Teoría

El paquete caret (Classification And REgression Training) es un paquete integral con una amplia variedad de algoritmos para el aprendizaje automático.

Iris

Instalar paquetes y llamar librerías

library(caret)
## Loading required package: ggplot2
## Loading required package: lattice
library(ggplot2) # Crear gráficos
library(datasets) # Usar la base de datos "Iris"
library(lattice) # Crear gráficos
library(DataExplorer)
library(mlbench)

Crear base de datos

df <- data.frame(iris)

Análisis Exploratorio

summary(df)
##   Sepal.Length    Sepal.Width     Petal.Length    Petal.Width   
##  Min.   :4.300   Min.   :2.000   Min.   :1.000   Min.   :0.100  
##  1st Qu.:5.100   1st Qu.:2.800   1st Qu.:1.600   1st Qu.:0.300  
##  Median :5.800   Median :3.000   Median :4.350   Median :1.300  
##  Mean   :5.843   Mean   :3.057   Mean   :3.758   Mean   :1.199  
##  3rd Qu.:6.400   3rd Qu.:3.300   3rd Qu.:5.100   3rd Qu.:1.800  
##  Max.   :7.900   Max.   :4.400   Max.   :6.900   Max.   :2.500  
##        Species  
##  setosa    :50  
##  versicolor:50  
##  virginica :50  
##                 
##                 
## 
str(df)
## 'data.frame':    150 obs. of  5 variables:
##  $ Sepal.Length: num  5.1 4.9 4.7 4.6 5 5.4 4.6 5 4.4 4.9 ...
##  $ Sepal.Width : num  3.5 3 3.2 3.1 3.6 3.9 3.4 3.4 2.9 3.1 ...
##  $ Petal.Length: num  1.4 1.4 1.3 1.5 1.4 1.7 1.4 1.5 1.4 1.5 ...
##  $ Petal.Width : num  0.2 0.2 0.2 0.2 0.2 0.4 0.3 0.2 0.2 0.1 ...
##  $ Species     : Factor w/ 3 levels "setosa","versicolor",..: 1 1 1 1 1 1 1 1 1 1 ...
create_report(df)
## 
## 
## processing file: report.rmd
## 
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## output file: C:/Users/lesda/OneDrive/Documentos/Concentracion IA/R Modulo 3/report.knit.md
## "C:/Program Files/RStudio/resources/app/bin/quarto/bin/tools/pandoc" +RTS -K512m -RTS "C:\Users\lesda\OneDrive\DOCUME~1\CONCEN~1\RMODUL~1\REPORT~1.MD" --to html4 --from markdown+autolink_bare_uris+tex_math_single_backslash --output pandoc42fc3679274e.html --lua-filter "C:\Users\lesda\AppData\Local\R\win-library\4.3\rmarkdown\rmarkdown\lua\pagebreak.lua" --lua-filter "C:\Users\lesda\AppData\Local\R\win-library\4.3\rmarkdown\rmarkdown\lua\latex-div.lua" --embed-resources --standalone --variable bs3=TRUE --section-divs --table-of-contents --toc-depth 6 --template "C:\Users\lesda\AppData\Local\R\win-library\4.3\rmarkdown\rmd\h\default.html" --no-highlight --variable highlightjs=1 --variable theme=yeti --mathjax --variable "mathjax-url=https://mathjax.rstudio.com/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML" --include-in-header "C:\Users\lesda\AppData\Local\Temp\RtmpOAEC5R\rmarkdown-str42fc231a51d0.html"
## 
## Output created: report.html
plot_missing(df)

plot_histogram(df)

plot_correlation(df)

Nota: La variable que queremos predecir debe tener formato de FACTOR

Partir datos 80-20

set.seed(123)
renglones_entrenamiento <-createDataPartition(df$Species, p=0.8, list=FALSE)
entrenamiento <- iris[renglones_entrenamiento, ]
prueba <- iris[-renglones_entrenamiento, ]

Distintos tipos de Métodos para Modelar

Los métodos más utilizados para modelar aprendizaje automático son:

** SVM: Support Vector Machine o Máquina de Vectores de Soporte. Hay varios subtipos: Lineal (svmLinear), Radial (svmRadial), Polinómicos (svmPoly), etc.

** Árbol de Decisión: rpart

** Redes Neuronales: nnet

** Random Forests o Bosques aleatorios: rf

1. Modelo con el métodos svmLineal

modelo1 <- train(Species ~ ., data= entrenamiento, method = "svmLinear", preProcess= c("scale", "center"), trControl = trainControl(method = "cv", number = 10), tuneGrid = data.frame(C=1)) #Cuando es svmLinear

resultado_entrenamiento1 <- predict(modelo1, entrenamiento)
resultado_prueba1 <- predict(modelo1, prueba)

Matriz de Confusión

mcre1 <- confusionMatrix(resultado_entrenamiento1, entrenamiento$Species)
mcre1 
## Confusion Matrix and Statistics
## 
##             Reference
## Prediction   setosa versicolor virginica
##   setosa         40          0         0
##   versicolor      0         39         0
##   virginica       0          1        40
## 
## Overall Statistics
##                                           
##                Accuracy : 0.9917          
##                  95% CI : (0.9544, 0.9998)
##     No Information Rate : 0.3333          
##     P-Value [Acc > NIR] : < 2.2e-16       
##                                           
##                   Kappa : 0.9875          
##                                           
##  Mcnemar's Test P-Value : NA              
## 
## Statistics by Class:
## 
##                      Class: setosa Class: versicolor Class: virginica
## Sensitivity                 1.0000            0.9750           1.0000
## Specificity                 1.0000            1.0000           0.9875
## Pos Pred Value              1.0000            1.0000           0.9756
## Neg Pred Value              1.0000            0.9877           1.0000
## Prevalence                  0.3333            0.3333           0.3333
## Detection Rate              0.3333            0.3250           0.3333
## Detection Prevalence        0.3333            0.3250           0.3417
## Balanced Accuracy           1.0000            0.9875           0.9938
mcrp1 <- confusionMatrix(resultado_prueba1, prueba$Species)
mcrp1
## Confusion Matrix and Statistics
## 
##             Reference
## Prediction   setosa versicolor virginica
##   setosa         10          0         0
##   versicolor      0         10         1
##   virginica       0          0         9
## 
## Overall Statistics
##                                           
##                Accuracy : 0.9667          
##                  95% CI : (0.8278, 0.9992)
##     No Information Rate : 0.3333          
##     P-Value [Acc > NIR] : 2.963e-13       
##                                           
##                   Kappa : 0.95            
##                                           
##  Mcnemar's Test P-Value : NA              
## 
## Statistics by Class:
## 
##                      Class: setosa Class: versicolor Class: virginica
## Sensitivity                 1.0000            1.0000           0.9000
## Specificity                 1.0000            0.9500           1.0000
## Pos Pred Value              1.0000            0.9091           1.0000
## Neg Pred Value              1.0000            1.0000           0.9524
## Prevalence                  0.3333            0.3333           0.3333
## Detection Rate              0.3333            0.3333           0.3000
## Detection Prevalence        0.3333            0.3667           0.3000
## Balanced Accuracy           1.0000            0.9750           0.9500

2. Modelo con el método svmRadial

modelo2 <- train(Species ~ ., data= entrenamiento, method = "svmRadial", preProcess= c("scale", "center"), trControl = trainControl(method = "cv", number = 10), tuneGrid = data.frame(sigma=1, C=1)) #Cambiar

resultado_entrenamiento2 <- predict(modelo2, entrenamiento)
resultado_prueba2 <- predict(modelo2, prueba)

Matriz de Confusión

mcre2 <- confusionMatrix(resultado_entrenamiento2, entrenamiento$Species)
mcre2 
## Confusion Matrix and Statistics
## 
##             Reference
## Prediction   setosa versicolor virginica
##   setosa         40          0         0
##   versicolor      0         39         0
##   virginica       0          1        40
## 
## Overall Statistics
##                                           
##                Accuracy : 0.9917          
##                  95% CI : (0.9544, 0.9998)
##     No Information Rate : 0.3333          
##     P-Value [Acc > NIR] : < 2.2e-16       
##                                           
##                   Kappa : 0.9875          
##                                           
##  Mcnemar's Test P-Value : NA              
## 
## Statistics by Class:
## 
##                      Class: setosa Class: versicolor Class: virginica
## Sensitivity                 1.0000            0.9750           1.0000
## Specificity                 1.0000            1.0000           0.9875
## Pos Pred Value              1.0000            1.0000           0.9756
## Neg Pred Value              1.0000            0.9877           1.0000
## Prevalence                  0.3333            0.3333           0.3333
## Detection Rate              0.3333            0.3250           0.3333
## Detection Prevalence        0.3333            0.3250           0.3417
## Balanced Accuracy           1.0000            0.9875           0.9938
mcrp2 <- confusionMatrix(resultado_prueba2, prueba$Species)
mcrp2
## Confusion Matrix and Statistics
## 
##             Reference
## Prediction   setosa versicolor virginica
##   setosa         10          0         0
##   versicolor      0         10         2
##   virginica       0          0         8
## 
## Overall Statistics
##                                           
##                Accuracy : 0.9333          
##                  95% CI : (0.7793, 0.9918)
##     No Information Rate : 0.3333          
##     P-Value [Acc > NIR] : 8.747e-12       
##                                           
##                   Kappa : 0.9             
##                                           
##  Mcnemar's Test P-Value : NA              
## 
## Statistics by Class:
## 
##                      Class: setosa Class: versicolor Class: virginica
## Sensitivity                 1.0000            1.0000           0.8000
## Specificity                 1.0000            0.9000           1.0000
## Pos Pred Value              1.0000            0.8333           1.0000
## Neg Pred Value              1.0000            1.0000           0.9091
## Prevalence                  0.3333            0.3333           0.3333
## Detection Rate              0.3333            0.3333           0.2667
## Detection Prevalence        0.3333            0.4000           0.2667
## Balanced Accuracy           1.0000            0.9500           0.9000

3. Modelo con el método svmPoly

modelo3 <- train(Species ~ ., data= entrenamiento, method = "svmPoly", preProcess= c("scale", "center"), trControl = trainControl(method = "cv", number = 10), tuneGrid = data.frame(degree=1,scale=1, C=1)) #Cambiar

resultado_entrenamiento3 <- predict(modelo3, entrenamiento)
resultado_prueba3 <- predict(modelo3, prueba)

Matriz de Confusión

mcre3 <- confusionMatrix(resultado_entrenamiento3, entrenamiento$Species)
mcre3 
## Confusion Matrix and Statistics
## 
##             Reference
## Prediction   setosa versicolor virginica
##   setosa         40          0         0
##   versicolor      0         39         0
##   virginica       0          1        40
## 
## Overall Statistics
##                                           
##                Accuracy : 0.9917          
##                  95% CI : (0.9544, 0.9998)
##     No Information Rate : 0.3333          
##     P-Value [Acc > NIR] : < 2.2e-16       
##                                           
##                   Kappa : 0.9875          
##                                           
##  Mcnemar's Test P-Value : NA              
## 
## Statistics by Class:
## 
##                      Class: setosa Class: versicolor Class: virginica
## Sensitivity                 1.0000            0.9750           1.0000
## Specificity                 1.0000            1.0000           0.9875
## Pos Pred Value              1.0000            1.0000           0.9756
## Neg Pred Value              1.0000            0.9877           1.0000
## Prevalence                  0.3333            0.3333           0.3333
## Detection Rate              0.3333            0.3250           0.3333
## Detection Prevalence        0.3333            0.3250           0.3417
## Balanced Accuracy           1.0000            0.9875           0.9938
mcrp3 <- confusionMatrix(resultado_prueba3, prueba$Species)
mcrp3
## Confusion Matrix and Statistics
## 
##             Reference
## Prediction   setosa versicolor virginica
##   setosa         10          0         0
##   versicolor      0         10         1
##   virginica       0          0         9
## 
## Overall Statistics
##                                           
##                Accuracy : 0.9667          
##                  95% CI : (0.8278, 0.9992)
##     No Information Rate : 0.3333          
##     P-Value [Acc > NIR] : 2.963e-13       
##                                           
##                   Kappa : 0.95            
##                                           
##  Mcnemar's Test P-Value : NA              
## 
## Statistics by Class:
## 
##                      Class: setosa Class: versicolor Class: virginica
## Sensitivity                 1.0000            1.0000           0.9000
## Specificity                 1.0000            0.9500           1.0000
## Pos Pred Value              1.0000            0.9091           1.0000
## Neg Pred Value              1.0000            1.0000           0.9524
## Prevalence                  0.3333            0.3333           0.3333
## Detection Rate              0.3333            0.3333           0.3000
## Detection Prevalence        0.3333            0.3667           0.3000
## Balanced Accuracy           1.0000            0.9750           0.9500

4. Modelo con el método Árbol de Decisión

modelo4 <- train(Species ~ ., data = entrenamiento, method = "rpart", preProcess = c("scale", "center"), trControl = trainControl(method="cv", number = 10), tuneLength = 10)

resultado_entrenamiento4 <- predict(modelo4, entrenamiento)
resultado_prueba4 <- predict(modelo4, prueba)

Matriz de Confusión

mcre4 <- confusionMatrix(resultado_entrenamiento4, entrenamiento$Species)
mcre4 
## Confusion Matrix and Statistics
## 
##             Reference
## Prediction   setosa versicolor virginica
##   setosa         40          0         0
##   versicolor      0         39         3
##   virginica       0          1        37
## 
## Overall Statistics
##                                           
##                Accuracy : 0.9667          
##                  95% CI : (0.9169, 0.9908)
##     No Information Rate : 0.3333          
##     P-Value [Acc > NIR] : < 2.2e-16       
##                                           
##                   Kappa : 0.95            
##                                           
##  Mcnemar's Test P-Value : NA              
## 
## Statistics by Class:
## 
##                      Class: setosa Class: versicolor Class: virginica
## Sensitivity                 1.0000            0.9750           0.9250
## Specificity                 1.0000            0.9625           0.9875
## Pos Pred Value              1.0000            0.9286           0.9737
## Neg Pred Value              1.0000            0.9872           0.9634
## Prevalence                  0.3333            0.3333           0.3333
## Detection Rate              0.3333            0.3250           0.3083
## Detection Prevalence        0.3333            0.3500           0.3167
## Balanced Accuracy           1.0000            0.9688           0.9563
mcrp4 <- confusionMatrix(resultado_prueba4, prueba$Species)
mcrp4
## Confusion Matrix and Statistics
## 
##             Reference
## Prediction   setosa versicolor virginica
##   setosa         10          0         0
##   versicolor      0         10         2
##   virginica       0          0         8
## 
## Overall Statistics
##                                           
##                Accuracy : 0.9333          
##                  95% CI : (0.7793, 0.9918)
##     No Information Rate : 0.3333          
##     P-Value [Acc > NIR] : 8.747e-12       
##                                           
##                   Kappa : 0.9             
##                                           
##  Mcnemar's Test P-Value : NA              
## 
## Statistics by Class:
## 
##                      Class: setosa Class: versicolor Class: virginica
## Sensitivity                 1.0000            1.0000           0.8000
## Specificity                 1.0000            0.9000           1.0000
## Pos Pred Value              1.0000            0.8333           1.0000
## Neg Pred Value              1.0000            1.0000           0.9091
## Prevalence                  0.3333            0.3333           0.3333
## Detection Rate              0.3333            0.3333           0.2667
## Detection Prevalence        0.3333            0.4000           0.2667
## Balanced Accuracy           1.0000            0.9500           0.9000

