1  1  2 11  1  2  2 10 10  1  1 10 10
## [1009]  2 10  2 11  2  1 10  2  2 10 10  2  1  2 11 11 10 10  2  1 10 12  1  3
## [1033] 11  1 10 10  3  2  2  2  2 11  2  2 10  1  2  3 10  1 10 12 10 10 10  2
## [1057]  2 10  1 10  2 10  1  7 10  2 10  2 10 10 10  2  2  2 10  2 10  2  2  2
## [1081]  2 11 10 10 10 10  1 12  7  7  3  2  2  2  2 11 10  2  2 10 12  1 11 11
## [1105]  2  1 10  2  2  7 11  7  2  1  2  2  2 10 10 10 11  2  7  2  1 10  2  2
## [1129]  2  1  2  1 11 10  2  1  2 10 10  2  2 10  2 10  2  1 10 10  7 10  2  2
## [1153]  2  2  7  2  2  2 10  2  2 12  1  2  2  2  2  2  2  2  2 11 11  2 10 10
## [1177] 10 10  2  7  2 10 11  2 11 10  1  1 10  2  2 11 10 10 11  1  1 10  1  1
## [1201] 10 10 10  2  1  7 10 10  2 10 10  2  2  2 11  7 11  2 10  1  2  1  2 11
## [1225]  2  2 10  2 10 10  7 10  3  2  2  2  1 11 11  2 11  7 10  2  2 10  2  2
## [1249] 10  2  2  2 10  2 10  2  2 11  2  4  2  2 11 10  4  2 11  2  7 10  2  7
## [1273] 10 10  2 11  2 10 10  2 10  2  1 10  7  2  2 10  2  1 11  2 11  1 10 10
## [1297]  2 10  2  7  7  2  2 10 10 10  1  2  2  1 11 10  2  1  1  2  2 10  2  2
## [1321]  7  2  2  2 10  3 10  2 10 11 11 10 11  1 10  2  2  2  2  2 10  2 10 10
## [1345] 11  7  2 10 10 11  2  2 10 11  1 10 10 10 11  1 10 10 10  2  1  2  2  2
## [1369] 11 10  2  2 11  7  1  2 10  1  1  1  1  7  2  1 11  2 10  1  1  2  2  2
## [1393] 10  7  2 11 10  1 12  2 10  2 10 11  1 10  2 10  3 11  2  1 10  1  7  1
## [1417] 11 10 10  2 10  1  2 10 10  2 10  1  2 10 10 11  2 10 10 10  2 11  2  2
## [1441]  2  1 10  2 10  2 10  2  2  2 10  2 10  1  2 11 11  2  2  2  2 10  2  2
## [1465]  1 10  2  2  1 11  1  1  2 11  2 11  1 11 10  2  2 10 10 10  2  7 10  2
## [1489]  2 11  2  1  2 10 10  1 10 10 11  2  2 10 10  2  2  2  2 12 10 10 10 10
## [1513]  2  2  2  2 10  2  2 11  2 12  2  1 11  2 10 10  2  2 11  2  1 10  2 10
## [1537]  2 10 10 10  2 10  2  2  7 10  2  1  2  2 10 10 10 10  2  2 11  1  2  1
## [1561] 10  2  2 10  2  2 10 10  2  2  2  2  2 11 11  3 10  2  1  2 10 11  7  2
## [1585] 10  2 10 10  2  2 11  7  1  1 10 10 10  2  2  2  1  2  1 11 10 11  1  1
## [1609]  2  2 10 11  2  2  2  2  2  2 10  2  2 11  2 10  2  2  2 10 10  2 10  2
## [1633]  1  5  7 10  2  2  2 10  2 10 10  2  2 10  1 10 10 10  2 10 10 10  1 10
## [1657]  2  2 10 10 10  4  2 10 10  2 10  1  2  2  2 11  2  2  2 10 10  2  3 10
## [1681]  2 10 10  1 10 12  2  2  2  1 11  2  2 10  2  2 10  2  2  2  1 11 11 10
## [1705] 11  2 10 11  2 11 10 11  2  2  2 10  2  2  2  1 10 10 11  2 11  1  3 10
## [1729]  2  1  1  2  2  2 10 10 10  1 10 11  1 10 10  1  2  2 10 10  2 10  2  7
## [1753] 10  2 10 11 10  2  2  2  2  2 10  2  2  2  2  2  2 11  2  2 11  2 10 10
## [1777]  2  2 11 11  2 10 10  1  2  2  2  2  2 10 11  1  2  2 10  2 10  2  1  1
## [1801]  1 10  3 10  2  1  2 10 10 10  1 10  2  2 10 10  2  7  2 11 10 10  2  1
## [1825]  1 11  2  2 10  2  1 10 12 10  2  2 10  1  1 11  2 10  2 11 10  1  1 10
## [1849]  1 10  