Arbol de decision Cancer
Ricardo Canive Valencia A01236496
18/02/2026
Instalar paquetes y llamar librerías
library(rpart)
library(rpart.plot)Importar la base de datos
cancer <- read.csv("C:\\Users\\sams\\Downloads\\cancer_de_mama.csv")Entender la base de datos
summary(cancer)## diagnosis radius_mean texture_mean perimeter_mean
## Length:569 Min. : 6.981 Min. : 9.71 Min. : 43.79
## Class :character 1st Qu.:11.700 1st Qu.:16.17 1st Qu.: 75.17
## Mode :character Median :13.370 Median :18.84 Median : 86.24
## Mean :14.127 Mean :19.29 Mean : 91.97
## 3rd Qu.:15.780 3rd Qu.:21.80 3rd Qu.:104.10
## Max. :28.110 Max. :39.28 Max. :188.50
## area_mean smoothness_mean compactness_mean concavity_mean
## Min. : 143.5 Min. :0.05263 Min. :0.01938 Min. :0.00000
## 1st Qu.: 420.3 1st Qu.:0.08637 1st Qu.:0.06492 1st Qu.:0.02956
## Median : 551.1 Median :0.09587 Median :0.09263 Median :0.06154
## Mean : 654.9 Mean :0.09636 Mean :0.10434 Mean :0.08880
## 3rd Qu.: 782.7 3rd Qu.:0.10530 3rd Qu.:0.13040 3rd Qu.:0.13070
## Max. :2501.0 Max. :0.16340 Max. :0.34540 Max. :0.42680
## concave.points_mean symmetry_mean fractal_dimension_mean radius_se
## Min. :0.00000 Min. :0.1060 Min. :0.04996 Min. :0.1115
## 1st Qu.:0.02031 1st Qu.:0.1619 1st Qu.:0.05770 1st Qu.:0.2324
## Median :0.03350 Median :0.1792 Median :0.06154 Median :0.3242
## Mean :0.04892 Mean :0.1812 Mean :0.06280 Mean :0.4052
## 3rd Qu.:0.07400 3rd Qu.:0.1957 3rd Qu.:0.06612 3rd Qu.:0.4789
## Max. :0.20120 Max. :0.3040 Max. :0.09744 Max. :2.8730
## texture_se perimeter_se area_se smoothness_se
## Min. :0.3602 Min. : 0.757 Min. : 6.802 Min. :0.001713
## 1st Qu.:0.8339 1st Qu.: 1.606 1st Qu.: 17.850 1st Qu.:0.005169
## Median :1.1080 Median : 2.287 Median : 24.530 Median :0.006380
## Mean :1.2169 Mean : 2.866 Mean : 40.337 Mean :0.007041
## 3rd Qu.:1.4740 3rd Qu.: 3.357 3rd Qu.: 45.190 3rd Qu.:0.008146
## Max. :4.8850 Max. :21.980 Max. :542.200 Max. :0.031130
## compactness_se concavity_se concave.points_se symmetry_se
## Min. :0.002252 Min. :0.00000 Min. :0.000000 Min. :0.007882
## 1st Qu.:0.013080 1st Qu.:0.01509 1st Qu.:0.007638 1st Qu.:0.015160
## Median :0.020450 Median :0.02589 Median :0.010930 Median :0.018730
## Mean :0.025478 Mean :0.03189 Mean :0.011796 Mean :0.020542
## 3rd Qu.:0.032450 3rd Qu.:0.04205 3rd Qu.:0.014710 3rd Qu.:0.023480
## Max. :0.135400 Max. :0.39600 Max. :0.052790 Max. :0.078950
## fractal_dimension_se radius_worst texture_worst perimeter_worst
## Min. :0.0008948 Min. : 7.93 Min. :12.02 Min. : 50.41
## 1st Qu.:0.0022480 1st Qu.:13.01 1st Qu.:21.08 1st Qu.: 84.11
## Median :0.0031870 Median :14.97 Median :25.41 Median : 97.66
## Mean :0.0037949 Mean :16.27 Mean :25.68 Mean :107.26
## 3rd Qu.:0.0045580 3rd Qu.:18.79 3rd Qu.:29.72 3rd Qu.:125.40
## Max. :0.0298400 Max. :36.04 Max. :49.54 Max. :251.20
## area_worst smoothness_worst compactness_worst concavity_worst
## Min. : 185.2 Min. :0.07117 Min. :0.02729 Min. :0.0000
## 1st Qu.: 515.3 1st Qu.:0.11660 1st Qu.:0.14720 1st Qu.:0.1145
## Median : 686.5 Median :0.13130 Median :0.21190 Median :0.2267
## Mean : 880.6 Mean :0.13237 Mean :0.25427 Mean :0.2722
## 3rd Qu.:1084.0 3rd Qu.:0.14600 3rd Qu.:0.33910 3rd Qu.:0.3829
## Max. :4254.0 Max. :0.22260 Max. :1.05800 Max. :1.2520
## concave.points_worst symmetry_worst fractal_dimension_worst
## Min. :0.00000 Min. :0.1565 Min. :0.05504
## 1st Qu.:0.06493 1st Qu.:0.2504 1st Qu.:0.07146
## Median :0.09993 Median :0.2822 Median :0.08004
## Mean :0.11461 Mean :0.2901 Mean :0.08395
## 3rd Qu.:0.16140 3rd Qu.:0.3179 3rd Qu.:0.09208
## Max. :0.29100 Max. :0.6638 Max. :0.20750str(cancer)## 'data.frame': 569 obs. of 31 variables:
## $ diagnosis : chr "M" "M" "M" "M" ...