5. Modelo con el método Neural Net

modelo5 <- train(Species ~ ., data = entrenamiento, method = "nnet", preProcess = c("scale", "center"), trControl = trainControl(method="cv", number = 10))
## # weights:  11
## initial  value 130.530132 
## iter  10 value 50.031494
## iter  20 value 48.622939
## iter  30 value 46.051782
## iter  40 value 45.435982
## iter  50 value 45.023331
## iter  60 value 41.544443
## iter  70 value 18.376424
## iter  80 value 4.629967
## iter  90 value 3.675228
## iter 100 value 3.275824
## final  value 3.275824 
## stopped after 100 iterations
## # weights:  27
## initial  value 132.517409 
## iter  10 value 22.263231
## iter  20 value 2.574680
## iter  30 value 0.008513
## final  value 0.000051 
## converged
## # weights:  43
## initial  value 136.160730 
## iter  10 value 3.642258
## iter  20 value 0.051614
## iter  30 value 0.013220
## iter  40 value 0.001249
## final  value 0.000086 
## converged
## # weights:  11
## initial  value 124.472165 
## iter  10 value 57.985437
## iter  20 value 43.232595
## final  value 43.170440 
## converged
## # weights:  27
## initial  value 118.611044 
## iter  10 value 30.413305
## iter  20 value 21.077103
## iter  30 value 20.192922
## iter  40 value 20.153936
## final  value 20.153924 
## converged
## # weights:  43
## initial  value 131.301286 
## iter  10 value 26.646865
## iter  20 value 17.682102
## iter  30 value 17.633586
## iter  40 value 17.623573
## iter  50 value 17.364993
## iter  60 value 17.295129
## iter  70 value 17.290694
## final  value 17.290666 
## converged
## # weights:  11
## initial  value 115.622911 
## iter  10 value 33.350769
## iter  20 value 4.676969
## iter  30 value 3.131052
## iter  40 value 2.922591
## iter  50 value 2.825976
## iter  60 value 2.769974
## iter  70 value 2.741299
## iter  80 value 2.741136
## iter  90 value 2.739093
## final  value 2.739035 
## converged
## # weights:  27
## initial  value 139.822975 
## iter  10 value 37.447376
## iter  20 value 1.445699
## iter  30 value 0.316497
## iter  40 value 0.287713
## iter  50 value 0.260591
## iter  60 value 0.236249
## iter  70 value 0.224761
## iter  80 value 0.215415
## iter  90 value 0.194816
## iter 100 value 0.189471
## final  value 0.189471 
## stopped after 100 iterations
## # weights:  43
## initial  value 123.298044 
## iter  10 value 4.177632
## iter  20 value 0.257205
## iter  30 value 0.224601
## iter  40 value 0.200241
## iter  50 value 0.193031
## iter  60 value 0.182082
## iter  70 value 0.164800
## iter  80 value 0.149792
## iter  90 value 0.144373
## iter 100 value 0.142810
## final  value 0.142810 
## stopped after 100 iterations
## # weights:  11
## initial  value 123.243079 
## iter  10 value 49.923348
## iter  20 value 49.909994
## iter  30 value 49.907880
## final  value 49.906719 
## converged
## # weights:  27
## initial  value 117.894759 
## iter  10 value 9.481781
## iter  20 value 0.026637
## iter  30 value 0.001156
## final  value 0.000052 
## converged
## # weights:  43
## initial  value 131.870976 
## iter  10 value 17.010430
## iter  20 value 0.698814
## iter  30 value 0.001401
## final  value 0.000067 
## converged
## # weights:  11
## initial  value 141.804121 
## iter  10 value 63.315182
## iter  20 value 44.532148
## iter  30 value 42.998412
## final  value 42.994034 
## converged
## # weights:  27
## initial  value 129.180442 
## iter  10 value 44.217928
## iter  20 value 19.729677
## iter  30 value 18.527378
## iter  40 value 18.411074
## iter  50 value 18.393711
## iter  60 value 18.393129
## final  value 18.393125 
## converged
## # weights:  43
## initial  value 143.533117 
## iter  10 value 21.063126
## iter  20 value 17.843661
## iter  30 value 17.106737
## iter  40 value 16.985544
## iter  50 value 16.981278
## iter  60 value 16.980626
## final  value 16.980585 
## converged
## # weights:  11
## initial  value 123.091645 
## iter  10 value 49.148390
## iter  20 value 35.943210
## iter  30 value 10.736283
## iter  40 value 2.021433
## iter  50 value 1.687392
## iter  60 value 1.640809
## iter  70 value 1.636953
## iter  80 value 1.613389
## iter  90 value 1.611928
## iter 100 value 1.611137
## final  value 1.611137 
## stopped after 100 iterations
## # weights:  27
## initial  value 113.416728 
## iter  10 value 6.236444
## iter  20 value 0.187917
## iter  30 value 0.166748
## iter  40 value 0.155642
## iter  50 value 0.144249
## iter  60 value 0.141208
## iter  70 value 0.138463
## iter  80 value 0.136774
## iter  90 value 0.134567
## iter 100 value 0.132971
## final  value 0.132971 
## stopped after 100 iterations
## # weights:  43
## initial  value 124.153763 
## iter  10 value 6.673362
## iter  20 value 0.166533
## iter  30 value 0.154159
## iter  40 value 0.149227
## iter  50 value 0.136832
## iter  60 value 0.125718
## iter  70 value 0.121478
## iter  80 value 0.115540
## iter  90 value 0.113390
## iter 100 value 0.110992
## final  value 0.110992 
## stopped after 100 iterations
## # weights:  11
## initial  value 128.347385 
## iter  10 value 55.157651
## iter  20 value 47.800562
## iter  30 value 47.763719
## iter  40 value 47.763542
## iter  50 value 47.762534
## final  value 47.762465 
## converged
## # weights:  27
## initial  value 115.590774 
## iter  10 value 5.054265
## iter  20 value 1.048058
## iter  30 value 0.000979
## final  value 0.000072 
## converged
## # weights:  43
## initial  value 123.951869 
## iter  10 value 13.178443
## iter  20 value 0.965118
## iter  30 value 0.002392
## final  value 0.000078 
## converged
## # weights:  11
## initial  value 123.195822 
## iter  10 value 53.656490
## iter  20 value 43.803131
## iter  30 value 43.734766
## final  value 43.734347 
## converged
## # weights:  27
## initial  value 123.651803 
## iter  10 value 29.880588
## iter  20 value 19.921143
## iter  30 value 19.707388
## iter  40 value 19.705704
## final  value 19.705624 
## converged
## # weights:  43
## initial  value 148.336280 
## iter  10 value 27.474145
## iter  20 value 18.301737
## iter  30 value 18.138015
## iter  40 value 18.086240
## iter  50 value 18.084155
## iter  60 value 18.083934
## final  value 18.083909 
## converged
## # weights:  11
## initial  value 122.563728 
## iter  10 value 32.122176
## iter  20 value 10.269949
## iter  30 value 4.526292
## iter  40 value 3.900620
## iter  50 value 3.805816
## iter  60 value 3.743349
## iter  70 value 3.733207
## iter  80 value 3.721238
## iter  90 value 3.713938
## iter 100 value 3.705684
## final  value 3.705684 
## stopped after 100 iterations
## # weights:  27
## initial  value 130.631378 
## iter  10 value 4.944652
## iter  20 value 0.903581
## iter  30 value 0.602599
## iter  40 value 0.449328
## iter  50 value 0.416076
## iter  60 value 0.405323
## iter  70 value 0.397568
## iter  80 value 0.392801
## iter  90 value 0.386606
## iter 100 value 0.380965
## final  value 0.380965 
## stopped after 100 iterations
## # weights:  43
## initial  value 152.884265 
## iter  10 value 11.737646
## iter  20 value 1.402922
## iter  30 value 0.553654
## iter  40 value 0.456488
## iter  50 value 0.433353
## iter  60 value 0.391721
## iter  70 value 0.350673
## iter  80 value 0.322382
## iter  90 value 0.309362
## iter 100 value 0.302224
## final  value 0.302224 
## stopped after 100 iterations
## # weights:  11
## initial  value 133.677265 
## iter  10 value 49.425529
## iter  20 value 45.125104
## iter  30 value 24.714814
## iter  40 value 6.951374
## iter  50 value 3.962940
## iter  60 value 3.585057
## iter  70 value 2.556588
## iter  80 value 2.219301
## iter  90 value 2.033936
## iter 100 value 2.011517
## final  value 2.011517 
## stopped after 100 iterations
## # weights:  27
## initial  value 120.219437 
## iter  10 value 20.105178
## iter  20 value 0.691846
## iter  30 value 0.000424
## final  value 0.000094 
## converged
## # weights:  43
## initial  value 130.013247 
## iter  10 value 6.990719
## iter  20 value 0.117056
## final  value 0.000078 
## converged
## # weights:  11
## initial  value 122.587894 
## iter  10 value 55.646479
## iter  20 value 44.073616
## iter  30 value 44.056707
## final  value 44.056649 
## converged
## # weights:  27
## initial  value 122.488484 
## iter  10 value 30.042105
## iter  20 value 22.364237
## iter  30 value 21.402694
## iter  40 value 21.391770
## final  value 21.391728 
## converged
## # weights:  43
## initial  value 151.848122 
## iter  10 value 27.150882
## iter  20 value 20.889994
## iter  30 value 19.061592
## iter  40 value 18.857339
## iter  50 value 18.636402
## iter  60 value 18.597842
## iter  70 value 18.581420
## final  value 18.581304 
## converged
## # weights:  11
## initial  value 125.447189 
## iter  10 value 42.432302
## iter  20 value 14.708081
## iter  30 value 5.928158
## iter  40 value 4.717183
## iter  50 value 4.261072
## iter  60 value 3.990872
## iter  70 value 3.894028
## iter  80 value 3.877352
## iter  90 value 3.868846
## iter 100 value 3.865924
## final  value 3.865924 
## stopped after 100 iterations
## # weights:  27
## initial  value 141.522247 
## iter  10 value 19.693351
## iter  20 value 2.060082
## iter  30 value 0.713635
## iter  40 value 0.684010
## iter  50 value 0.651024
## iter  60 value 0.599068
## iter  70 value 0.534726
## iter  80 value 0.525302
## iter  90 value 0.477461
## iter 100 value 0.468104
## final  value 0.468104 
## stopped after 100 iterations
## # weights:  43
## initial  value 117.492171 
## iter  10 value 5.474776
## iter  20 value 0.633193
## iter  30 value 0.523049
## iter  40 value 0.506835
## iter  50 value 0.486677
## iter  60 value 0.470314
## iter  70 value 0.423468
## iter  80 value 0.413761
## iter  90 value 0.406423
## iter 100 value 0.383741
## final  value 0.383741 
## stopped after 100 iterations
## # weights:  11
## initial  value 128.494859 
## iter  10 value 67.868204
## iter  20 value 40.370984
## iter  30 value 8.030160
## iter  40 value 3.602779
## iter  50 value 3.354456
## iter  60 value 3.245703
## iter  70 value 3.148381
## iter  80 value 3.017232
## iter  90 value 2.916738
## iter 100 value 2.698927
## final  value 2.698927 
## stopped after 100 iterations
## # weights:  27
## initial  value 121.387618 
## iter  10 value 17.333188
## iter  20 value 6.562404
## iter  30 value 4.218606
## iter  40 value 0.023796
## iter  50 value 0.013835
## iter  60 value 0.007181
## iter  70 value 0.000265
## final  value 0.000094 
## converged
## # weights:  43
## initial  value 131.764022 
## iter  10 value 6.923964
## iter  20 value 0.585918
## iter  30 value 0.001510
## final  value 0.000094 
## converged
## # weights:  11
## initial  value 117.924376 
## iter  10 value 59.153858
## iter  20 value 45.980503
## iter  30 value 43.965813
## final  value 43.965807 
## converged
## # weights:  27
## initial  value 122.524569 
## iter  10 value 28.252379
## iter  20 value 20.308998
## iter  30 value 19.983255
## iter  40 value 19.969846
## final  value 19.969845 
## converged
## # weights:  43
## initial  value 175.722543 
## iter  10 value 24.152694
## iter  20 value 19.351652
## iter  30 value 18.570128
## iter  40 value 18.540253
## iter  50 value 18.531786
## iter  60 value 18.531273
## final  value 18.531272 
## converged
## # weights:  11
## initial  value 125.626851 
## iter  10 value 50.695359
## iter  20 value 28.615271
## iter  30 value 12.424432
## iter  40 value 5.029030
## iter  50 value 4.166888
## iter  60 value 3.979676
## iter  70 value 3.882211
## iter  80 value 3.873043
## iter  90 value 3.872674
## iter 100 value 3.871442
## final  value 3.871442 
## stopped after 100 iterations
## # weights:  27
## initial  value 123.025871 
## iter  10 value 27.020381
## iter  20 value 2.694706
## iter  30 value 1.092737
## iter  40 value 0.872715
## iter  50 value 0.758401
## iter  60 value 0.630276
## iter  70 value 0.571755
## iter  80 value 0.515264
## iter  90 value 0.475373
## iter 100 value 0.452080
## final  value 0.452080 
## stopped after 100 iterations
## # weights:  43
## initial  value 134.385829 
## iter  10 value 5.396493
## iter  20 value 1.952502
## iter  30 value 0.810078
## iter  40 value 0.740163
## iter  50 value 0.700944
## iter  60 value 0.648312
## iter  70 value 0.581811
## iter  80 value 0.540064
## iter  90 value 0.513923
## iter 100 value 0.483298
## final  value 0.483298 
## stopped after 100 iterations
## # weights:  11
## initial  value 124.033991 
## iter  10 value 53.598901
## iter  20 value 53.094417
## iter  30 value 51.710795
## iter  40 value 44.732729
## iter  50 value 17.281237
## iter  60 value 6.529030
## iter  70 value 3.473730
## iter  80 value 3.279187
## iter  90 value 3.156556
## iter 100 value 2.981555
## final  value 2.981555 
## stopped after 100 iterations
## # weights:  27
## initial  value 126.207925 
## iter  10 value 6.867316
## iter  20 value 0.342203
## iter  30 value 0.000889
## final  value 0.000071 
## converged
## # weights:  43
## initial  value 146.268437 
## iter  10 value 7.061711
## iter  20 value 1.073309
## iter  30 value 0.000467
## final  value 0.000066 
## converged
## # weights:  11
## initial  value 120.866935 
## iter  10 value 85.950877
## iter  20 value 60.671406
## iter  30 value 50.749580
## iter  40 value 43.846120
## final  value 43.846095 
## converged
## # weights:  27
## initial  value 126.514320 
## iter  10 value 46.451931
## iter  20 value 22.288378
## iter  30 value 21.611509
## iter  40 value 21.142364
## iter  50 value 20.374688
## iter  60 value 19.975509
## iter  70 value 19.860029
## final  value 19.859991 
## converged
## # weights:  43
## initial  value 113.521981 
## iter  10 value 27.307122
## iter  20 value 19.069629
## iter  30 value 18.496103
## iter  40 value 18.414947
## iter  50 value 18.412091
## iter  60 value 18.411932
## final  value 18.411927 
## converged
## # weights:  11
## initial  value 119.931364 
## iter  10 value 33.212563
## iter  20 value 6.825543
## iter  30 value 4.153607
## iter  40 value 3.996719
## iter  50 value 3.936301
## iter  60 value 3.900913
## iter  70 value 3.868653
## iter  80 value 3.868193
## iter  90 value 3.864798
## iter 100 value 3.860658
## final  value 3.860658 
## stopped after 100 iterations
## # weights:  27
## initial  value 125.980953 
## iter  10 value 3.828376
## iter  20 value 1.757039
## iter  30 value 1.084888
## iter  40 value 0.779504
## iter  50 value 0.534913
## iter  60 value 0.521705
## iter  70 value 0.515783
## iter  80 value 0.504124
## iter  90 value 0.485201
## iter 100 value 0.483827
## final  value 0.483827 
## stopped after 100 iterations
## # weights:  43
## initial  value 143.013185 
## iter  10 value 7.195354
## iter  20 value 1.984745
## iter  30 value 0.713672
## iter  40 value 0.552459
## iter  50 value 0.437450
## iter  60 value 0.403627
## iter  70 value 0.363382
## iter  80 value 0.356303
## iter  90 value 0.346628
## iter 100 value 0.337926
## final  value 0.337926 
## stopped after 100 iterations
## # weights:  11
## initial  value 119.603843 
## iter  10 value 66.519353
## iter  20 value 48.085237
## iter  30 value 10.691129
## iter  40 value 4.343493
## iter  50 value 3.486657
## iter  60 value 2.937962
## iter  70 value 2.185862
## iter  80 value 1.910157
## iter  90 value 1.802781
## iter 100 value 1.791736
## final  value 1.791736 
## stopped after 100 iterations
## # weights:  27
## initial  value 120.493313 
## iter  10 value 14.568437
## iter  20 value 1.413139
## iter  30 value 0.002421
## final  value 0.000049 
## converged
## # weights:  43
## initial  value 131.990396 
## iter  10 value 3.607345
## iter  20 value 0.869522
## iter  30 value 0.000776
## final  value 0.000079 
## converged
## # weights:  11
## initial  value 127.213395 
## iter  10 value 58.997762
## iter  20 value 44.424763
## final  value 43.139243 
## converged
## # weights:  27
## initial  value 117.195869 
## iter  10 value 28.619024
## iter  20 value 19.206476
## iter  30 value 18.621574
## iter  40 value 18.619068
## iter  40 value 18.619068
## iter  40 value 18.619068
## final  value 18.619068 
## converged
## # weights:  43
## initial  value 165.598734 
## iter  10 value 24.205649
## iter  20 value 17.629535
## iter  30 value 17.222776
## iter  40 value 17.168752
## iter  50 value 17.168464
## iter  60 value 17.168428
## iter  60 value 17.168428
## iter  60 value 17.168428
## final  value 17.168428 
## converged
## # weights:  11
## initial  value 115.941037 
## iter  10 value 48.705139
## iter  20 value 47.783092
## iter  30 value 43.562064
## iter  40 value 11.101593
## iter  50 value 4.031437
## iter  60 value 3.116711
## iter  70 value 3.019260
## iter  80 value 2.993105
## iter  90 value 2.981303
## iter 100 value 2.969047
## final  value 2.969047 
## stopped after 100 iterations
## # weights:  27
## initial  value 132.813339 
## iter  10 value 3.715700
## iter  20 value 1.056815
## iter  30 value 0.558748
## iter  40 value 0.530262
## iter  50 value 0.467614
## iter  60 value 0.445847
## iter  70 value 0.424130
## iter  80 value 0.373259
## iter  90 value 0.354379
## iter 100 value 0.342801
## final  value 0.342801 
## stopped after 100 iterations
## # weights:  43
## initial  value 126.886256 
## iter  10 value 3.942342
## iter  20 value 1.736816
## iter  30 value 0.630651
## iter  40 value 0.552680
## iter  50 value 0.489807
## iter  60 value 0.396264
## iter  70 value 0.356221
## iter  80 value 0.340605
## iter  90 value 0.328238
## iter 100 value 0.321359
## final  value 0.321359 
## stopped after 100 iterations
## # weights:  11
## initial  value 128.489378 
## iter  10 value 49.909576
## iter  20 value 49.876540
## iter  30 value 47.945970
## iter  40 value 39.847983
## iter  50 value 8.016537
## iter  60 value 4.619364
## iter  70 value 2.386452
## iter  80 value 1.338165
## iter  90 value 1.178344
## iter 100 value 1.100248
## final  value 1.100248 
## stopped after 100 iterations
## # weights:  27
## initial  value 141.912242 
## iter  10 value 7.102731
## iter  20 value 0.339738
## final  value 0.000079 
## converged
## # weights:  43
## initial  value 128.771330 
## iter  10 value 21.354630
## iter  20 value 2.784172
## iter  30 value 0.013786
## iter  40 value 0.000332
## final  value 0.000076 
## converged
## # weights:  11
## initial  value 120.181179 
## iter  10 value 46.347790
## iter  20 value 43.064428
## iter  30 value 43.054040
## final  value 43.054021 
## converged
## # weights:  27
## initial  value 126.647230 
## iter  10 value 25.682812
## iter  20 value 20.660342
## iter  30 value 19.500529
## iter  40 value 19.121600
## iter  50 value 19.088454
## iter  60 value 19.083697
## final  value 19.083689 
## converged
## # weights:  43
## initial  value 132.234904 
## iter  10 value 29.615687
## iter  20 value 19.279132
## iter  30 value 17.877712
## iter  40 value 17.806996
## iter  50 value 17.793960
## iter  60 value 17.793819
## final  value 17.793686 
## converged
## # weights:  11
## initial  value 121.579687 
## iter  10 value 49.472914
## iter  20 value 48.410085
## iter  30 value 45.340464
## iter  40 value 37.104905
## iter  50 value 8.129202
## iter  60 value 4.703745
## iter  70 value 4.278312
## iter  80 value 3.668066
## iter  90 value 3.605900
## iter 100 value 3.568123
## final  value 3.568123 
## stopped after 100 iterations
## # weights:  27
## initial  value 135.360878 
## iter  10 value 10.436945
## iter  20 value 2.222820
## iter  30 value 0.763058
## iter  40 value 0.725440
## iter  50 value 0.677966
## iter  60 value 0.570628
## iter  70 value 0.518380
## iter  80 value 0.502364
## iter  90 value 0.462332
## iter 100 value 0.455880
## final  value 0.455880 
## stopped after 100 iterations
## # weights:  43
## initial  value 125.924213 
## iter  10 value 3.865138
## iter  20 value 1.025246
## iter  30 value 0.422681
## iter  40 value 0.379135
## iter  50 value 0.353145
## iter  60 value 0.335865
## iter  70 value 0.319622
## iter  80 value 0.303895
## iter  90 value 0.289299
## iter 100 value 0.271561
## final  value 0.271561 
## stopped after 100 iterations
## # weights:  11
## initial  value 114.925820 
## iter  10 value 45.333263
## iter  20 value 21.250608
## iter  30 value 6.082611
## iter  40 value 4.448976
## iter  50 value 3.266614
## iter  60 value 1.880390
## iter  70 value 1.733764
## iter  80 value 1.089267
## iter  90 value 1.045776
## iter 100 value 0.950636
## final  value 0.950636 
## stopped after 100 iterations
## # weights:  27
## initial  value 116.607224 
## iter  10 value 6.159810
## iter  20 value 1.197702
## iter  30 value 0.000196
## final  value 0.000057 
## converged
## # weights:  43
## initial  value 123.125697 
## iter  10 value 4.793414
## iter  20 value 0.073094
## iter  30 value 0.000393
## final  value 0.000088 
## converged
## # weights:  11
## initial  value 120.471214 
## iter  10 value 45.420303
## iter  20 value 43.694661
## iter  30 value 43.690235
## final  value 43.690202 
## converged
## # weights:  27
## initial  value 168.714249 
## iter  10 value 28.073376
## iter  20 value 21.126580
## iter  30 value 20.968508
## iter  40 value 20.968134
## final  value 20.968117 
## converged
## # weights:  43
## initial  value 134.057733 
## iter  10 value 44.240823
## iter  20 value 19.621880
## iter  30 value 18.596469
## iter  40 value 18.220014
## iter  50 value 18.200869
## iter  60 value 18.194706
## final  value 18.194547 
## converged
## # weights:  11
## initial  value 137.081572 
## iter  10 value 53.546736
## iter  20 value 49.263649
## iter  30 value 49.116099
## iter  40 value 49.041348
## iter  50 value 48.683090
## iter  60 value 48.634845
## iter  70 value 48.489442
## iter  80 value 48.480790
## iter  90 value 48.451846
## iter 100 value 48.179024
## final  value 48.179024 
## stopped after 100 iterations
## # weights:  27
## initial  value 143.490043 
## iter  10 value 4.357251
## iter  20 value 1.321252
## iter  30 value 0.645280
## iter  40 value 0.616636
## iter  50 value 0.565996
## iter  60 value 0.521660
## iter  70 value 0.508617
## iter  80 value 0.487870
## iter  90 value 0.483152
## iter 100 value 0.479423
## final  value 0.479423 
## stopped after 100 iterations
## # weights:  43
## initial  value 178.832632 
## iter  10 value 8.121158
## iter  20 value 1.422046
## iter  30 value 0.568662
## iter  40 value 0.518952
## iter  50 value 0.434974
## iter  60 value 0.392568
## iter  70 value 0.345835
## iter  80 value 0.285289
## iter  90 value 0.268178
## iter 100 value 0.253675
## final  value 0.253675 
## stopped after 100 iterations
## # weights:  11
## initial  value 123.307045 
## iter  10 value 43.672929
## iter  20 value 8.049676
## iter  30 value 3.773651
## iter  40 value 3.173208
## iter  50 value 3.060201
## iter  60 value 2.971167
## iter  70 value 2.563371
## iter  80 value 2.471224
## iter  90 value 2.341221
## iter 100 value 2.320048
## final  value 2.320048 
## stopped after 100 iterations
## # weights:  27
## initial  value 129.270569 
## iter  10 value 10.575847
## iter  20 value 2.930770
## iter  30 value 1.689612
## iter  40 value 0.097359
## iter  50 value 0.000123
## iter  50 value 0.000057
## iter  50 value 0.000057
## final  value 0.000057 
## converged
## # weights:  43
## initial  value 119.634242 
## iter  10 value 6.310691
## iter  20 value 1.591412
## iter  30 value 0.028391
## iter  40 value 0.000902
## final  value 0.000069 
## converged
## # weights:  11
## initial  value 120.069235 
## iter  10 value 60.195069
## iter  20 value 51.394914
## iter  30 value 43.991436
## final  value 43.991141 
## converged
## # weights:  27
## initial  value 152.809198 
## iter  10 value 25.471737
## iter  20 value 21.511163
## iter  30 value 21.387357
## iter  40 value 21.386800
## final  value 21.386800 
## converged
## # weights:  43
## initial  value 137.024287 
## iter  10 value 22.447246
## iter  20 value 19.002967
## iter  30 value 18.519064
## iter  40 value 18.404215
## iter  50 value 18.397540
## iter  60 value 18.396716
## final  value 18.396607 
## converged
## # weights:  11
## initial  value 121.726735 
## iter  10 value 50.373336
## iter  20 value 50.105529
## iter  30 value 49.998791
## iter  40 value 49.958270
## iter  50 value 49.774790
## iter  60 value 48.541266
## iter  70 value 18.978222
## iter  80 value 6.742676
## iter  90 value 4.056469
## iter 100 value 3.922763
## final  value 3.922763 
## stopped after 100 iterations
## # weights:  27
## initial  value 146.633351 
## iter  10 value 6.579898
## iter  20 value 0.624311
## iter  30 value 0.562510
## iter  40 value 0.514462
## iter  50 value 0.457198
## iter  60 value 0.403961
## iter  70 value 0.382785
## iter  80 value 0.371306
## iter  90 value 0.358751
## iter 100 value 0.317469
## final  value 0.317469 
## stopped after 100 iterations
## # weights:  43
## initial  value 127.981900 
## iter  10 value 7.369546
## iter  20 value 0.839917
## iter  30 value 0.675447
## iter  40 value 0.617273
## iter  50 value 0.540482
## iter  60 value 0.477520
## iter  70 value 0.443309
## iter  80 value 0.359346
## iter  90 value 0.308424
## iter 100 value 0.292198
## final  value 0.292198 
## stopped after 100 iterations
## # weights:  11
## initial  value 133.510869 
## iter  10 value 66.279276
## iter  20 value 49.065891
## iter  30 value 46.607987
## final  value 46.598156 
## converged
resultado_entrenamiento5 <- predict(modelo5, entrenamiento)
resultado_prueba5 <- predict(modelo5, prueba)