2 10 10  2 10  1  1  1  1 10  2 11  2  2  2 10 10  1 10 10  2  2
## [1873]  2  2  1  2 10  2 10  2 10  2 10 10  2 10  2 10  2 10  2  2  2  2 10  2
## [1897]  2  2  1 10  7  3  1  2 10 10  2  2  2  2  2 10 11  2  1 11 10  2 10  2
## [1921] 10  2 12 11  1  2  2  2  3  2  2  1 11 10 11 10  2  2  1 10  2  2  2  1
## [1945] 11 11  2  3  2 10  1  7  1 10  7  2  1 10  1  1  7  3  2  2  2 10  1 10
## [1969] 10 10  2  1 10  2  2  8 10 10  2 10  1 10 10  2  1  2  1  7 11 10 10 10
## [1993]  2 10 10  2  1  7  2  1 10 10 11 10  2 10  2  2 10  2 10  1 10 11 10  1
## [2017]  1 10  1 11 11 10 10 10  1 10  3  2  2 10  1  2  2  7 10  2  2  2 10  2
## [2041]  2 10  2 10  2 11  3 10  1 11  4 10  2 10  2 10 10 10  2  2 10 10  2  2
## [2065] 11  2  2 11 10 10 10  1 10  2 10  2  2  7  2 10  2 11 10 10 10 10 10 11
## [2089] 10 10  7  2 10 11  7 10  2 10  7  2 10 10 10  2  2  2 10  1  2 10 10 10
## [2113] 11 10 10  1  2  2 10  2 11  2  2 10 10 11 11  2  1  2 11  1  1 11  1  2
## [2137] 10  2 10  5  2  2 10 10  2 10  2 10  7  1  2 10  2 10 10 10  7  2  2 10
## [2161] 12 10 10  2 10  2  2  2  2  2 10 10  2 11 11 10 10 10 10 10 10 10 10 10
## [2185] 12 11  2 10  1 10 10  7 10 10 10  1 10  2  1  2 10  2  1 10  2 10 10  2
## [2209] 10 10 11 10  2 10  1  7  1  2  2  2  2  2 10  1  2  2  2 10  2  2 10  2
## [2233]  2  2  1 10  1  2  2  1 10 10  2  2  2  2  2  2  2  2  2  7 11 10  2  2
## [2257] 10 10 10 10 10  1  7  7  2  7  7  2 10  1 10 10  1  1  3 10  7  2  2  1
## [2281] 10  1  2  2  2  2 11 11  2 10 11 10 11  2 10 10 10  2 11  2 11 10  7 10
## [2305] 10  2  2  1  2  2  2 11  2 11  1  2 10  2 10  2 11 10 10  2  2 10  2  2
## [2329]  2 10 11  2 10 10  2  7  2  2  2 11  2  2 10  2  2 10  2 10 10 10  2 10
## [2353] 11 11  2  2  2 11  2 10 10  2 11  2  3  2 10  1 10 11 10  2 10 10 11  1
## [2377] 11  2 10  2 10  7 10  2  2  1  2 10 10  2 10 10 10  1  2  2  2 10 11  2
## [2401]  2 10  7 10  2  2  2 10  1  1  2  7  1 10  2 10 10  2 11  2  2  2  2 11
## [2425]  2 11 10 10 10  2  1  2 10  2  1  2  2  2  2 10  2 11  1  1 10  2  2 10
## [2449]  1  2 10  2  2  1  2 11 10  2  2  2 10  2 10  2  8 11 10  2  2 10  2 10
## [2473]  2  2 10  1  1 10  2 12  1 10  2  2 10  2  2  7  2 10 12 10 10  2  1 10
## [2497]  1 11  1 10 10 10 10 10 11 11 10 10  7  2 10 10 10  1  1 10  1  2 10 10
## [2521]  2  1  1 11 10  1 10  7  1  2  2 10 12 10  2 10  2  2 11  2  2  2  2 11
## [2545]  2  3 10 10  2 11  2  2 10 10  2 11  2 10  2  1  2 10  2  2  2  2  2  2
## [2569]  2  1  2  2  2 10  2 10  2  1  2  2 10  2  2  2  2  2  2 10  2 10 10  2
## [2593]  2 10 11 10  2  2  2 11  2 10 10  2 12 10  2 10 10  2 11 11 10  2  2  2
## [2617]  2  2 10 11 10  1 10  2  1  7  1 11 10 11  1  2  2  2 10  2 10 10  2  1
## [2641]  4  1  2  2 10  2  2  2 11 10  3  2  2  2  2  2 11 10  1  2  2 10  2  2
## [2665]  3 10 10 11  2 10 10  2 10  7  2  2 10  2 10  2 10  1  1  2  1 10  2 10
## [2689] 10 10 10 10 10  1  2 11  2 10  2  1  1 10  2  2  2 10  2 10 