## $ radius_mean : num 18 20.6 19.7 11.4 20.3 ...
## $ texture_mean : num 10.4 17.8 21.2 20.4 14.3 ...
## $ perimeter_mean : num 122.8 132.9 130 77.6 135.1 ...
## $ area_mean : num 1001 1326 1203 386 1297 ...
## $ smoothness_mean : num 0.1184 0.0847 0.1096 0.1425 0.1003 ...
## $ compactness_mean : num 0.2776 0.0786 0.1599 0.2839 0.1328 ...
## $ concavity_mean : num 0.3001 0.0869 0.1974 0.2414 0.198 ...
## $ concave.points_mean : num 0.1471 0.0702 0.1279 0.1052 0.1043 ...
## $ symmetry_mean : num 0.242 0.181 0.207 0.26 0.181 ...
## $ fractal_dimension_mean : num 0.0787 0.0567 0.06 0.0974 0.0588 ...
## $ radius_se : num 1.095 0.543 0.746 0.496 0.757 ...
## $ texture_se : num 0.905 0.734 0.787 1.156 0.781 ...
## $ perimeter_se : num 8.59 3.4 4.58 3.44 5.44 ...
## $ area_se : num 153.4 74.1 94 27.2 94.4 ...
## $ smoothness_se : num 0.0064 0.00522 0.00615 0.00911 0.01149 ...
## $ compactness_se : num 0.049 0.0131 0.0401 0.0746 0.0246 ...
## $ concavity_se : num 0.0537 0.0186 0.0383 0.0566 0.0569 ...
## $ concave.points_se : num 0.0159 0.0134 0.0206 0.0187 0.0188 ...
## $ symmetry_se : num 0.03 0.0139 0.0225 0.0596 0.0176 ...
## $ fractal_dimension_se : num 0.00619 0.00353 0.00457 0.00921 0.00511 ...
## $ radius_worst : num 25.4 25 23.6 14.9 22.5 ...
## $ texture_worst : num 17.3 23.4 25.5 26.5 16.7 ...
## $ perimeter_worst : num 184.6 158.8 152.5 98.9 152.2 ...
## $ area_worst : num 2019 1956 1709 568 1575 ...
## $ smoothness_worst : num 0.162 0.124 0.144 0.21 0.137 ...
## $ compactness_worst : num 0.666 0.187 0.424 0.866 0.205 ...
## $ concavity_worst : num 0.712 0.242 0.45 0.687 0.4 ...
## $ concave.points_worst : num 0.265 0.186 0.243 0.258 0.163 ...
## $ symmetry_worst : num 0.46 0.275 0.361 0.664 0.236 ...
## $ fractal_dimension_worst: num 0.1189 0.089 0.0876 0.173 0.0768 ...head(cancer)## diagnosis radius_mean texture_mean perimeter_mean area_mean smoothness_mean
## 1 M 17.99 10.38 122.80 1001.0 0.11840
## 2 M 20.57 17.77 132.90 1326.0 0.08474
## 3 M 19.69 21.25 130.00 1203.0 0.10960
## 4 M 11.42 20.38 77.58 386.1 0.14250
## 5 M 20.29 14.34 135.10 1297.0 0.10030
## 6 M 12.45 15.70 82.57 477.1 0.12780
## compactness_mean concavity_mean concave.points_mean symmetry_mean
## 1 0.27760 0.3001 0.14710 0.2419
## 2 0.07864 0.0869 0.07017 0.1812
## 3 0.15990 0.1974 0.12790 0.2069
## 4 0.28390 0.2414 0.10520 0.2597
## 5 0.13280 0.1980 0.10430 0.1809
## 6 0.17000 0.1578 0.08089 0.2087
## fractal_dimension_mean radius_se texture_se perimeter_se area_se
## 1 0.07871 1.0950 0.9053 8.589 153.40
## 2 0.05667 0.5435 0.7339 3.398 74.08
## 3 0.05999 0.7456 0.7869 4.585 94.03
## 4 0.09744 0.4956 1.1560 3.445 27.23
## 5 0.05883 0.7572 0.7813 5.438 94.44
## 6 0.07613 0.3345 0.8902 2.217 27.19
## smoothness_se compactness_se concavity_se concave.points_se symmetry_se
## 1 0.006399 0.04904 0.05373 0.01587 0.03003
## 2 0.005225 0.01308 0.01860 0.01340 0.01389
## 3 0.006150 0.04006 0.03832 0.02058 0.02250
## 4 0.009110 0.07458 0.05661 0.01867 0.05963
## 5 0.011490 0.02461 0.05688 0.01885 0.01756
## 6 0.007510 0.03345 0.03672 0.01137 0.02165
## fractal_dimension_se radius_worst texture_worst perimeter_worst area_worst
## 1 0.006193 25.38 