Matriz de Confusión

mcre5 <- confusionMatrix(resultado_entrenamiento5, entrenamiento$Species)
mcre5 
## Confusion Matrix and Statistics
## 
##             Reference
## Prediction   setosa versicolor virginica
##   setosa         40          0         0
##   versicolor      0         36         0
##   virginica       0          4        40
## 
## Overall Statistics
##                                           
##                Accuracy : 0.9667          
##                  95% CI : (0.9169, 0.9908)
##     No Information Rate : 0.3333          
##     P-Value [Acc > NIR] : < 2.2e-16       
##                                           
##                   Kappa : 0.95            
##                                           
##  Mcnemar's Test P-Value : NA              
## 
## Statistics by Class:
## 
##                      Class: setosa Class: versicolor Class: virginica
## Sensitivity                 1.0000            0.9000           1.0000
## Specificity                 1.0000            1.0000           0.9500
## Pos Pred Value              1.0000            1.0000           0.9091
## Neg Pred Value              1.0000            0.9524           1.0000
## Prevalence                  0.3333            0.3333           0.3333
## Detection Rate              0.3333            0.3000           0.3333
## Detection Prevalence        0.3333            0.3000           0.3667
## Balanced Accuracy           1.0000            0.9500           0.9750
mcrp5 <- confusionMatrix(resultado_prueba5, prueba$Species)
mcrp5
## Confusion Matrix and Statistics
## 
##             Reference
## Prediction   setosa versicolor virginica
##   setosa         10          0         0
##   versicolor      0          9         0
##   virginica       0          1        10
## 
## Overall Statistics
##                                           
##                Accuracy : 0.9667          
##                  95% CI : (0.8278, 0.9992)
##     No Information Rate : 0.3333          
##     P-Value [Acc > NIR] : 2.963e-13       
##                                           
##                   Kappa : 0.95            
##                                           
##  Mcnemar's Test P-Value : NA              
## 
## Statistics by Class:
## 
##                      Class: setosa Class: versicolor Class: virginica
## Sensitivity                 1.0000            0.9000           1.0000
## Specificity                 1.0000            1.0000           0.9500
## Pos Pred Value              1.0000            1.0000           0.9091
## Neg Pred Value              1.0000            0.9524           1.0000
## Prevalence                  0.3333            0.3333           0.3333
## Detection Rate              0.3333            0.3000           0.3333
## Detection Prevalence        0.3333            0.3000           0.3667
## Balanced Accuracy           1.0000            0.9500           0.9750

