Redes Neuronales
Carla Lievano
2025-08-25
Teoría
Una Red Neuronal Artificial (ANN) modela la relación entre un conjunto de entradas y una salida, resolviendo un problema de aprendizaje.
Ejemplos prácticos de aplicación de redes neuronales son:
- La recomendación de contenido de Netflix
- El feed de Instagram o Tiktok
- Determinar el número o letra escrito a mano
Instalar paquetes y llamar librerías
#install.packages("neuralnet")
library(neuralnet)Alinear con ejemplos
examen <- c(20,10,30,20,80,30)
proyecto <- c(90,20,40,50,50,80)
estatus <- c(1,0,0,0,0,1)
df <- data.frame(examen,proyecto,estatus)Generar la red neuronal
red_neuronal <- neuralnet(estatus~., data=df)
plot(red_neuronal, rep="best")
Ejercicio Cáncer de mama
cancer <- read.csv("~/Downloads/cancer_de_mama (1).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 0.12440Matriz de correlación
#plot_correlation(cancer)Árbol de decisión
cancer_factor <- cancer
cancer_factor$diagnosis <- as.factor(cancer$diagnosis)
str(cancer_factor)## 'data.frame': 569 obs. of 31 variables:
## $ diagnosis : Factor w/ 2 levels "B","M": 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 ...
## $ 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 ...#arbol_cancer <-rpart(diagnosis ~., data=cancer_factor)
#rpart.plot(arbol_cancer)#prp(arbol_cancer, extra=2, prefix= "fracción\n")Red neuronal
cancer_num <- cancer
# diagnosis como numérica (M=1, B=0)
cancer_num$diagnosis <- factor(cancer_num$diagnosis, levels = c("B","M"))red_neuronal <- neuralnet(diagnosis~., data=cancer_num)
plot(red_neuronal, rep= "best")
# Dividir en entrenamiento y prueba
#set.seed(123)
#idx <- createDataPartition(cancer_num$diagnosis, p = 0.8, list = FALSE)
#entrenamiento <- cancer_num[idx, ]
#prueba <- cancer_num[-idx, ]Generar red neuronal
#set.seed(123)
#ctrl <- trainControl(method = "cv", number = 10)
#red_cancer <- train(
# diagnosis ~ ., data = entrenamiento,
# method = "nnet",
# preProcess = c("center","scale"),
# trControl = ctrl,
# tuneLength = 5,
# trace = FALSE,
# MaxNWts = 20000
#)Predecir con la red
#pred_train <- predict(red_cancer, entrenamiento, type = "raw")
#pred_test <- predict(red_cancer, prueba, type = "raw")
#pred_train <- factor(pred_train, levels = levels(entrenamiento$diagnosis))
#pred_test <- factor(pred_test, levels = levels(prueba$diagnosis))
#Matriz de Confusión del Resultado de prueba
#mcrp_cancer <- confusionMatrix(resultado_prueba_red_cancer, prueba$diagnosis)
#mcrp_cancerMatriz de confusión
#mcre_cancer <- confusionMatrix(pred_train, entrenamiento$diagnosis)
#mcrp_cancer <- confusionMatrix(pred_test, prueba$diagnosis)
#mcre_cancer
#mcrp_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