17.33 184.60 2019.0
## 2 0.003532 24.99 23.41 158.80 1956.0
## 3 0.004571 23.57 25.53 152.50 1709.0
## 4 0.009208 14.91 26.50 98.87 567.7
## 5 0.005115 22.54 16.67 152.20 1575.0
## 6 0.005082 15.47 23.75 103.40 741.6
## smoothness_worst compactness_worst concavity_worst concave.points_worst
## 1 0.1622 0.6656 0.7119 0.2654
## 2 0.1238 0.1866 0.2416 0.1860
## 3 0.1444 0.4245 0.4504 0.2430
## 4 0.2098 0.8663 0.6869 0.2575
## 5 0.1374 0.2050 0.4000 0.1625
## 6 0.1791 0.5249 0.5355 0.1741
## symmetry_worst fractal_dimension_worst
## 1 0.4601 0.11890
## 2 0.2750 0.08902
## 3 0.3613 0.08758
## 4 0.6638 0.17300
## 5 0.2364 0.07678
## 6 0.3985 0.12440Crear árbol de decisión
cancer <- cancer[, c("diagnosis",
"radius_worst",
"concave.points_worst",
"texture_worst",
"smoothness_worst")]
cancer$diagnosis <- as.factor(cancer$diagnosis) # B/M
str(cancer)## 'data.frame': 569 obs. of 5 variables:
## $ diagnosis : Factor w/ 2 levels "B","M": 2 2 2 2 2 2 2 2 2 2 ...
## $ radius_worst : num 25.4 25 23.6 14.9 22.5 ...
## $ concave.points_worst: num 0.265 0.186 0.243 0.258 0.163 ...
## $ texture_worst : num 17.3 23.4 25.5 26.5 16.7 ...
## $ smoothness_worst : num 0.162 0.124 0.144 0.21 0.137 ...arbol_cancer <- rpart(diagnosis ~ ., data = cancer, method = "class")
rpart.plot(arbol_cancer)
prp(arbol_cancer, extra = 7, prefix = "fracción\n")
# Tabla de hojas: te dice cuántos casos caen en cada hoja y la
probabilidad por clase
frame <- arbol_cancer$frame
y2 <- as.data.frame(frame$yval2)
colnames(y2)[1:3] <- c("clase_pred", "n", "perdidas")
k <- length(levels(cancer$diagnosis))
prob_cols <- paste0("prob_", levels(cancer$diagnosis))
colnames(y2)[4:(3+k)] <- prob_cols
if (ncol(y2) >= (4 + k)) colnames(y2)[4 + k] <- "prob_nodo"
hojas <- cbind(
nodo = as.numeric(rownames(frame)),
var = frame$var,
y2
)
hojas <- hojas[hojas$var == "<leaf>", ]
hojas[order(-hojas$prob_M, hojas$prob_B), ]## nodo var clase_pred n perdidas prob_B prob_M prob_nodo
## 7 3 <leaf> 2 11 179 0.05789474 0.94210526 0.33391916
## 6 11 <leaf> 2 3 24 0.11111111 0.88888889 0.04745167
## 5 10 <leaf> 1 15 4 0.78947368 0.21052632 0.03339192
## 3 4 <leaf> 1 328 5 0.98498498 0.01501502 0.58523726#Conclusiones El modelo de árbol de decisión logró dividir la muestra en cuatro grupos bien diferenciados. En términos generales, se observa que el algoritmo consigue identificar con bastante claridad los patrones asociados tanto a casos benignos como malignos, generando segmentos donde la probabilidad de clasificación es alta y consistente.
Uno de los grupos más amplios se inclina claramente hacia diagnósticos benignos, mostrando un nivel de seguridad elevado cuando un caso pertenece a esa región del árbol. De manera similar, también se identifica un segmento importante con fuerte asociación a malignidad, lo que refleja que el modelo es capaz de detectar características relevantes para distinguir este tipo de casos.
Sin embargo, existen algunos nodos con muy pocos registros. Aunque presentan una tendencia definida hacia una categoría específica, su tamaño reducido hace que sus resultados deban analizarse con mayor prudencia, ya que podrían no representar de manera sólida el comportamiento general de la población.
En conjunto, el árbol muestra un desempeño adecuado al generar divisiones claras y probabilidades consistentes, aunque como todo modelo, requiere considerar la representatividad de cada grupo antes de sacar conclusiones definitivas.