10  2 10  2
## [2713]  7  1  2 10 10  2 10  7 10 10  2  2  2 11  1  2  2 10 10  2 10  2 10 12
## [2737]  1 10  1  3 10  1  2  2 10  1  1 10  2 11  2 10  2  2 10 12 10 11  2 10
## [2761]  1 11  2 10 10  3 10 10  2  2  2 10 10 10  2  2  7 10 12 10  2 10 11 11
## [2785]  2  2  2 11 10 10  1 10 10  2 10  2  2 10 10 10  7  1 10  2 10  2  7  2
## [2809] 10 10  7 10  2  2 10  1 10  2  2  2 10  2 12 11  1  2  1 10  2  2 10  2
## [2833] 12 11  1  2  7  7  2  1  2 10  7 10 10 10  1  1  1  1 12  2 10 10  2 10
## [2857] 11 10 10  2  2 12 10  2  1 10 10  2  2 11 10 10 10  1  2  2  2  2  2 11
## [2881]  1  2  2  7  2  2  2  1  1  2  2  2  1 10  2  2 10  2  2 11  2  2  2  1
## [2905] 11  1  2  2  2 10 11 10 10  2  1 10  2  2  1  1  2  1 12 10 10  2  2  2
## [2929] 10  2 11 10 10  7  2 10 11  2  2 10  2  2 11 10  2  2 10  2  2 10  2  2
## [2953]  3 10  2 10 11  2 10 10  2 10  2  2  2  1  2  2  2  2  9 10  2 10 10 10
## [2977]  2 10 10  2 11 10  2  2 10 10  2  2  2  2  2  2 10  2 10  2  2  1  2  2
## [3001]  2 10  2  1 10  7  2  1  1  2  2  2 10  1  1  2 10  2 10  2 10  2  2  2
## [3025]  2 10 11  3 10  2  2 10  2 12 10  1  1 10  2 10 10 11 10 10  2 11 10  2
## [3049]  1  2 11 10  2  7  2  2 10  2 11 10 10 10 10  2 10  2 10 10  2  2  2 11
## [3073]  2  2 10  2  2  2  2  2  1  2 11  1  2  2 10  1  1  2  2  1  2  2  2  2
## [3097] 10 10 11 10 10  2  1  2 10 11 10  2 10  1 10  2 10  1  7  1  2  1 11  2
## [3121]  2  2 10  2  2 10  2 10 11  1 11  2 10 11  2  2 10  2 12  2 10 10  2  2
## [3145]  1  2  2  2  7 11 11 11  2  1  1 11 10 11 11 10 10 10  1  1 10  2 10 11
## [3169] 10  2 10 10 10 11  2  1  2 10 10  2 10 10 10  2 11 11 10 10  2 12  2  2
## [3193] 12  1  2  2 10 10 10  1  1 11  2  1 11  2 10  2 10  2  2 11 10  2  2 11
## [3217]  2 10 11  2 10  2 10  2  2  2 11 10 10  7 10 10  2  2  2 10  2  2 10 10
## [3241] 10 11 11  2 11 11  1 10  2 10 10  2  2 10  2 10 10  2  2 11 10  3 10 10
## [3265] 11  2  2 10  2 10  2  2  2  2 10 10  2  2  2  2 10  2  7 10  2  2  2 10
## [3289]  2  2  2  2  2  1  2  2  2  2  2  2  2 10 12 10 11 10  2  2 10  2 11  2
## [3313]  2  2 10 10  2 11  2 11 10  2  2 11  2  2 11  2 10 10 10  1  7 11 10 11
## [3337] 10  2  2 10 10  2  2 11  2 10  2  2  2  2  2  2 10 10  2  2 10  2 10 10
## [3361]  1 10 10 12  1  7  2  2  2  2 10  2  2  2  2 11  1  1  2  2  2 10  2  1
## [3385] 11 10 10  2  2  2  2  2 10  2  2 10  2  2  7  2 10 10  2 10  7  2  1 10
## [3409] 10  1  1  2 10  1 10 10  1  2 11  2  2 10 11 11 10 11 10  2 10  2  2  2
## [3433]  2  7 10 12 10 10  1 10 11 10 10 10 10  2  1 10  2 10 12  2  2  2  2 10
## [3457]  2  2 10 10  2 10 10 10  2  2  1  1  2  2 10  7 10  1  1  2 10  2  1  2
## [3481] 10  2  2 10  1  1 11  2 10  2  2 10  2 10  1  2 10 10  2  2  2  1  2  2
## [3505] 10  2  2 10  2  2  7  2 10  1 10 10  2 11  2 10  2  2 11  2 11  2 10  2
## [3529] 10  2 11  2 11 11  2  2  2 10  2  2 11 10  1  3  7  2 10 10  2 10  2  2
## [3553]  2  2  2 10  2  2 10  2  2  2  1  