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.

Instalar paquetes y llamas librerias

library(cluster)
library(ggplot2)
library(factoextra)
library(data.table)
library(tidyverse)
library(dplyr)
library(randomForest)  # Cargar la librería

Importar la base de datos

datos <- USArrests

Entender la base de datos

summary(datos)
##      Murder          Assault         UrbanPop          Rape      
##  Min.   : 0.800   Min.   : 45.0   Min.   :32.00   Min.   : 7.30  
##  1st Qu.: 4.075   1st Qu.:109.0   1st Qu.:54.50   1st Qu.:15.07  
##  Median : 7.250   Median :159.0   Median :66.00   Median :20.10  
##  Mean   : 7.788   Mean   :170.8   Mean   :65.54   Mean   :21.23  
##  3rd Qu.:11.250   3rd Qu.:249.0   3rd Qu.:77.75   3rd Qu.:26.18  
##  Max.   :17.400   Max.   :337.0   Max.   :91.00   Max.   :46.00

Escalar base de datos

# Escalar la base de datos
datos_escalados <- scale(USArrests)

# Verificar la media y desviación estándar después del escalado
apply(datos_escalados, 2, mean)  # Debería estar cerca de 0
##        Murder       Assault      UrbanPop          Rape 
## -7.663087e-17  1.112408e-16 -4.332808e-16  8.942391e-17
apply(datos_escalados, 2, sd)    # Debería estar cerca de 1
##   Murder  Assault UrbanPop     Rape 
##        1        1        1        1

Generar los segmentos

set.seed(123)
grupos <- 4
segmentos <- kmeans(datos_escalados, centers = grupos, nstart = 25)

Asignar grupos a los datos

asignacion <- cbind(datos, cluster = 
                      segmentos$cluster)

Graficar los clusters

fviz_cluster(segmentos, data = datos_escalados)

## Optimizar la cantidad de grupos

#La cantidad optima de grupos corresponde al punto mas alto de la grafica
set.seed(123)
optimizacion <- clusGap(datos_escalados, 
                        FUN = function(x, k) kmeans(x, k, nstart = 25), 
                        K.max = 10)
plot(optimizacion, xlab = "Número de clusters k")

## Comparar segmentos

promedio <- aggregate(asignacion, by = list(asignacion$cluster), FUN = mean)
print(promedio)
##   Group.1   Murder   Assault UrbanPop     Rape cluster
## 1       1 13.93750 243.62500 53.75000 21.41250       1
## 2       2  3.60000  78.53846 52.07692 12.17692       2
## 3       3  5.65625 138.87500 73.87500 18.78125       3
## 4       4 10.81538 257.38462 76.00000 33.19231       4
table(asignacion$cluster)
## 
##  1  2  3  4 
##  8 13 16 13

Obtener Mapa de USA y Unir Datos

# Obtener el mapa de EE.UU.
library(tigris)  # Carga la librería
us_map <- states(cb = TRUE)
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# Normalizar nombres de los estados para que coincidan
asignacion$state <- tolower(rownames(asignacion))
us_map$NAME <- tolower(us_map$NAME)

# Unir el mapa con la clasificación de clusters
us_clustered <- left_join(us_map, asignacion, by = c("NAME" = "state"))

Clasificación de seguridad basada en los clusters

# Agregar la clasificación de seguridad basada en los clusters
set.seed(123)
asignacion$nivel_seguridad <- case_when(
  asignacion$cluster == 1 ~ "Bajo",
  asignacion$cluster == 2 ~ "Medio",
  asignacion$cluster == 3 ~ "Alto",
  asignacion$cluster == 4 ~ "Muy Alto",
  TRUE ~ "Desconocido"  # Para manejar cualquier error
)

# Verificar la base con la nueva columna
head(asignacion)
##            Murder Assault UrbanPop Rape cluster      state nivel_seguridad
## Alabama      13.2     236       58 21.2       1    alabama            Bajo
## Alaska       10.0     263       48 44.5       4     alaska        Muy Alto
## Arizona       8.1     294       80 31.0       4    arizona        Muy Alto
## Arkansas      8.8     190       50 19.5       1   arkansas            Bajo
## California    9.0     276       91 40.6       4 california        Muy Alto
## Colorado      7.9     204       78 38.7       4   colorado        Muy Alto

Graficar los clusters en el mapa

# Definir colores según el nivel de seguridad
colores_seguridad <- c("Bajo" = "darkgreen", 
                       "Medio" = "yellow", 
                       "Alto" = "orange", 
                       "Muy Alto" = "red")

# Convertir los nombres de los estados a minúsculas en ambas bases
asignacion$state <- tolower(rownames(asignacion))
us_map$NAME <- tolower(us_map$NAME)
# Hacer el left_join nuevamente
us_clustered <- dplyr::left_join(us_map, asignacion, by = c("NAME" = "state"))


# Graficar el mapa
ggplot(data = us_clustered) +
  geom_sf(aes(fill = nivel_seguridad), color = "black") +  
  scale_fill_manual(values = colores_seguridad, name = "Nivel de Seguridad") +
  labs(title = "Mapa de Seguridad en EE.UU. (1973)",
       subtitle = "Clasificación basada en tasas de criminalidad",
       caption = "Fuente: USArrests") +
  theme_minimal()

Construcción del Modelo Random Forest

# Convertir la variable de salida en un factor
asignacion$nivel_seguridad <- as.factor(asignacion$nivel_seguridad)

# Modelo de Random Forest
set.seed(123)
modelo_rf <- randomForest(
  nivel_seguridad ~ Murder + Assault + Rape + UrbanPop, 
  data = asignacion,
  ntree = 100
)
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