6. Modelo con el método Random Forest

modelo6 <- train(Species ~ ., data = entrenamiento, method = "rf", preProcess = c("scale", "center"), trControl = trainControl(method="cv", number = 10), tuneGrid = expand.grid(mtry =c(2,4,6)))
## Warning in randomForest.default(x, y, mtry = param$mtry, ...): invalid mtry:
## reset to within valid range

## Warning in randomForest.default(x, y, mtry = param$mtry, ...): invalid mtry:
## reset to within valid range

## Warning in randomForest.default(x, y, mtry = param$mtry, ...): invalid mtry:
## reset to within valid range

## Warning in randomForest.default(x, y, mtry = param$mtry, ...): invalid mtry:
## reset to within valid range

## Warning in randomForest.default(x, y, mtry = param$mtry, ...): invalid mtry:
## reset to within valid range

## Warning in randomForest.default(x, y, mtry = param$mtry, ...): invalid mtry:
## reset to within valid range

## Warning in randomForest.default(x, y, mtry = param$mtry, ...): invalid mtry:
## reset to within valid range

## Warning in randomForest.default(x, y, mtry = param$mtry, ...): invalid mtry:
## reset to within valid range

## Warning in randomForest.default(x, y, mtry = param$mtry, ...): invalid mtry:
## reset to within valid range

## Warning in randomForest.default(x, y, mtry = param$mtry, ...): invalid mtry:
## reset to within valid range
resultado_entrenamiento6 <- predict(modelo6, entrenamiento)
resultado_prueba6 <- predict(modelo6, prueba)

Matriz de Confusión

mcre6 <- confusionMatrix(resultado_entrenamiento6, entrenamiento$Species)
mcre6 
## Confusion Matrix and Statistics
## 
##             Reference
## Prediction   setosa versicolor virginica
##   setosa         40          0         0
##   versicolor      0         40         0
##   virginica       0          0        40
## 
## Overall Statistics
##                                      
##                Accuracy : 1          
##                  95% CI : (0.9697, 1)
##     No Information Rate : 0.3333     
##     P-Value [Acc > NIR] : < 2.2e-16  
##                                      
##                   Kappa : 1          
##                                      
##  Mcnemar's Test P-Value : NA         
## 
## Statistics by Class:
## 
##                      Class: setosa Class: versicolor Class: virginica
## Sensitivity                 1.0000            1.0000           1.0000
## Specificity                 1.0000            1.0000           1.0000
## Pos Pred Value              1.0000            1.0000           1.0000
## Neg Pred Value              1.0000            1.0000           1.0000
## Prevalence                  0.3333            0.3333           0.3333
## Detection Rate              0.3333            0.3333           0.3333
## Detection Prevalence        0.3333            0.3333           0.3333
## Balanced Accuracy           1.0000            1.0000           1.0000
mcrp6 <- confusionMatrix(resultado_prueba6, prueba$Species)
mcrp6
## Confusion Matrix and Statistics
## 
##             Reference
## Prediction   setosa versicolor virginica
##   setosa         10          0         0
##   versicolor      0         10         2
##   virginica       0          0         8
## 
## Overall Statistics
##                                           
##                Accuracy : 0.9333          
##                  95% CI : (0.7793, 0.9918)
##     No Information Rate : 0.3333          
##     P-Value [Acc > NIR] : 8.747e-12       
##                                           
##                   Kappa : 0.9             
##                                           
##  Mcnemar's Test P-Value : NA              
## 
## Statistics by Class:
## 
##                      Class: setosa Class: versicolor Class: virginica
## Sensitivity                 1.0000            1.0000           0.8000
## Specificity                 1.0000            0.9000           1.0000
## Pos Pred Value              1.0000            0.8333           1.0000
## Neg Pred Value              1.0000            1.0000           0.9091
## Prevalence                  0.3333            0.3333           0.3333
## Detection Rate              0.3333            0.3333           0.2667
## Detection Prevalence        0.3333            0.4000           0.2667
## Balanced Accuracy           1.0000            0.9500           0.9000

Resumen de Resultados

resumen <- data.frame(
  "svmLinear" = c(mcre1$overall["Accuracy"], mcre1$overall["Accuracy"]),
  "svmRadial" = c(mcre2$overall["Accuracy"], mcrp2$overall["Accuracy"]),
  "svmPoly" = c(mcre3$overall["Accuracy"], mcrp3$overall["Accuracy"]),
  "rpart" = c(mcre4$overall["Accuracy"], mcrp4$overall["Accuracy"]),
  "NeuralNet" = c(mcre5$overall["Accuracy"], mcrp5$overall["Accuracy"]),
  "RandomForest" = c(mcre6$overall["Accuracy"], mcrp6$overall["Accuracy"])
)

rownames(resumen) <- c("Precision de entrenamiento", "Precision de prueba")
resumen
##                            svmLinear svmRadial   svmPoly     rpart NeuralNet
## Precision de entrenamiento 0.9916667 0.9916667 0.9916667 0.9666667 0.9666667
## Precision de prueba        0.9916667 0.9333333 0.9666667 0.9333333 0.9666667
##                            RandomForest
## Precision de entrenamiento    1.0000000
## Precision de prueba           0.9333333

Conclusión

El modelo con el método de bosques aleatorios presenta sobreajuste, ya que tiene una alta precisión en entrenamiento, pero baja en prueba.

Acorde al resumen de resultados, el mejor modelo es el de Máquina de Vectores de Soporte Lineal.

Breast Cancer

data(BreastCancer)
df <- data.frame(BreastCancer)

Análisis Exploratorio

summary(df)
##       Id             Cl.thickness   Cell.size     Cell.shape  Marg.adhesion
##  Length:699         1      :145   1      :384   1      :353   1      :407  
##  Class :character   5      :130   10     : 67   2      : 59   2      : 58  
##  Mode  :character   3      :108   3      : 52   10     : 58   3      : 58  
##                     4      : 80   2      : 45   3      : 56   10     : 55  
##                     10     : 69   4      : 40   4      : 44   4      : 33  
##                     2      : 50   5      : 30   5      : 34   8      : 25  
##                     (Other):117   (Other): 81   (Other): 95   (Other): 63  
##   Epith.c.size  Bare.nuclei   Bl.cromatin  Normal.nucleoli    Mitoses   
##  2      :386   1      :402   2      :166   1      :443     1      :579  
##  3      : 72   10     :132   3      :165   10     : 61     2      : 35  
##  4      : 48   2      : 30   1      :152   3      : 44     3      : 33  
##  1      : 47   5      : 30   7      : 73   2      : 36     10     : 14  
##  6      : 41   3      : 28   4      : 40   8      : 24     4      : 12  
##  5      : 39   (Other): 61   5      : 34   6      : 22     7      :  9  
##  (Other): 66   NA's   : 16   (Other): 69   (Other): 69     (Other): 17  
##        Class    
##  benign   :458  
##  malignant:241  
##                 
##                 
##                 
##                 
## 
str(df)
## 'data.frame':    699 obs. of  11 variables:
##  $ Id             : chr  "1000025" "1002945" "1015425" "1016277" ...
##  $ Cl.thickness   : Ord.factor w/ 10 levels "1"<"2"<"3"<"4"<..: 5 5 3 6 4 8 1 2 2 4 ...
##  $ Cell.size      : Ord.factor w/ 10 levels "1"<"2"<"3"<"4"<..: 1 4 1 8 1 10 1 1 1 2 ...
##  $ Cell.shape     : Ord.factor w/ 10 levels "1"<"2"<"3"<"4"<..: 1 4 1 8 1 10 1 2 1 1 ...
##  $ Marg.adhesion  : Ord.factor w/ 10 levels "1"<"2"<"3"<"4"<..: 1 5 1 1 3 8 1 1 1 1 ...
##  $ Epith.c.size   : Ord.factor w/ 10 levels "1"<"2"<"3"<"4"<..: 2 7 2 3 2 7 2 2 2 2 ...
##  $ Bare.nuclei    : Factor w/ 10 levels "1","2","3","4",..: 1 10 2 4 1 10 10 1 1 1 ...
##  $ Bl.cromatin    : Factor w/ 10 levels "1","2","3","4",..: 3 3 3 3 3 9 3 3 1 2 ...
##  $ Normal.nucleoli: Factor w/ 10 levels "1","2","3","4",..: 1 2 1 7 1 7 1 1 1 1 ...
##  $ Mitoses        : Factor w/ 9 levels "1","2","3","4",..: 1 1 1 1 1 1 1 1 5 1 ...
##  $ Class          : Factor w/ 2 levels "benign","malignant": 1 1 1 1 1 2 1 1 1 1 ...
# Limpieza
df$Id <- NULL

df$Cl.thickness <- as.numeric(df$Cl.thickness)
df$Cell.size <- as.numeric(df$Cell.size)
df$Cell.shape <- as.numeric(df$Cell.shape)
df$Marg.adhesion <- as.numeric(df$Marg.adhesion)
df$Epith.c.size <- as.numeric(df$Epith.c.size)
df$Bare.nuclei <- as.numeric(df$Bare.nuclei)
df$Bl.cromatin <- as.numeric(df$Bl.cromatin)
df$Normal.nucleoli <- as.numeric(df$Normal.nucleoli)
df$Mitoses <- as.numeric(df$Mitoses)
df$Class <- as.factor(df$Class)

#Quitar 16 nulos presentes en la variable Normal.nucleoli
df <- na.omit(df)


create_report(df)
## 
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## processing file: report.rmd
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## output file: C:/Users/lesda/OneDrive/Documentos/Concentracion IA/R Modulo 3/report.knit.md
## "C:/Program Files/RStudio/resources/app/bin/quarto/bin/tools/pandoc" +RTS -K512m -RTS "C:\Users\lesda\OneDrive\DOCUME~1\CONCEN~1\RMODUL~1\REPORT~1.MD" --to html4 --from markdown+autolink_bare_uris+tex_math_single_backslash --output pandoc42fc6de215e.html --lua-filter "C:\Users\lesda\AppData\Local\R\win-library\4.3\rmarkdown\rmarkdown\lua\pagebreak.lua" --lua-filter "C:\Users\lesda\AppData\Local\R\win-library\4.3\rmarkdown\rmarkdown\lua\latex-div.lua" --embed-resources --standalone --variable bs3=TRUE --section-divs --table-of-contents --toc-depth 6 --template "C:\Users\lesda\AppData\Local\R\win-library\4.3\rmarkdown\rmd\h\default.html" --no-highlight --variable highlightjs=1 --variable theme=yeti --mathjax --variable "mathjax-url=https://mathjax.rstudio.com/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML" --include-in-header "C:\Users\lesda\AppData\Local\Temp\RtmpOAEC5R\rmarkdown-str42fc6d6b5ebb.html"
## 
## Output created: report.html
plot_missing(df)

plot_histogram(df)

plot_correlation(df)

Nota: La variable que queremos predecir debe tener formato de FACTOR

Partir datos 80-20

set.seed(123)
renglones_entrenamiento <-createDataPartition(df$Class, p=0.8, list=FALSE)
entrenamiento <- df[renglones_entrenamiento, ]
prueba <- df[-renglones_entrenamiento, ]

1. Modelo con el métodos svmLineal

modelo1 <- train(Class ~ ., data= entrenamiento, method = "svmLinear", preProcess= c("scale", "center"), trControl = trainControl(method = "cv", number = 10), tuneGrid = data.frame(C=1)) #Cuando es svmLinear

resultado_entrenamiento1 <- predict(modelo1, entrenamiento)
resultado_prueba1 <- predict(modelo1, prueba)

Matriz de Confusión

mcre1 <- confusionMatrix(resultado_entrenamiento1, entrenamiento$Class)
mcre1 
## Confusion Matrix and Statistics
## 
##            Reference
## Prediction  benign malignant
##   benign       347         7
##   malignant      9       185
##                                          
##                Accuracy : 0.9708         
##                  95% CI : (0.953, 0.9832)
##     No Information Rate : 0.6496         
##     P-Value [Acc > NIR] : <2e-16         
##                                          
##                   Kappa : 0.936          
##                                          
##  Mcnemar's Test P-Value : 0.8026         
##                                          
##             Sensitivity : 0.9747         
##             Specificity : 0.9635         
##          Pos Pred Value : 0.9802         
##          Neg Pred Value : 0.9536         
##              Prevalence : 0.6496         
##          Detection Rate : 0.6332         
##    Detection Prevalence : 0.6460         
##       Balanced Accuracy : 0.9691         
##                                          
##        'Positive' Class : benign         
## 
mcrp1 <- confusionMatrix(resultado_prueba1, prueba$Class)
mcrp1
## Confusion Matrix and Statistics
## 
##            Reference
## Prediction  benign malignant
##   benign        87         2
##   malignant      1        45
##                                           
##                Accuracy : 0.9778          
##                  95% CI : (0.9364, 0.9954)
##     No Information Rate : 0.6519          
##     P-Value [Acc > NIR] : <2e-16          
##                                           
##                   Kappa : 0.9508          
##                                           
##  Mcnemar's Test P-Value : 1               
##                                           
##             Sensitivity : 0.9886          
##             Specificity : 0.9574          
##          Pos Pred Value : 0.9775          
##          Neg Pred Value : 0.9783          
##              Prevalence : 0.6519          
##          Detection Rate : 0.6444          
##    Detection Prevalence : 0.6593          
##       Balanced Accuracy : 0.9730          
##                                           
##        'Positive' Class : benign          
## 

2. Modelo con el método svmRadial

modelo2 <- train(Class ~ ., data= entrenamiento, method = "svmRadial", preProcess= c("scale", "center"), trControl = trainControl(method = "cv", number = 10), tuneGrid = data.frame(sigma=1, C=1)) #Cambiar

resultado_entrenamiento2 <- predict(modelo2, entrenamiento)
resultado_prueba2 <- predict(modelo2, prueba)