2  1  2  2  1 10  2  2  2 10 10  1 11
## [3577]  2  2  2  2  2  2  2 11  2  1  2 12 11  3  7 10 10  2  2  2 10  2  2  1
## [3601]  2  1  7  2  7 10  2  2  2 11  2  2  2 10  2  7  7  2  2  2  2  2  2  2
## [3625] 11  1  2 11  2  2  2  2  2  2  2 11 10  3  2  2  2 10 10 10 10  3  2  2
## [3649]  2  7 10  2 10 11 10 12 10  1  2 10  2 10  2 10  1  7  2 11  2 10 10 10
## [3673]  7  2  3  2  2 10  2 10 10  2 10  2 10  2 10 10  4  2  2  2  2  2 10 10
## [3697] 10  2  2 10 10 10 10  2 10  2  2  2  1 10  2 10  2 10 11 10  2 10 10  1
## [3721] 10  2  2 10 11  1 10 10 10  1 10  4 11  1  2  2  2  2 10  1  2  2  2  2
## [3745] 10 10  2 11 11 10  2  2  2 10  2 10  2  2  2  2  2 10  2 12 10  2  2  2
## [3769]  2  2  2  2 10  1 10 10  2  2  2 11  2  2  2  3  2  1 10 10  1  1 10  1
## [3793]  1  2 10 12  2  2  7 10  2  2  2 11 10 11 10  2  2 10  2  2 10  1 10  1
## [3817]  2 11  2  2 10 11 10 10  2  1 10  2 11 10  2 10  7  2 11 11 10  2 10 10
## [3841] 10 11  2 10 10 10 10  2  1  2 10 12 10 10  3  2  3 10  7  2 10  2 10  7
## [3865] 11  2  2  2 10 10 11 10  2  1 10 10 10 10 11 11  2  2  2  2  1  2 10 11
## [3889]  2 11 10  1  1 10 11  7  7 11 10 10 10  2 11  2  2 10 10  2 10  2  2 10
## [3913] 11  2 10  3 11 10  2  1  2 10  2 10  1 11  2  2  2 10  2  2  2  2  2  2
## [3937]  2 10  1  2 11  2 10  2  2 10 11 11 10  1  1 11  3  2 10  2  2  1 10 10
## [3961] 10  7  2  2  2  2  2 11  1 10  5  2 12  2  2  3  2  2  2 10  7 11  2  2
## [3985] 11 10  1  2 11 10  2  2 11  2 10  2  2 10  2 10  2  2  2  2 10  2  2  2
## [4009] 10  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2 10  2  2 10  2  7 11  2
## [4033]  2 10  2  2  2  2 10  2 10 10  2 10  1  2 11 10  2  2  2 10  3  2 10 11
## [4057]  2  2  2  1  2  3  2  2 11  2  2 10  2  1  2 10  2 11 10 10 10  2 10  2
## [4081]  1  2  2  2  2  2  2  2 11  2  2  2  2 10 11  2  2  2  2  2  2 10  2  2
## [4105]  2  1  2  2  2  2  2  2  2  2  2  2 11  2  2 11  2  2  2 10  1 10  2  2
## [4129] 11  2 10 11 10 10  2 10  2  2 11  1 11 11  2  7  1  2  1  2 10  2 12  2
## [4153]  7  1 10 10 10 10  2  2  4  1  2 10 10  3  2  2  2  2  2 10  3  2  2 10
## [4177] 10 10 10  2  2  2 10  7  2 10  2  7  1  1 11  1  2  2  2  2 10  2  2 10
## [4201]  2  1 10 10 10 10 10  2  2 10  2 11  1  2 10  2 10 10 10 10 10  2 10  1
## [4225]  1  2  2  7  2  7 10 11  2 10  2  1 10  2 10  2  2  2 10 10 10 10 11 10
## [4249]  2 10 11  2 11 11  2 10 11 10 10  2 10  1  2  2 10 10 11  1 10 10 10  2
## [4273] 10  4 10  2 11  1 10  2  2 10 10  2  2  2  1  2  2 10  2  2  2  2  2 11
## [4297]  1  6
## 
## Within cluster sum of squares by cluster:
##  [1] 2.5383447 3.4323340 3.9121518 7.3948538 4.0007985 0.0000000 2.5629165
##  [8] 0.3643482 7.6489770 2.8416771 3.6110120 2.6703749
##  (between_SS / total_SS =  99.5 %)
## 
## Available components:
## 
## [1] "cluster"      "centers"      "totss"        "withinss"     "tot.withinss"
## [6] "betweenss"    "size"         "iter"         "ifault"

