Arbol de Decisión - Cancer de Mama
Salvador Rodriguez A00837963
2026-08-21
Teoría
El arbol de decisión es un diagrama de Aprendizaje Automatico que modela las opciones, eventos y posibles resultados de una decisión de forma visual.
Sus partes principales son:
- Nodo raíz: Inicio del diagrama.
- Ramas: Opciones disponibles.
- Nodos internos: Nuevas decisiones.
- Hojas: Resultado final de cada camino.
En este ejercicio se busca utilizar un arbol de decisión para clasificar si un tumor de mama es benigno o maligno a partir de algunas de sus características.
Importar la base de datos
# file.choose()
cancer <- read.csv("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
## N.unique : 2 1st Qu.:11.700 1st Qu.:16.17 1st Qu.: 75.17
## N.blank : 0 Median :13.370 Median :18.84 Median : 86.24
## Min.nchar: 1 Mean :14.127 Mean :19.29 Mean : 91.97
## Max.nchar: 1 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 ...Filtrar la base de datos
Cancer <- cancer[,c("diagnosis","radius_mean","texture_mean","concavity_mean","concave.points_mean")]
Cancer$diagnosis <- as.factor(ifelse(Cancer$diagnosis=="M", "Maligno", "Benigno"))
str(Cancer)## 'data.frame': 569 obs. of 5 variables:
## $ diagnosis : Factor w/ 2 levels "Benigno","Maligno": 2 2 2 2 2 2 2 2 2 2 ...
## $ 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 ...
## $ 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 ...sum(is.na(Cancer))## [1] 0sapply(Cancer, function(x) sum(is.na(x)))## diagnosis radius_mean texture_mean concavity_mean
## 0 0 0 0
## concave.points_mean
## 0Cancer <- na.omit(Cancer)Arbol de decision
# install.packages("rpart")
library(rpart)
arbol <- rpart(formula=diagnosis ~ ., data = Cancer)
arbol## n= 569
##
## node), split, n, loss, yval, (yprob)
## * denotes terminal node
##
## 1) root 569 212 Benigno (0.62741652 0.37258348)
## 2) concave.points_mean< 0.05142 349 20 Benigno (0.94269341 0.05730659)
## 4) radius_mean< 14.98 329 9 Benigno (0.97264438 0.02735562) *
## 5) radius_mean>=14.98 20 9 Maligno (0.45000000 0.55000000)
## 10) texture_mean< 18.68 8 1 Benigno (0.87500000 0.12500000) *
## 11) texture_mean>=18.68 12 2 Maligno (0.16666667 0.83333333) *
## 3) concave.points_mean>=0.05142 220 28 Maligno (0.12727273 0.87272727)
## 6) texture_mean< 16.395 28 11 Benigno (0.60714286 0.39285714)
## 12) concave.points_mean< 0.07905 17 1 Benigno (0.94117647 0.05882353) *
## 13) concave.points_mean>=0.07905 11 1 Maligno (0.09090909 0.90909091) *
## 7) texture_mean>=16.395 192 11 Maligno (0.05729167 0.94270833) *# install.packages("rpart.plot")
library(rpart.plot)
rpart.plot(arbol)
prp(arbol,extra = 7,prefix = "fraccion")
Conclusiones
El arbol muestra que la variable que mas ayuda a separar los casos benignos de los malignos es concave.points_mean. Cuando este valor es menor a 0.051, la mayoria de los casos terminan siendo benignos, mientras que cuando es mas alto, hay mucha mayor presencia de casos malignos. Entonces se puede decir que esta variable tiene bastante peso para hacer la clasificacion.
Despues, el modelo usa otras variables como radius_mean y texture_mean para decidir en los casos que no quedan tan claros desde el inicio. Por ejemplo, dependiendo del tamaño y la textura del tumor, el arbol va separando mejor los casos hasta llegar a una clasificacion final. En general, se ve que el modelo logra formar grupos bastante claros entre benignos y malignos.
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