Matriz de Confusión

mcre2 <- confusionMatrix(resultado_entrenamiento2, entrenamiento$Class)
mcre2 
## Confusion Matrix and Statistics
## 
##            Reference
## Prediction  benign malignant
##   benign       354         0
##   malignant      2       192
##                                           
##                Accuracy : 0.9964          
##                  95% CI : (0.9869, 0.9996)
##     No Information Rate : 0.6496          
##     P-Value [Acc > NIR] : <2e-16          
##                                           
##                   Kappa : 0.992           
##                                           
##  Mcnemar's Test P-Value : 0.4795          
##                                           
##             Sensitivity : 0.9944          
##             Specificity : 1.0000          
##          Pos Pred Value : 1.0000          
##          Neg Pred Value : 0.9897          
##              Prevalence : 0.6496          
##          Detection Rate : 0.6460          
##    Detection Prevalence : 0.6460          
##       Balanced Accuracy : 0.9972          
##                                           
##        'Positive' Class : benign          
## 
mcrp2 <- confusionMatrix(resultado_prueba2, prueba$Class)
mcrp2
## Confusion Matrix and Statistics
## 
##            Reference
## Prediction  benign malignant
##   benign        82         0
##   malignant      6        47
##                                           
##                Accuracy : 0.9556          
##                  95% CI : (0.9058, 0.9835)
##     No Information Rate : 0.6519          
##     P-Value [Acc > NIR] : < 2e-16         
##                                           
##                   Kappa : 0.9049          
##                                           
##  Mcnemar's Test P-Value : 0.04123         
##                                           
##             Sensitivity : 0.9318          
##             Specificity : 1.0000          
##          Pos Pred Value : 1.0000          
##          Neg Pred Value : 0.8868          
##              Prevalence : 0.6519          
##          Detection Rate : 0.6074          
##    Detection Prevalence : 0.6074          
##       Balanced Accuracy : 0.9659          
##                                           
##        'Positive' Class : benign          
## 

3. Modelo con el método svmPoly

modelo3 <- train(Class ~ ., data= entrenamiento, method = "svmPoly", preProcess= c("scale", "center"), trControl = trainControl(method = "cv", number = 10), tuneGrid = data.frame(degree=1,scale=1, C=1)) #Cambiar

resultado_entrenamiento3 <- predict(modelo3, entrenamiento)
resultado_prueba3 <- predict(modelo3, prueba)

Matriz de Confusión

mcre3 <- confusionMatrix(resultado_entrenamiento3, entrenamiento$Class)
mcre3 
## Confusion Matrix and Statistics
## 
##            Reference
## Prediction  benign malignant
##   benign       347         7
##   malignant      9       185
##                                          
##                Accuracy : 0.9708         
##                  95% CI : (0.953, 0.9832)
##     No Information Rate : 0.6496         
##     P-Value [Acc > NIR] : <2e-16         
##                                          
##                   Kappa : 0.936          
##                                          
##  Mcnemar's Test P-Value : 0.8026         
##                                          
##             Sensitivity : 0.9747         
##             Specificity : 0.9635         
##          Pos Pred Value : 0.9802         
##          Neg Pred Value : 0.9536         
##              Prevalence : 0.6496         
##          Detection Rate : 0.6332         
##    Detection Prevalence : 0.6460         
##       Balanced Accuracy : 0.9691         
##                                          
##        'Positive' Class : benign         
## 
mcrp3 <- confusionMatrix(resultado_prueba3, prueba$Class)
mcrp3
## Confusion Matrix and Statistics
## 
##            Reference
## Prediction  benign malignant
##   benign        87         2
##   malignant      1        45
##                                           
##                Accuracy : 0.9778          
##                  95% CI : (0.9364, 0.9954)
##     No Information Rate : 0.6519          
##     P-Value [Acc > NIR] : <2e-16          
##                                           
##                   Kappa : 0.9508          
##                                           
##  Mcnemar's Test P-Value : 1               
##                                           
##             Sensitivity : 0.9886          
##             Specificity : 0.9574          
##          Pos Pred Value : 0.9775          
##          Neg Pred Value : 0.9783          
##              Prevalence : 0.6519          
##          Detection Rate : 0.6444          
##    Detection Prevalence : 0.6593          
##       Balanced Accuracy : 0.9730          
##                                           
##        'Positive' Class : benign          
## 

4. Modelo con el método Árbol de Decisión

modelo4 <- train(Class ~ ., data = entrenamiento, method = "rpart", preProcess = c("scale", "center"), trControl = trainControl(method="cv", number = 10), tuneLength = 10)

resultado_entrenamiento4 <- predict(modelo4, entrenamiento)
resultado_prueba4 <- predict(modelo4, prueba)

Matriz de Confusión

mcre4 <- confusionMatrix(resultado_entrenamiento4, entrenamiento$Class)
mcre4 
## Confusion Matrix and Statistics
## 
##            Reference
## Prediction  benign malignant
##   benign       345         9
##   malignant     11       183
##                                           
##                Accuracy : 0.9635          
##                  95% CI : (0.9442, 0.9776)
##     No Information Rate : 0.6496          
##     P-Value [Acc > NIR] : <2e-16          
##                                           
##                   Kappa : 0.92            
##                                           
##  Mcnemar's Test P-Value : 0.8231          
##                                           
##             Sensitivity : 0.9691          
##             Specificity : 0.9531          
##          Pos Pred Value : 0.9746          
##          Neg Pred Value : 0.9433          
##              Prevalence : 0.6496          
##          Detection Rate : 0.6296          
##    Detection Prevalence : 0.6460          
##       Balanced Accuracy : 0.9611          
##                                           
##        'Positive' Class : benign          
## 
mcrp4 <- confusionMatrix(resultado_prueba4, prueba$Class)
mcrp4
## Confusion Matrix and Statistics
## 
##            Reference
## Prediction  benign malignant
##   benign        87         5
##   malignant      1        42
##                                           
##                Accuracy : 0.9556          
##                  95% CI : (0.9058, 0.9835)
##     No Information Rate : 0.6519          
##     P-Value [Acc > NIR] : <2e-16          
##                                           
##                   Kappa : 0.9001          
##                                           
##  Mcnemar's Test P-Value : 0.2207          
##                                           
##             Sensitivity : 0.9886          
##             Specificity : 0.8936          
##          Pos Pred Value : 0.9457          
##          Neg Pred Value : 0.9767          
##              Prevalence : 0.6519          
##          Detection Rate : 0.6444          
##    Detection Prevalence : 0.6815          
##       Balanced Accuracy : 0.9411          
##                                           
##        'Positive' Class : benign          
## 