Optimizar el número de grupos

set.seed(123)
optimizacion3 <- clusGap(datos_cluster, FUN=kmeans, nstart=25, K.max = 15, B=50)
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 214900)
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 214900)
## Warning: did not converge in 10 iterations
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 214900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 214900)
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 214900)
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 214900)
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 214900)
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations
plot(optimizacion3, xlab="Número de clusters K", main="Optimización de clusters")

#El óptimo es el primer punto más alto

Graficar los grupos

fviz_cluster(clusters3, data=datos_cluster)

Agregar grupos a la base de datos

clientes_cluster$cluster <- clusters3$cluster
head(clientes_cluster)
## # A tibble: 6 × 4
##   Cliente Ticket_Promedio Frecuencia_Compra cluster
##     <int>           <dbl>             <int>   <int>
## 1   12346          77184.                 1       9
## 2   12347            616.                 7       1
## 3   12349           1758.                 1      12
## 4   12350            334.                 1      10
## 5   12352            313.                 8      11
## 6   12353             89                  1       2
clientes_cluster %>%
  group_by(cluster) %>%
  summarise(
    Ticket_Promedio = mean(Ticket_Promedio),
    Frecuencia_Compra = mean(Frecuencia_Compra),
    Clientes = n()
  )
## # A tibble: 12 × 4
##    cluster Ticket_Promedio Frecuencia_Compra Clientes
##      <int>           <dbl>             <dbl>    <int>
##  1       1            602.              3.24      516
##  2       2            160.              2.38     1739
##  3       3            483.             33.5        62
##  4       4           4132.             14          21
##  5       5            338.            117.          6
##  6       6            490.           3500           1
##  7       7           1030.              3.81      181
##  8       8          14075.              3           2
##  9       9          80710.              1.5         2
## 10      10            352.              2.68     1322
## 11      11            321.             12.3       387
## 12      12           1888.              4.51       59
head(clientes_cluster)
## # A tibble: 6 × 4
##   Cliente Ticket_Promedio Frecuencia_Compra cluster
##     <int>           <dbl>             <int>   <int>
## 1   12346          77184.                 1       9
## 2   12347            616.                 7       1
## 3   12349           1758.                 1      12
## 4   12350            334.                 1      10
## 5   12352            313.                 8      11
## 6   12353             89                  1       2