5. Modelo con el método Neural Nety

modelo5 <- train(Class ~ ., data = entrenamiento, method = "nnet", preProcess = c("scale", "center"), trControl = trainControl(method="cv", number = 10))
## # weights:  12
## initial  value 376.477149 
## iter  10 value 42.437195
## iter  20 value 37.383594
## iter  30 value 37.366404
## iter  40 value 36.703788
## iter  50 value 32.802253
## iter  60 value 32.783185
## iter  70 value 32.780576
## iter  80 value 32.780352
## iter  90 value 32.780267
## iter 100 value 32.779932
## final  value 32.779932 
## stopped after 100 iterations
## # weights:  34
## initial  value 398.967389 
## iter  10 value 41.580064
## iter  20 value 32.819841
## iter  30 value 30.580631
## iter  40 value 30.171660
## iter  50 value 29.018950
## iter  60 value 26.270274
## iter  70 value 25.101938
## iter  80 value 24.289120
## iter  90 value 23.970739
## iter 100 value 23.966875
## final  value 23.966875 
## stopped after 100 iterations
## # weights:  56
## initial  value 392.380535 
## iter  10 value 36.130217
## iter  20 value 16.520603
## iter  30 value 7.379376
## iter  40 value 4.979779
## iter  50 value 1.881997
## iter  60 value 1.413958
## iter  70 value 1.397572
## iter  80 value 1.389584
## iter  90 value 1.386721
## iter 100 value 1.386332
## final  value 1.386332 
## stopped after 100 iterations
## # weights:  12
## initial  value 350.410635 
## iter  10 value 74.916798
## iter  20 value 58.878074
## iter  30 value 49.960077
## iter  40 value 49.661904
## final  value 49.661892 
## converged
## # weights:  34
## initial  value 349.539635 
## iter  10 value 115.137963
## iter  20 value 45.339839
## iter  30 value 41.959631
## iter  40 value 38.444785
## iter  50 value 37.928940
## iter  60 value 37.672510
## iter  70 value 37.662808
## final  value 37.662804 
## converged
## # weights:  56
## initial  value 385.799685 
## iter  10 value 41.550941
## iter  20 value 37.775498
## iter  30 value 37.351510
## iter  40 value 37.203503
## iter  50 value 36.881480
## iter  60 value 36.816477
## iter  70 value 36.815808
## iter  80 value 36.815763
## iter  80 value 36.815763
## final  value 36.815763 
## converged
## # weights:  12
## initial  value 411.250561 
## iter  10 value 128.481791
## iter  20 value 48.775343
## iter  30 value 48.108500
## iter  40 value 45.630536
## iter  50 value 42.789720
## iter  60 value 42.600620
## iter  70 value 39.693498
## iter  80 value 39.678498
## iter  90 value 39.673171
## iter 100 value 39.665081
## final  value 39.665081 
## stopped after 100 iterations
## # weights:  34
## initial  value 396.907245 
## iter  10 value 36.935107
## iter  20 value 27.845747
## iter  30 value 24.064004
## iter  40 value 22.507661
## iter  50 value 22.161343
## iter  60 value 21.912002
## iter  70 value 21.436179
## iter  80 value 21.176493
## iter  90 value 21.115826
## iter 100 value 20.994492
## final  value 20.994492 
## stopped after 100 iterations
## # weights:  56
## initial  value 470.209121 
## iter  10 value 36.854692
## iter  20 value 29.775951
## iter  30 value 26.512592
## iter  40 value 23.490629
## iter  50 value 21.091000
## iter  60 value 14.528279
## iter  70 value 14.146366
## iter  80 value 12.978601
## iter  90 value 12.838590
## iter 100 value 12.809161
## final  value 12.809161 
## stopped after 100 iterations
## # weights:  12
## initial  value 355.508036 
## iter  10 value 52.186983
## iter  20 value 49.731412
## iter  30 value 42.751850
## iter  40 value 42.589636
## iter  50 value 40.970318
## iter  60 value 39.558646
## iter  70 value 39.543586
## iter  80 value 39.515130
## iter  90 value 39.503451
## iter 100 value 39.499587
## final  value 39.499587 
## stopped after 100 iterations
## # weights:  34
## initial  value 345.293855 
## iter  10 value 38.850419
## iter  20 value 35.299467
## iter  30 value 29.063227
## iter  40 value 25.318280
## iter  50 value 22.886781
## iter  60 value 21.721975
## iter  70 value 21.281773
## iter  80 value 21.101509
## iter  90 value 21.071842
## iter 100 value 21.066196
## final  value 21.066196 
## stopped after 100 iterations
## # weights:  56
## initial  value 318.370065 
## iter  10 value 40.055119
## iter  20 value 24.416365
## iter  30 value 13.343905
## iter  40 value 12.497316
## iter  50 value 12.101419
## iter  60 value 11.714407
## iter  70 value 10.562188
## iter  80 value 10.084774
## iter  90 value 9.803909
## iter 100 value 9.692054
## final  value 9.692054 
## stopped after 100 iterations
## # weights:  12
## initial  value 383.405588 
## iter  10 value 70.986072
## iter  20 value 54.771996
## iter  30 value 53.597555
## iter  40 value 53.544775
## iter  40 value 53.544774
## iter  40 value 53.544774
## final  value 53.544774 
## converged
## # weights:  34
## initial  value 437.860910 
## iter  10 value 52.917571
## iter  20 value 47.485871
## iter  30 value 43.339800
## iter  40 value 42.347250
## iter  50 value 41.987058
## iter  60 value 41.759375
## iter  70 value 41.757165
## iter  70 value 41.757165
## final  value 41.757165 
## converged
## # weights:  56
## initial  value 432.938183 
## iter  10 value 53.241057
## iter  20 value 42.793023
## iter  30 value 40.750430
## iter  40 value 40.140010
## iter  50 value 40.065188
## iter  60 value 40.059476
## iter  70 value 40.058576
## final  value 40.058575 
## converged
## # weights:  12
## initial  value 370.559464 
## iter  10 value 56.330575
## iter  20 value 45.487568
## iter  30 value 40.718222
## iter  40 value 39.656038
## iter  50 value 39.640343
## iter  60 value 39.639341
## iter  70 value 39.638382
## iter  80 value 39.638099
## iter  90 value 39.638035
## iter 100 value 39.637985
## final  value 39.637985 
## stopped after 100 iterations
## # weights:  34
## initial  value 371.184689 
## iter  10 value 42.069486
## iter  20 value 36.888133
## iter  30 value 35.233768
## iter  40 value 31.583861
## iter  50 value 29.951169
## iter  60 value 27.882573
## iter  70 value 27.350766
## iter  80 value 27.191197
## iter  90 value 27.149604
## iter 100 value 26.994128
## final  value 26.994128 
## stopped after 100 iterations
## # weights:  56
## initial  value 324.010663 
## iter  10 value 35.285669
## iter  20 value 18.983575
## iter  30 value 8.864095
## iter  40 value 8.493163
## iter  50 value 8.373325
## iter  60 value 5.023711
## iter  70 value 4.414094
## iter  80 value 4.245991
## iter  90 value 4.032493
## iter 100 value 1.218699
## final  value 1.218699 
## stopped after 100 iterations
## # weights:  12
## initial  value 376.965522 
## iter  10 value 57.458884
## iter  20 value 48.268436
## iter  30 value 45.450565
## iter  40 value 43.475756
## iter  50 value 39.525989
## iter  60 value 39.499126
## iter  70 value 39.494123
## iter  80 value 39.484240
## iter  90 value 39.481187
## iter 100 value 39.480996
## final  value 39.480996 
## stopped after 100 iterations
## # weights:  34
## initial  value 461.169324 
## iter  10 value 37.143796
## iter  20 value 28.209150
## iter  30 value 19.639361
## iter  40 value 17.612668
## iter  50 value 17.529577
## iter  60 value 17.528701
## final  value 17.528675 
## converged
## # weights:  56
## initial  value 291.377968 
## iter  10 value 34.872750
## iter  20 value 27.020476
## iter  30 value 21.365333
## iter  40 value 18.322587
## iter  50 value 14.852247
## iter  60 value 14.005387
## iter  70 value 13.813886
## iter  80 value 13.627385
## iter  90 value 13.580207
## iter 100 value 13.561449
## final  value 13.561449 
## stopped after 100 iterations
## # weights:  12
## initial  value 350.760977 
## iter  10 value 62.985282
## iter  20 value 52.810932
## iter  30 value 52.778785
## final  value 52.777991 
## converged
## # weights:  34
## initial  value 325.655243 
## iter  10 value 53.894733
## iter  20 value 47.675190
## iter  30 value 45.276035
## iter  40 value 43.160908
## iter  50 value 41.825807
## iter  60 value 41.617544
## iter  70 value 41.610425
## iter  80 value 41.555818
## iter  90 value 41.553218
## iter  90 value 41.553218
## iter  90 value 41.553218
## final  value 41.553218 
## converged
## # weights:  56
## initial  value 290.669028 
## iter  10 value 85.091956
## iter  20 value 49.886743
## iter  30 value 44.222060
## iter  40 value 40.735343
## iter  50 value 39.664872
## iter  60 value 39.313892
## iter  70 value 38.909658
## iter  80 value 38.818642
## iter  90 value 38.811901
## iter 100 value 38.811641
## final  value 38.811641 
## stopped after 100 iterations
## # weights:  12
## initial  value 429.343504 
## iter  10 value 48.000220
## iter  20 value 43.121829
## iter  30 value 41.515601
## iter  40 value 37.669596
## iter  50 value 37.396040
## iter  60 value 37.383183
## iter  70 value 37.341077
## iter  80 value 37.328979
## iter  90 value 37.320610
## iter 100 value 37.293722
## final  value 37.293722 
## stopped after 100 iterations
## # weights:  34
## initial  value 476.188548 
## iter  10 value 48.622911
## iter  20 value 32.034715
## iter  30 value 28.036310
## iter  40 value 24.999756
## iter  50 value 23.129264
## iter  60 value 22.975342
## iter  70 value 22.913586
## iter  80 value 22.892855
## iter  90 value 22.858722
## iter 100 value 22.833042
## final  value 22.833042 
## stopped after 100 iterations
## # weights:  56
## initial  value 378.900773 
## iter  10 value 36.248260
## iter  20 value 20.146364
## iter  30 value 11.327904
## iter  40 value 9.748409
## iter  50 value 9.432211
## iter  60 value 9.055354
## iter  70 value 8.966362
## iter  80 value 8.935854
## iter  90 value 8.917093
## iter 100 value 8.902201
## final  value 8.902201 
## stopped after 100 iterations
## # weights:  12
## initial  value 344.806105 
## iter  10 value 53.314981
## iter  20 value 51.864827
## iter  30 value 48.439608
## iter  40 value 47.074809
## iter  50 value 45.171586
## iter  60 value 45.010562
## iter  70 value 44.965893
## iter  80 value 44.919082
## iter  90 value 44.853411
## iter 100 value 44.822481
## final  value 44.822481 
## stopped after 100 iterations
## # weights:  34
## initial  value 324.352768 
## iter  10 value 33.754090
## iter  20 value 26.301046
## iter  30 value 21.302920
## iter  40 value 20.470135
## iter  50 value 20.022692
## iter  60 value 19.903231
## iter  70 value 19.895252
## iter  80 value 19.894923
## iter  90 value 19.894423
## final  value 19.894412 
## converged
## # weights:  56
## initial  value 301.048227 
## iter  10 value 31.006045
## iter  20 value 26.243828
## iter  30 value 20.745469
## iter  40 value 18.745178
## iter  50 value 18.149255
## iter  60 value 17.208233
## iter  70 value 17.128135
## iter  80 value 16.974997
## iter  90 value 16.891304
## iter 100 value 16.845548
## final  value 16.845548 
## stopped after 100 iterations
## # weights:  12
## initial  value 441.401693 
## iter  10 value 52.177398
## iter  20 value 47.978570
## iter  30 value 46.688911
## final  value 46.686683 
## converged
## # weights:  34
## initial  value 400.891990 
## iter  10 value 38.167635
## iter  20 value 36.493121
## iter  30 value 36.422004
## iter  40 value 36.355602
## iter  50 value 36.351007
## final  value 36.351006 
## converged
## # weights:  56
## initial  value 354.480594 
## iter  10 value 40.204286
## iter  20 value 36.276416
## iter  30 value 34.831402
## iter  40 value 34.638085
## iter  50 value 34.632346
## final  value 34.630418 
## converged
## # weights:  12
## initial  value 382.278414 
## iter  10 value 51.491238
## iter  20 value 42.900868
## iter  30 value 36.397646
## iter  40 value 36.365532
## iter  50 value 36.354776
## iter  60 value 36.352952
## iter  70 value 36.351207
## iter  80 value 36.350648
## iter  90 value 36.350404
## iter 100 value 36.350228
## final  value 36.350228 
## stopped after 100 iterations
## # weights:  34
## initial  value 385.229559 
## iter  10 value 48.761838
## iter  20 value 34.609357
## iter  30 value 22.131388
## iter  40 value 17.743321
## iter  50 value 16.603890
## iter  60 value 16.337978
## iter  70 value 16.142615
## iter  80 value 16.099878
## iter  90 value 16.066547
## iter 100 value 16.036148
## final  value 16.036148 
## stopped after 100 iterations
## # weights:  56
## initial  value 517.073810 
## iter  10 value 208.699725
## iter  20 value 22.379999
## iter  30 value 16.405697
## iter  40 value 14.761128
## iter  50 value 14.203133
## iter  60 value 13.855094
## iter  70 value 13.643576
## iter  80 value 13.000759
## iter  90 value 10.690633
## iter 100 value 10.101124
## final  value 10.101124 
## stopped after 100 iterations
## # weights:  12
## initial  value 292.895306 
## iter  10 value 52.551393
## iter  20 value 47.795990
## iter  30 value 43.326449
## iter  40 value 42.498683
## iter  50 value 42.483639
## iter  60 value 42.481460
## iter  70 value 42.480221
## iter  80 value 42.478425
## iter  90 value 42.476811
## iter 100 value 42.476437
## final  value 42.476437 
## stopped after 100 iterations
## # weights:  34
## initial  value 370.482153 
## iter  10 value 38.851578
## iter  20 value 33.185345
## iter  30 value 26.837372
## iter  40 value 23.550785
## iter  50 value 22.282349
## iter  60 value 21.741716
## iter  70 value 21.617553
## iter  80 value 21.606068
## iter  90 value 21.594047
## iter 100 value 21.590763
## final  value 21.590763 
## stopped after 100 iterations
## # weights:  56
## initial  value 331.163435 
## iter  10 value 45.763128
## iter  20 value 29.174052
## iter  30 value 22.347069
## iter  40 value 16.843208
## iter  50 value 15.554057
## iter  60 value 15.069029
## iter  70 value 14.686925
## iter  80 value 14.395084
## iter  90 value 13.924073
## iter 100 value 13.613552
## final  value 13.613552 
## stopped after 100 iterations
## # weights:  12
## initial  value 445.911318 
## iter  10 value 50.664074
## iter  20 value 49.103146
## iter  30 value 48.764748
## final  value 48.764740 
## converged
## # weights:  34
## initial  value 539.171803 
## iter  10 value 71.174738
## iter  20 value 44.888487
## iter  30 value 40.773068
## iter  40 value 39.291940
## iter  50 value 38.948505
## iter  60 value 38.805208
## iter  70 value 38.789757
## iter  80 value 38.777548
## iter  90 value 38.777242
## final  value 38.777240 
## converged
## # weights:  56
## initial  value 300.526929 
## iter  10 value 92.670644
## iter  20 value 45.607100
## iter  30 value 38.482565
## iter  40 value 37.620450
## iter  50 value 37.333679
## iter  60 value 37.305632
## iter  70 value 37.304888
## final  value 37.304880 
## converged
## # weights:  12
## initial  value 342.113667 
## iter  10 value 39.784475
## iter  20 value 37.502481
## iter  30 value 37.235549
## iter  40 value 37.094419
## iter  50 value 36.355221
## iter  60 value 36.235421
## iter  70 value 35.963827
## iter  80 value 35.822521
## iter  90 value 35.822367
## iter 100 value 35.821303
## final  value 35.821303 
## stopped after 100 iterations
## # weights:  34
## initial  value 379.416717 
## iter  10 value 42.835820
## iter  20 value 38.625630
## iter  30 value 33.091455
## iter  40 value 32.424501
## iter  50 value 31.958173
## iter  60 value 31.780375
## iter  70 value 31.571136
## iter  80 value 31.479145
## iter  90 value 31.464511
## iter 100 value 31.417168
## final  value 31.417168 
## stopped after 100 iterations
## # weights:  56
## initial  value 369.465817 
## iter  10 value 36.101780
## iter  20 value 17.316087
## iter  30 value 10.213775
## iter  40 value 7.378137
## iter  50 value 6.626386
## iter  60 value 6.505362
## iter  70 value 6.344177
## iter  80 value 5.833663
## iter  90 value 5.743775
## iter 100 value 5.674803
## final  value 5.674803 
## stopped after 100 iterations
## # weights:  12
## initial  value 321.197058 
## iter  10 value 37.992700
## iter  20 value 35.792204
## iter  30 value 35.389851
## iter  40 value 35.128294
## iter  50 value 34.925662
## iter  60 value 34.886890
## iter  70 value 34.877191
## iter  80 value 34.875236
## iter  90 value 34.873956
## iter 100 value 34.872360
## final  value 34.872360 
## stopped after 100 iterations
## # weights:  34
## initial  value 389.682359 
## iter  10 value 33.677993
## iter  20 value 21.377728
## iter  30 value 14.878733
## iter  40 value 10.094345
## iter  50 value 9.445055
## iter  60 value 9.423292
## iter  70 value 9.419223
## iter  80 value 9.418886
## iter  90 value 9.418811
## iter 100 value 9.418768
## final  value 9.418768 
## stopped after 100 iterations
## # weights:  56
## initial  value 266.773981 
## iter  10 value 23.397408
## iter  20 value 12.453893
## iter  30 value 9.921559
## iter  40 value 9.334908
## iter  50 value 9.183171
## iter  60 value 9.172849
## iter  70 value 9.127471
## iter  80 value 9.054126
## iter  90 value 8.984186
## iter 100 value 8.955991
## final  value 8.955991 
## stopped after 100 iterations
## # weights:  12
## initial  value 320.530859 
## iter  10 value 60.495799
## iter  20 value 46.020850
## iter  30 value 44.525762
## final  value 44.523218 
## converged
## # weights:  34
## initial  value 407.705422 
## iter  10 value 54.162248
## iter  20 value 34.360603
## iter  30 value 34.038423
## iter  40 value 34.035667
## final  value 34.035016 
## converged
## # weights:  56
## initial  value 454.017135 
## iter  10 value 69.049091
## iter  20 value 33.996446
## iter  30 value 31.515000
## iter  40 value 31.231004
## iter  50 value 30.903611
## iter  60 value 30.710978
## iter  70 value 30.627870
## iter  80 value 30.624795
## iter  80 value 30.624795
## iter  80 value 30.624795
## final  value 30.624795 
## converged
## # weights:  12
## initial  value 400.796335 
## iter  10 value 36.480916
## iter  20 value 32.950616
## iter  30 value 32.894397
## iter  40 value 32.885858
## iter  50 value 32.882953
## iter  60 value 32.875174
## iter  70 value 32.873837
## iter  80 value 32.873014
## iter  90 value 32.870765
## iter 100 value 32.499479
## final  value 32.499479 
## stopped after 100 iterations
## # weights:  34
## initial  value 382.700891 
## iter  10 value 35.650965
## iter  20 value 23.665512
## iter  30 value 17.281386
## iter  40 value 10.154502
## iter  50 value 6.686735
## iter  60 value 6.244087
## iter  70 value 6.211796
## iter  80 value 6.196180
## iter  90 value 6.162809
## iter 100 value 6.152142
## final  value 6.152142 
## stopped after 100 iterations
## # weights:  56
## initial  value 297.860371 
## iter  10 value 27.305970
## iter  20 value 15.483042
## iter  30 value 9.690338
## iter  40 value 8.129648
## iter  50 value 6.973134
## iter  60 value 6.906713
## iter  70 value 6.869101
## iter  80 value 6.840714
## iter  90 value 6.822533
## iter 100 value 6.807764
## final  value 6.807764 
## stopped after 100 iterations
## # weights:  12
## initial  value 339.456790 
## iter  10 value 158.046015
## iter  20 value 65.717796
## iter  30 value 46.787679
## iter  40 value 38.271207
## iter  50 value 36.848772
## iter  60 value 36.575077
## iter  70 value 36.226322
## iter  80 value 36.046114
## iter  90 value 36.039011
## iter 100 value 35.936969
## final  value 35.936969 
## stopped after 100 iterations
## # weights:  34
## initial  value 396.446083 
## iter  10 value 49.591717
## iter  20 value 33.545530
## iter  30 value 29.656480
## iter  40 value 27.447190
## iter  50 value 26.319019
## iter  60 value 24.899691
## iter  70 value 24.678830
## iter  80 value 24.516449
## iter  90 value 24.098363
## iter 100 value 23.606689
## final  value 23.606689 
## stopped after 100 iterations
## # weights:  56
## initial  value 325.372656 
## iter  10 value 34.301235
## iter  20 value 20.901145
## iter  30 value 13.020419
## iter  40 value 12.256197
## iter  50 value 12.250246
## iter  60 value 12.250019
## iter  70 value 12.249909
## iter  80 value 12.033269
## iter  90 value 11.818460
## iter 100 value 11.811156
## final  value 11.811156 
## stopped after 100 iterations
## # weights:  12
## initial  value 327.906693 
## iter  10 value 61.219539
## iter  20 value 49.734517
## iter  30 value 49.118216
## iter  40 value 49.101690
## iter  40 value 49.101690
## iter  40 value 49.101690
## final  value 49.101690 
## converged
## # weights:  34
## initial  value 323.934935 
## iter  10 value 46.152240
## iter  20 value 40.840436
## iter  30 value 39.749908
## iter  40 value 39.514367
## iter  50 value 39.426968
## final  value 39.426886 
## converged
## # weights:  56
## initial  value 449.227090 
## iter  10 value 81.409576
## iter  20 value 46.841838
## iter  30 value 43.443981
## iter  40 value 41.657814
## iter  50 value 40.991857
## iter  60 value 40.891983
## iter  70 value 40.873833
## iter  80 value 40.872856
## final  value 40.872681 
## converged
## # weights:  12
## initial  value 326.766631 
## iter  10 value 44.353548
## iter  20 value 37.431520
## iter  30 value 33.556132
## iter  40 value 30.479939
## iter  50 value 30.467985
## iter  60 value 30.463700
## iter  70 value 30.458655
## iter  80 value 30.458144
## iter  90 value 30.457322
## final  value 30.457314 
## converged
## # weights:  34
## initial  value 428.667035 
## iter  10 value 43.686421
## iter  20 value 30.592240
## iter  30 value 26.969605
## iter  40 value 24.266306
## iter  50 value 23.839056
## iter  60 value 22.804244
## iter  70 value 22.668007
## iter  80 value 22.540927
## iter  90 value 22.469181
## iter 100 value 22.427528
## final  value 22.427528 
## stopped after 100 iterations
## # weights:  56
## initial  value 408.874223 
## iter  10 value 34.951565
## iter  20 value 12.870980
## iter  30 value 6.483366
## iter  40 value 6.307095
## iter  50 value 6.206916
## iter  60 value 6.150471
## iter  70 value 6.133738
## iter  80 value 6.117790
## iter  90 value 6.088511
## iter 100 value 6.066790
## final  value 6.066790 
## stopped after 100 iterations
## # weights:  12
## initial  value 321.754451 
## iter  10 value 42.735297
## iter  20 value 36.553903
## iter  30 value 36.425583
## iter  40 value 36.361319
## iter  50 value 36.346991
## iter  60 value 36.339317
## iter  70 value 36.331902
## iter  80 value 36.324998
## iter  90 value 36.321886
## iter 100 value 36.318710
## final  value 36.318710 
## stopped after 100 iterations
## # weights:  34
## initial  value 300.446391 
## iter  10 value 41.961751
## iter  20 value 30.257550
## iter  30 value 28.183516
## iter  40 value 22.689069
## iter  50 value 20.829621
## iter  60 value 19.144793
## iter  70 value 16.434296
## iter  80 value 15.874639
## iter  90 value 15.741785
## iter 100 value 15.574467
## final  value 15.574467 
## stopped after 100 iterations
## # weights:  56
## initial  value 282.021100 
## iter  10 value 32.901459
## iter  20 value 16.152079
## iter  30 value 12.074062
## iter  40 value 10.867879
## iter  50 value 10.565675
## iter  60 value 10.464206
## iter  70 value 10.422227
## iter  80 value 10.405932
## iter  90 value 10.394482
## iter 100 value 10.390740
## final  value 10.390740 
## stopped after 100 iterations
## # weights:  12
## initial  value 338.542762 
## iter  10 value 58.364417
## iter  20 value 47.889755
## iter  30 value 46.959061
## iter  40 value 46.913157
## final  value 46.913156 
## converged
## # weights:  34
## initial  value 389.067606 
## iter  10 value 64.563624
## iter  20 value 47.862307
## iter  30 value 41.700191
## iter  40 value 38.501372
## iter  50 value 37.391377
## iter  60 value 37.049787
## iter  70 value 36.855211
## iter  80 value 36.830464
## iter  90 value 36.830243
## final  value 36.830243 
## converged
## # weights:  56
## initial  value 314.006605 
## iter  10 value 39.786364
## iter  20 value 36.825762
## iter  30 value 36.042459
## iter  40 value 35.790063
## iter  50 value 35.749193
## iter  60 value 35.630582
## iter  70 value 34.800295
## iter  80 value 34.775821
## final  value 34.775630 
## converged
## # weights:  12
## initial  value 317.842554 
## iter  10 value 55.219614
## iter  20 value 42.411436
## iter  30 value 41.698575
## iter  40 value 36.533028
## iter  50 value 36.474702
## iter  60 value 36.466201
## iter  70 value 36.462348
## iter  80 value 36.458830
## iter  90 value 36.457076
## iter 100 value 36.456465
## final  value 36.456465 
## stopped after 100 iterations
## # weights:  34
## initial  value 315.805100 
## iter  10 value 35.696766
## iter  20 value 25.008868
## iter  30 value 19.314407
## iter  40 value 18.470075
## iter  50 value 18.313588
## iter  60 value 18.124856
## iter  70 value 17.847941
## iter  80 value 17.803263
## iter  90 value 17.693457
## iter 100 value 17.476898
## final  value 17.476898 
## stopped after 100 iterations
## # weights:  56
## initial  value 336.033457 
## iter  10 value 29.843576
## iter  20 value 19.062788
## iter  30 value 12.266330
## iter  40 value 9.990162
## iter  50 value 9.510100
## iter  60 value 7.360044
## iter  70 value 5.808872
## iter  80 value 5.238995
## iter  90 value 5.006698
## iter 100 value 3.884926
## final  value 3.884926 
## stopped after 100 iterations
## # weights:  12
## initial  value 373.448951 
## iter  10 value 45.158611
## iter  20 value 44.096037
## iter  30 value 43.343767
## iter  40 value 42.568253
## iter  50 value 42.525430
## final  value 42.525369 
## converged
## # weights:  34
## initial  value 303.311657 
## iter  10 value 39.258404
## iter  20 value 35.907574
## iter  30 value 32.926632
## iter  40 value 31.719819
## iter  50 value 31.054627
## iter  60 value 30.301461
## iter  70 value 29.207742
## iter  80 value 28.417600
## iter  90 value 27.315400
## iter 100 value 26.573440
## final  value 26.573440 
## stopped after 100 iterations
## # weights:  56
## initial  value 297.717687 
## iter  10 value 34.910317
## iter  20 value 19.097253
## iter  30 value 12.162892
## iter  40 value 11.962253
## iter  50 value 11.882074
## iter  60 value 11.825032
## iter  70 value 11.803696
## iter  80 value 11.799958
## iter  90 value 11.789507
## iter 100 value 11.633687
## final  value 11.633687 
## stopped after 100 iterations
## # weights:  12
## initial  value 323.344070 
## iter  10 value 59.196471
## iter  20 value 54.572127
## iter  30 value 54.313230
## final  value 54.265527 
## converged
## # weights:  34
## initial  value 422.110821 
## iter  10 value 46.135214
## iter  20 value 42.100740
## iter  30 value 41.349736
## iter  40 value 40.946203
## iter  50 value 40.871524
## iter  60 value 40.864045
## iter  70 value 40.862853
## iter  80 value 40.859037
## iter  90 value 40.856820
## final  value 40.856812 
## converged
## # weights:  56
## initial  value 306.653715 
## iter  10 value 61.734533
## iter  20 value 46.398463
## iter  30 value 42.976429
## iter  40 value 40.535781
## iter  50 value 38.903458
## iter  60 value 38.436156
## iter  70 value 38.371343
## iter  80 value 37.583306
## iter  90 value 37.167963
## iter 100 value 37.139218
## final  value 37.139218 
## stopped after 100 iterations
## # weights:  12
## initial  value 302.848084 
## iter  10 value 86.222643
## iter  20 value 62.549374
## iter  30 value 50.117326
## iter  40 value 42.790245
## iter  50 value 42.746444
## iter  60 value 42.704572
## iter  70 value 42.700133
## iter  80 value 42.697799
## iter  90 value 42.695362
## iter 100 value 42.693661
## final  value 42.693661 
## stopped after 100 iterations
## # weights:  34
## initial  value 357.848719 
## iter  10 value 50.353275
## iter  20 value 33.751623
## iter  30 value 32.033219
## iter  40 value 29.597684
## iter  50 value 28.331533
## iter  60 value 28.273034
## iter  70 value 28.207846
## iter  80 value 28.122741
## iter  90 value 28.036842
## iter 100 value 27.937599
## final  value 27.937599 
## stopped after 100 iterations
## # weights:  56
## initial  value 401.661057 
## iter  10 value 36.655848
## iter  20 value 16.011617
## iter  30 value 6.895899
## iter  40 value 6.428734
## iter  50 value 6.185441
## iter  60 value 6.111802
## iter  70 value 6.021786
## iter  80 value 5.957063
## iter  90 value 4.807588
## iter 100 value 4.566685
## final  value 4.566685 
## stopped after 100 iterations
## # weights:  12
## initial  value 341.667320 
## iter  10 value 50.797393
## iter  20 value 39.826114
## iter  30 value 39.597097
## iter  40 value 39.548037
## iter  50 value 39.525868
## iter  60 value 39.514783
## iter  70 value 39.503536
## iter  80 value 39.500868
## iter  90 value 39.494332
## iter 100 value 39.491669
## final  value 39.491669 
## stopped after 100 iterations
## # weights:  34
## initial  value 330.883225 
## iter  10 value 33.931619
## iter  20 value 20.963873
## iter  30 value 14.558637
## iter  40 value 13.880806
## iter  50 value 13.768648
## iter  60 value 13.766768
## iter  70 value 13.766501
## iter  80 value 13.766430
## final  value 13.766410 
## converged
## # weights:  56
## initial  value 366.759875 
## iter  10 value 31.998240
## iter  20 value 19.326931
## iter  30 value 13.284252
## iter  40 value 13.139520
## iter  50 value 13.128890
## final  value 13.128861 
## converged
## # weights:  12
## initial  value 360.723364 
## iter  10 value 79.764384
## iter  20 value 58.554909
## iter  30 value 51.915182
## iter  40 value 48.699427
## final  value 48.688574 
## converged
## # weights:  34
## initial  value 421.298943 
## iter  10 value 85.137440
## iter  20 value 41.359032
## iter  30 value 38.548152
## iter  40 value 36.875606
## iter  50 value 36.830442
## final  value 36.830432 
## converged
## # weights:  56
## initial  value 304.019070 
## iter  10 value 43.255238
## iter  20 value 38.254552
## iter  30 value 36.850424
## iter  40 value 36.648594
## iter  50 value 36.550726
## iter  60 value 36.327745
## iter  70 value 36.271464
## iter  80 value 36.254873
## iter  90 value 36.253762
## final  value 36.253760 
## converged
## # weights:  12
## initial  value 328.582102 
## iter  10 value 46.350500
## iter  20 value 40.087911
## iter  30 value 39.780897
## iter  40 value 39.642761
## iter  50 value 39.626044
## iter  60 value 39.620422
## iter  70 value 39.617573
## iter  80 value 39.616729
## iter  90 value 39.616403
## iter 100 value 39.616162
## final  value 39.616162 
## stopped after 100 iterations
## # weights:  34
## initial  value 420.985148 
## iter  10 value 40.782041
## iter  20 value 31.436978
## iter  30 value 29.810226
## iter  40 value 29.752897
## iter  50 value 29.731764
## iter  60 value 29.722300
## iter  70 value 29.708030
## iter  80 value 29.701166
## iter  90 value 29.695962
## iter 100 value 29.687023
## final  value 29.687023 
## stopped after 100 iterations
## # weights:  56
## initial  value 305.807773 
## iter  10 value 32.868515
## iter  20 value 28.672268
## iter  30 value 23.994374
## iter  40 value 22.396665
## iter  50 value 22.173441
## iter  60 value 22.095568
## iter  70 value 21.691671
## iter  80 value 20.200593
## iter  90 value 19.546081
## iter 100 value 19.371937
## final  value 19.371937 
## stopped after 100 iterations
## # weights:  34
## initial  value 326.919377 
## iter  10 value 36.157512
## iter  20 value 30.097667
## iter  30 value 23.574816
## iter  40 value 23.268963
## iter  50 value 23.077785
## iter  60 value 20.578788
## iter  70 value 19.367780
## iter  80 value 19.204978
## iter  90 value 18.867899
## iter 100 value 18.771267
## final  value 18.771267 
## stopped after 100 iterations
resultado_entrenamiento5 <- predict(modelo5, entrenamiento)
resultado_prueba5 <- predict(modelo5, prueba)

Matriz de Confusión

mcre5 <- confusionMatrix(resultado_entrenamiento5, entrenamiento$Class)
mcre5 
## Confusion Matrix and Statistics
## 
##            Reference
## Prediction  benign malignant
##   benign       351         0
##   malignant      5       192
##                                          
##                Accuracy : 0.9909         
##                  95% CI : (0.9788, 0.997)
##     No Information Rate : 0.6496         
##     P-Value [Acc > NIR] : < 2e-16        
##                                          
##                   Kappa : 0.9801         
##                                          
##  Mcnemar's Test P-Value : 0.07364        
##                                          
##             Sensitivity : 0.9860         
##             Specificity : 1.0000         
##          Pos Pred Value : 1.0000         
##          Neg Pred Value : 0.9746         
##              Prevalence : 0.6496         
##          Detection Rate : 0.6405         
##    Detection Prevalence : 0.6405         
##       Balanced Accuracy : 0.9930         
##                                          
##        'Positive' Class : benign         
## 
mcrp5 <- confusionMatrix(resultado_prueba5, prueba$Class)
mcrp5
## Confusion Matrix and Statistics
## 
##            Reference
## Prediction  benign malignant
##   benign        86         4
##   malignant      2        43
##                                           
##                Accuracy : 0.9556          
##                  95% CI : (0.9058, 0.9835)
##     No Information Rate : 0.6519          
##     P-Value [Acc > NIR] : <2e-16          
##                                           
##                   Kappa : 0.9011          
##                                           
##  Mcnemar's Test P-Value : 0.6831          
##                                           
##             Sensitivity : 0.9773          
##             Specificity : 0.9149          
##          Pos Pred Value : 0.9556          
##          Neg Pred Value : 0.9556          
##              Prevalence : 0.6519          
##          Detection Rate : 0.6370          
##    Detection Prevalence : 0.6667          
##       Balanced Accuracy : 0.9461          
##                                           
##        'Positive' Class : benign          
## 

6. Modelo con el método Random Forest

modelo6 <- train(Class ~ ., data = entrenamiento, method = "rf", preProcess = c("scale", "center"), trControl = trainControl(method="cv", number = 10), tuneGrid = expand.grid(mtry =c(2,4,6)))

resultado_entrenamiento6 <- predict(modelo6, entrenamiento)
resultado_prueba6 <- predict(modelo6, prueba)

Matriz de Confusión

mcre6 <- confusionMatrix(resultado_entrenamiento6, entrenamiento$Class)
mcre6 
## Confusion Matrix and Statistics
## 
##            Reference
## Prediction  benign malignant
##   benign       356         1
##   malignant      0       191
##                                      
##                Accuracy : 0.9982     
##                  95% CI : (0.9899, 1)
##     No Information Rate : 0.6496     
##     P-Value [Acc > NIR] : <2e-16     
##                                      
##                   Kappa : 0.996      
##                                      
##  Mcnemar's Test P-Value : 1          
##                                      
##             Sensitivity : 1.0000     
##             Specificity : 0.9948     
##          Pos Pred Value : 0.9972     
##          Neg Pred Value : 1.0000     
##              Prevalence : 0.6496     
##          Detection Rate : 0.6496     
##    Detection Prevalence : 0.6515     
##       Balanced Accuracy : 0.9974     
##                                      
##        'Positive' Class : benign     
## 
mcrp6 <- confusionMatrix(resultado_prueba6, prueba$Class)
mcrp6
## Confusion Matrix and Statistics
## 
##            Reference
## Prediction  benign malignant
##   benign        85         1
##   malignant      3        46
##                                           
##                Accuracy : 0.9704          
##                  95% CI : (0.9259, 0.9919)
##     No Information Rate : 0.6519          
##     P-Value [Acc > NIR] : <2e-16          
##                                           
##                   Kappa : 0.9354          
##                                           
##  Mcnemar's Test P-Value : 0.6171          
##                                           
##             Sensitivity : 0.9659          
##             Specificity : 0.9787          
##          Pos Pred Value : 0.9884          
##          Neg Pred Value : 0.9388          
##              Prevalence : 0.6519          
##          Detection Rate : 0.6296          
##    Detection Prevalence : 0.6370          
##       Balanced Accuracy : 0.9723          
##                                           
##        'Positive' Class : benign          
## 

Resumen de Resultados

resumen <- data.frame(
  "svmLinear" = c(mcre1$overall["Accuracy"], mcre1$overall["Accuracy"]),
  "svmRadial" = c(mcre2$overall["Accuracy"], mcrp2$overall["Accuracy"]),
  "svmPoly" = c(mcre3$overall["Accuracy"], mcrp3$overall["Accuracy"]),
  "rpart" = c(mcre4$overall["Accuracy"], mcrp4$overall["Accuracy"]),
  "NeuralNet" = c(mcre5$overall["Accuracy"], mcrp5$overall["Accuracy"]),
  "RandomForest" = c(mcre6$overall["Accuracy"], mcrp6$overall["Accuracy"])
)

rownames(resumen) <- c("Precision de entrenamiento", "Precision de prueba")
resumen
##                            svmLinear svmRadial   svmPoly     rpart NeuralNet
## Precision de entrenamiento 0.9708029 0.9963504 0.9708029 0.9635036 0.9908759
## Precision de prueba        0.9708029 0.9555556 0.9777778 0.9555556 0.9555556
##                            RandomForest
## Precision de entrenamiento    0.9981752
## Precision de prueba           0.9703704

Conclusión

El modelo con el método de neural net presenta sobreajuste, ya que tiene una alta precisión en entrenamiento, pero esta disminuye en prueba.