Conclusiones

La técica de clustering permite identificar patrones o grupos naturales en los datos sin necesidad de etiquetas previas

---
title: "Clústers - Puntos USArrests y Clientes"
author: "Natalia Borjas Mendez - A01029448"
date: "2026-08-25"
output: 
  html_document:
    toc: TRUE
    toc_float: TRUE
    code_download: TRUE
    theme: flatly
---

![](https://media3.giphy.com/media/v1.Y2lkPTc5MGI3NjExaDdmdHdndnRzYnZ4N2hrbDVybTZvM211cWtnZWI3bXJ2c3BnMG56NyZlcD12MV9pbnRlcm5hbF9naWZfYnlfaWQmY3Q9Zw/12vVAGkaqHUqCQ/giphy.gif)


# <span style="color:#D81B60">Teoría</span>
**Agrupamiento** o *Clustering* es una técnica de aprendizaje automático no supervidaso que agrupa datos en función de su similitud.  

Algunos usos típicos de esta técnica son: 

* Segmentación de clientes  
* Detección de anormalidades  
* Categorización de documentos

# <span style="color:#D81B60">Instalar paquetes y llamar librerías</span>
```{r message=FALSE, warning=FALSE}
#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 de número de clústers
library(factoextra)
#install.packages("datasets")
library(datasets)
#install.packages("tidyverse")
library(tidyverse)
```

# <span style="color:#D81B60">Ejercicio 1. Puntos</span>
## <span style="color:#F48FB1">Contexto</span>
Agrupa los siguientes ocho puntos. 

## <span style="color:#F48FB1">Obtener datos</span>
```{r}
df1 <- data.frame(x=c(2,2,8,5,7,6,1,4), y=c(10,5,4,8,5,4,2,9))
```

## <span style="color:#F48FB1">Entender datos</span>
```{r}
summary(df1)
str(df1)
plot(df1$x, df1$y)
```

## <span style="color:#F48FB1">Escalar datos</span>
```{r}
# datos_escalados <- scale(datos_originales)
```

## <span style="color:#F48FB1">Asignar numero de grupos</span>
```{r}
grupos1 <- 3
```

## <span style="color:#F48FB1">Agrupar los puntos</span>
```{r}
set.seed(123)
clusters1 <- kmeans(df1, grupos1)
clusters1
```

## <span style="color:#F48FB1">Optimizar el número de grupos</span>
```{r}
set.seed(123)
optimizacion1 <- clusGap(df1, FUN=kmeans, nstart=2, K.max = 7)
plot(optimizacion1, xlab="Número de clusters K", main="Optimización de clusters")
#El óptimo es el primer punto más alto
```

## <span style="color:#F48FB1">Graficar los grupos</span>
```{r}
fviz_cluster(clusters1, data=df1)
```

## <span style="color:#F48FB1">Agregar grupos a la base de datos</span>
```{r}
df1_clusters <- cbind(df1, cluster = clusters1$cluster)
head(df1_clusters)
```

## <span style="color:#F48FB1">Conclusiones</span>
La técica de *clustering* permite identificar patrones o grupos naturales en los datos sin necesidad de etiquetas previas


# <span style="color:#D81B60">Ejercicio 2. USArrests</span>

## <span style="color:#F48FB1">Contexto</span>
La base de datos **USArrests** contiene estadísticas en arrestos por cada 100,000 residentes por agresión, asesinato y violación en cada uno de los 50 estados de EE.UU. en 1973.  

## <span style="color:#F48FB1">Obtener datos</span>
```{r}
df2 <- USArrests
df2 <- df2 %>% select(-UrbanPop)
```

## <span style="color:#F48FB1">Entender datos</span>
```{r}
summary(df2)
str(df2)
```

## <span style="color:#F48FB1">Escalar datos</span>
```{r}
df2_escalado <- scale(df2)
summary(df2_escalado)
```

## <span style="color:#F48FB1">Asignar numero de grupos</span>
```{r}
grupos2 <- 5
```

## <span style="color:#F48FB1">Agrupar los puntos</span>
```{r}
set.seed(123)
clusters2 <- kmeans(df2_escalado, grupos2)
clusters2
```