Acorde al resumen de resultados, los mejores modelos son los de Máquina de Vectores de Soporte Lineal y también el de Máquina de Vectores Poly, al mantener un buen equilibrio entre ambas métricas y sin sobreajuste.

---
title: "Machine Learning"
author: "Lesly Darian Romero Vazquez - A01771127"
date: "2024-03-03"
output: 
 html_document:
    toc: true
    toc_float: true
    code_download: true 
    theme: cosmo
---

![](C:\\Users\\lesda\\OneDrive\\Documentos\\Concentracion IA\\R Modulo 3\\flor.gif)

# <span style= "color: blue;">Teoría</span>
El paquete caret (Classification And REgression Training) es un paquete integral con una amplia variedad de algoritmos para el aprendizaje automático.

# <span style= "color: blue;">Iris</span>

## <span style= "color: blue;">Instalar paquetes y llamar librerías</span>
```{r}
library(caret)
library(ggplot2) # Crear gráficos
library(datasets) # Usar la base de datos "Iris"
library(lattice) # Crear gráficos
library(DataExplorer)
library(mlbench)
```

## <span style= "color: blue;">Crear base de datos</span>
```{r}
df <- data.frame(iris)
```

## <span style= "color: blue;">Análisis Exploratorio</span>
```{r}
summary(df)
str(df)
create_report(df)
plot_missing(df)
plot_histogram(df)
plot_correlation(df)
```

Nota: La variable que queremos predecir debe tener formato de FACTOR

## <span style= "color: blue;">Partir datos 80-20</span>
```{r}
set.seed(123)
renglones_entrenamiento <-createDataPartition(df$Species, p=0.8, list=FALSE)
entrenamiento <- iris[renglones_entrenamiento, ]
prueba <- iris[-renglones_entrenamiento, ]
```

## <span style= "color: blue;">Distintos tipos de Métodos para Modelar</span>
Los métodos más utilizados para modelar aprendizaje automático son:

  ** SVM: Support Vector Machine o Máquina de Vectores de Soporte. Hay varios subtipos: Lineal (svmLinear), Radial (svmRadial), Polinómicos (svmPoly), etc.

  ** Árbol de Decisión: rpart

  ** Redes Neuronales: nnet

  ** Random Forests o Bosques aleatorios: rf

## <span style= "color: blue;">1. Modelo con el métodos svmLineal</span>
```{r}
modelo1 <- train(Species ~ ., data= entrenamiento, method = "svmLinear", preProcess= c("scale", "center"), trControl = trainControl(method = "cv", number = 10), tuneGrid = data.frame(C=1)) #Cuando es svmLinear

resultado_entrenamiento1 <- predict(modelo1, entrenamiento)
resultado_prueba1 <- predict(modelo1, prueba)
```

## <span style= "color: blue;">Matriz de Confusión</span>
```{r}
mcre1 <- confusionMatrix(resultado_entrenamiento1, entrenamiento$Species)
mcre1 
mcrp1 <- confusionMatrix(resultado_prueba1, prueba$Species)
mcrp1
```

## <span style= "color: blue;">2. Modelo con el método svmRadial</span>
```{r}
modelo2 <- train(Species ~ ., data= entrenamiento, method = "svmRadial", preProcess= c("scale", "center"), trControl = trainControl(method = "cv", number = 10), tuneGrid = data.frame(sigma=1, C=1)) #Cambiar

resultado_entrenamiento2 <- predict(modelo2, entrenamiento)
resultado_prueba2 <- predict(modelo2, prueba)
```

## <span style= "color: blue;">Matriz de Confusión</span>
```{r}
mcre2 <- confusionMatrix(resultado_entrenamiento2, entrenamiento$Species)
mcre2 
mcrp2 <- confusionMatrix(resultado_prueba2, prueba$Species)
mcrp2
```

## <span style= "color: blue;">3. Modelo con el método svmPoly</span>
```{r}
modelo3 <- train(Species ~ ., data= entrenamiento, method = "svmPoly", preProcess= c("scale", "center"), trControl = trainControl(method = "cv", number = 10), tuneGrid = data.frame(degree=1,scale=1, C=1)) #Cambiar

resultado_entrenamiento3 <- predict(modelo3, entrenamiento)
resultado_prueba3 <- predict(modelo3, prueba)
```

## <span style= "color: blue;">Matriz de Confusión</span>
```{r}
mcre3 <- confusionMatrix(resultado_entrenamiento3, entrenamiento$Species)
mcre3 
mcrp3 <- confusionMatrix(resultado_prueba3, prueba$Species)
mcrp3
```

## <span style= "color: blue;">4. Modelo con el método Árbol de Decisión</span>
```{r}
modelo4 <- train(Species ~ ., data = entrenamiento, method = "rpart", preProcess = c("scale", "center"), trControl = trainControl(method="cv", number = 10), tuneLength = 10)

resultado_entrenamiento4 <- predict(modelo4, entrenamiento)
resultado_prueba4 <- predict(modelo4, prueba)
```

## <span style= "color: blue;">Matriz de Confusión</span>
```{r}
mcre4 <- confusionMatrix(resultado_entrenamiento4, entrenamiento$Species)
mcre4 
mcrp4 <- confusionMatrix(resultado_prueba4, prueba$Species)
mcrp4
```

## <span style= "color: blue;">5. Modelo con el método Neural Net</span>
```{r}
modelo5 <- train(Species ~ ., data = entrenamiento, method = "nnet", preProcess = c("scale", "center"), trControl = trainControl(method="cv", number = 10))
resultado_entrenamiento5 <- predict(modelo5, entrenamiento)
resultado_prueba5 <- predict(modelo5, prueba)
```

## <span style= "color: blue;">Matriz de Confusión</span>
```{r}
mcre5 <- confusionMatrix(resultado_entrenamiento5, entrenamiento$Species)
mcre5 
mcrp5 <- confusionMatrix(resultado_prueba5, prueba$Species)
mcrp5
```

## <span style= "color: blue;">6. Modelo con el método Random Forest</span>
```{r}
modelo6 <- train(Species ~ ., data = entrenamiento, method = "rf", preProcess = c("scale", "center"), trControl = trainControl(method="cv", number = 10), tuneGrid = expand.grid(mtry =c(2,4,6)))
resultado_entrenamiento6 <- predict(modelo6, entrenamiento)
resultado_prueba6 <- predict(modelo6, prueba)
```

## <span style= "color: blue;">Matriz de Confusión</span>
```{r}
mcre6 <- confusionMatrix(resultado_entrenamiento6, entrenamiento$Species)
mcre6 
mcrp6 <- confusionMatrix(resultado_prueba6, prueba$Species)
mcrp6
```


## <span style= "color: blue;">Resumen de Resultados</span>
```{r}
resumen <- data.frame(
  "svmLinear" = c(mcre1$overall["Accuracy"], mcre1$overall["Accuracy"]),
  "svmRadial" = c(mcre2$overall["Accuracy"], mcrp2$overall["Accuracy"]),
  "svmPoly" = c(mcre3$overall["Accuracy"], mcrp3$overall["Accuracy"]),
  "rpart" = c(mcre4$overall["Accuracy"], mcrp4$overall["Accuracy"]),
  "NeuralNet" = c(mcre5$overall["Accuracy"], mcrp5$overall["Accuracy"]),
  "RandomForest" = c(mcre6$overall["Accuracy"], mcrp6$overall["Accuracy"])
)

rownames(resumen) <- c("Precision de entrenamiento", "Precision de prueba")
resumen
```

## <span style= "color: blue;">Conclusión</span>
El modelo con el método de bosques aleatorios presenta sobreajuste, ya que tiene una alta precisión en entrenamiento, pero baja en prueba.

Acorde al resumen de resultados, el mejor modelo es el de **Máquina de Vectores de Soporte Lineal**.

# <span style= "color: blue;">Breast Cancer</span>
```{r}
data(BreastCancer)
df <- data.frame(BreastCancer)
```

## <span style= "color: blue;">Análisis Exploratorio</span>
```{r}
summary(df)
str(df)
```

```{r}
# Limpieza
df$Id <- NULL

df$Cl.thickness <- as.numeric(df$Cl.thickness)
df$Cell.size <- as.numeric(df$Cell.size)
df$Cell.shape <- as.numeric(df$Cell.shape)
df$Marg.adhesion <- as.numeric(df$Marg.adhesion)
df$Epith.c.size <- as.numeric(df$Epith.c.size)
df$Bare.nuclei <- as.numeric(df$Bare.nuclei)
df$Bl.cromatin <- as.numeric(df$Bl.cromatin)
df$Normal.nucleoli <- as.numeric(df$Normal.nucleoli)
df$Mitoses <- as.numeric(df$Mitoses)
df$Class <- as.factor(df$Class)

#Quitar 16 nulos presentes en la variable Normal.nucleoli
df <- na.omit(df)


create_report(df)
plot_missing(df)

plot_histogram(df)

plot_correlation(df)
```

Nota: La variable que queremos predecir debe tener formato de FACTOR

## <span style= "color: blue;">Partir datos 80-20</span>
```{r}
set.seed(123)
renglones_entrenamiento <-createDataPartition(df$Class, p=0.8, list=FALSE)
entrenamiento <- df[renglones_entrenamiento, ]
prueba <- df[-renglones_entrenamiento, ]
```

## <span style= "color: blue;">1. Modelo con el métodos svmLineal</span>
```{r}
modelo1 <- train(Class ~ ., data= entrenamiento, method = "svmLinear", preProcess= c("scale", "center"), trControl = trainControl(method = "cv", number = 10), tuneGrid = data.frame(C=1)) #Cuando es svmLinear

resultado_entrenamiento1 <- predict(modelo1, entrenamiento)
resultado_prueba1 <- predict(modelo1, prueba)
```

## <span style= "color: blue;">Matriz de Confusión
</span>
```{r}
mcre1 <- confusionMatrix(resultado_entrenamiento1, entrenamiento$Class)
mcre1 

mcrp1 <- confusionMatrix(resultado_prueba1, prueba$Class)
mcrp1
```

## <span style= "color: blue;">2. Modelo con el método svmRadial</span>
```{r}
modelo2 <- train(Class ~ ., data= entrenamiento, method = "svmRadial", preProcess= c("scale", "center"), trControl = trainControl(method = "cv", number = 10), tuneGrid = data.frame(sigma=1, C=1)) #Cambiar

resultado_entrenamiento2 <- predict(modelo2, entrenamiento)
resultado_prueba2 <- predict(modelo2, prueba)
```

## <span style= "color: blue;">Matriz de Confusión</span>
```{r}
mcre2 <- confusionMatrix(resultado_entrenamiento2, entrenamiento$Class)
mcre2 
mcrp2 <- confusionMatrix(resultado_prueba2, prueba$Class)
mcrp2
```

## <span style= "color: blue;">3. Modelo con el método svmPoly</span>
```{r}
modelo3 <- train(Class ~ ., data= entrenamiento, method = "svmPoly", preProcess= c("scale", "center"), trControl = trainControl(method = "cv", number = 10), tuneGrid = data.frame(degree=1,scale=1, C=1)) #Cambiar

resultado_entrenamiento3 <- predict(modelo3, entrenamiento)
resultado_prueba3 <- predict(modelo3, prueba)
```

## <span style= "color: blue;">Matriz de Confusión</span>
```{r}
mcre3 <- confusionMatrix(resultado_entrenamiento3, entrenamiento$Class)
mcre3 
mcrp3 <- confusionMatrix(resultado_prueba3, prueba$Class)
mcrp3
```

## <span style= "color: blue;">4. Modelo con el método Árbol de Decisión</span>
```{r}
modelo4 <- train(Class ~ ., data = entrenamiento, method = "rpart", preProcess = c("scale", "center"), trControl = trainControl(method="cv", number = 10), tuneLength = 10)

resultado_entrenamiento4 <- predict(modelo4, entrenamiento)
resultado_prueba4 <- predict(modelo4, prueba)
```

## <span style= "color: blue;">Matriz de Confusión</span>
```{r}
mcre4 <- confusionMatrix(resultado_entrenamiento4, entrenamiento$Class)
mcre4 
mcrp4 <- confusionMatrix(resultado_prueba4, prueba$Class)
mcrp4
```

## <span style= "color: blue;">5. Modelo con el método Neural Nety</span>
```{r}
modelo5 <- train(Class ~ ., data = entrenamiento, method = "nnet", preProcess = c("scale", "center"), trControl = trainControl(method="cv", number = 10))

resultado_entrenamiento5 <- predict(modelo5, entrenamiento)
resultado_prueba5 <- predict(modelo5, prueba)
```

## <span style= "color: blue;">Matriz de Confusión</span>
```{r}
mcre5 <- confusionMatrix(resultado_entrenamiento5, entrenamiento$Class)
mcre5 
mcrp5 <- confusionMatrix(resultado_prueba5, prueba$Class)
mcrp5
```

## <span style= "color: blue;">6. Modelo con el método Random Forest</span>
```{r}
modelo6 <- train(Class ~ ., data = entrenamiento, method = "rf", preProcess = c("scale", "center"), trControl = trainControl(method="cv", number = 10), tuneGrid = expand.grid(mtry =c(2,4,6)))

resultado_entrenamiento6 <- predict(modelo6, entrenamiento)
resultado_prueba6 <- predict(modelo6, prueba)
```

## <span style= "color: blue;">Matriz de Confusión</span>
```{r}
mcre6 <- confusionMatrix(resultado_entrenamiento6, entrenamiento$Class)
mcre6 
mcrp6 <- confusionMatrix(resultado_prueba6, prueba$Class)
mcrp6
```

## <span style= "color: blue;">Resumen de Resultados</span>
```{r}
resumen <- data.frame(
  "svmLinear" = c(mcre1$overall["Accuracy"], mcre1$overall["Accuracy"]),
  "svmRadial" = c(mcre2$overall["Accuracy"], mcrp2$overall["Accuracy"]),
  "svmPoly" = c(mcre3$overall["Accuracy"], mcrp3$overall["Accuracy"]),
  "rpart" = c(mcre4$overall["Accuracy"], mcrp4$overall["Accuracy"]),
  "NeuralNet" = c(mcre5$overall["Accuracy"], mcrp5$overall["Accuracy"]),
  "RandomForest" = c(mcre6$overall["Accuracy"], mcrp6$overall["Accuracy"])
)

rownames(resumen) <- c("Precision de entrenamiento", "Precision de prueba")
resumen
```

## <span style= "color: blue;">Conclusión</span>
El modelo con el método de neural net presenta sobreajuste, ya que tiene una alta precisión en entrenamiento, pero esta disminuye en prueba.

Acorde al resumen de resultados, los mejores modelos son los de **Máquina de Vectores de Soporte Lineal** y también el de **Máquina de Vectores Poly**, al mantener un buen equilibrio entre ambas métricas y sin sobreajuste.