## <span style="color:#F48FB1">Optimizar el número de grupos</span>
```{r}
set.seed(123)
optimizacion2 <- clusGap(df2_escalado, FUN=kmeans, nstart=1, K.max = 10)
plot(optimizacion2, xlab="Número de clusters K", main="Optimización de clusters")
#El óptimo es el primer punto más alto
```

## <span style="color:#F48FB1">Graficar los grupos</span>
```{r}
fviz_cluster(clusters2, data=df2_escalado)
```

## <span style="color:#F48FB1">Agregar grupos a la base de datos</span>
```{r}
df2_clusters <- cbind(df2, cluster = clusters2$cluster)
head(df2_clusters)

df2_clusters %>% group_by(cluster) %>% summarise_all(mean) %>% mutate(indicador_inseguridad = Murder + Assault + Rape)

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)
```

## <span style="color:#F48FB1">Conclusiones</span>
La técica de *clustering* permite identificar patrones o grupos naturales en los datos sin necesidad de etiquetas previas.


# <span style="color:#D81B60">Ejercicio 3. Segmentación de clientes</span>
## <span style="color:#F48FB1">Contexto</span>
La base de datos **ventas** tiene los registros entre el 1 de diciembre del 2010 y el 9 de diciembre del 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 sis clientes son mayoristas.  
Objetivo: Segmentar clientes, asignarles nombres y características de comportamiento y proponer sugerencias a las empresas para aumentar las ventas. 

## <span style="color:#F48FB1">Obtener datos</span>
```{r}
df3 <- read.csv("C:\\Users\\natal\\OneDrive\\Carrera\\7moSemestre\\Modulo2\\ventas.csv")
```

## <span style="color:#F48FB1">Entender datos</span>
```{r}
summary(df3)
str(df3)
```

## <span style="color:#F48FB1">Crear variables a analizar</span>
```{r}
df3$Venta <- df3$Cantidad * df3$Precio

library(dplyr)

tickets_cliente <- df3 %>%
  group_by(Cliente, Ticket) %>%
  summarise(
    Total_Ticket = sum(Venta, na.rm = TRUE),
    .groups = "drop"
  )

ticket_promedio <- tickets_cliente %>%
  group_by(Cliente) %>%
  summarise(
    Ticket_Promedio = mean(Total_Ticket, na.rm = TRUE),
    .groups = "drop"
  )

frecuencia <- df3 %>%
  group_by(Cliente) %>%
  summarise(
    Frecuencia_Compra = n_distinct(Ticket),
    .groups = "drop"
  )

```

```{r}
clientes_cluster <- ticket_promedio %>%
  left_join(frecuencia, by = "Cliente")

datos_cluster <- clientes_cluster %>%
  select(Ticket_Promedio, Frecuencia_Compra) %>%
  scale()

```


## <span style="color:#F48FB1">Asignar numero de grupos</span>
```{r}
grupos3 <- 12
```

## <span style="color:#F48FB1">Agrupar los puntos</span>
```{r}
set.seed(123)
clusters3 <- kmeans(
  datos_cluster,
  centers = grupos3,
  nstart = 25
)

clusters3

```

## <span style="color:#F48FB1">Optimizar el número de grupos</span>
```{r}
set.seed(123)
optimizacion3 <- clusGap(datos_cluster, FUN=kmeans, nstart=25, K.max = 15, B=50)
plot(optimizacion3, xlab="Número de clusters K", main="Optimización de clusters")
#El óptimo es el primer punto más alto
```

## <span style="color:#F48FB1">Graficar los grupos</span>
```{r}
fviz_cluster(clusters3, data=datos_cluster)
```

## <span style="color:#F48FB1">Agregar grupos a la base de datos</span>
```{r}
clientes_cluster$cluster <- clusters3$cluster
head(clientes_cluster)

clientes_cluster %>%
  group_by(cluster) %>%
  summarise(
    Ticket_Promedio = mean(Ticket_Promedio),
    Frecuencia_Compra = mean(Frecuencia_Compra),
    Clientes = n()
  )

head(clientes_cluster)
```

# <span style="color:#D81B60">Conclusiones</span>
La técica de *clustering* permite identificar patrones o grupos naturales en los datos sin necesidad de etiquetas previas
