Teoria

El paquete caret (Clasification and Regression Training) es un paquete integral con una amplia variedad de algoritmos para el aprendizaje automatico.

Instalar paquetes y librerias

#install.packages("ggplot2") #Graficas con mejor diseno
library(ggplot2)
## Warning: package 'ggplot2' was built under R version 4.3.2
#install.packages("lattice") #Usar la base de datos de iris
library(lattice)
## Warning: package 'lattice' was built under R version 4.3.2
#install.packages("caret") #Algoritmos de aprendizajea automatico
library(caret)
## Warning: package 'caret' was built under R version 4.3.2
#install.packages("datasets") #Usar la base de datos de iris
library(datasets)
#install.packages("DataExplorer") #Usar la base de datos de iris
library(DataExplorer)
## Warning: package 'DataExplorer' was built under R version 4.3.2

Crear base de datos

df <- data.frame(iris)
df
##     Sepal.Length Sepal.Width Petal.Length Petal.Width    Species
## 1            5.1         3.5          1.4         0.2     setosa
## 2            4.9         3.0          1.4         0.2     setosa
## 3            4.7         3.2          1.3         0.2     setosa
## 4            4.6         3.1          1.5         0.2     setosa
## 5            5.0         3.6          1.4         0.2     setosa
## 6            5.4         3.9          1.7         0.4     setosa
## 7            4.6         3.4          1.4         0.3     setosa
## 8            5.0         3.4          1.5         0.2     setosa
## 9            4.4         2.9          1.4         0.2     setosa
## 10           4.9         3.1          1.5         0.1     setosa
## 11           5.4         3.7          1.5         0.2     setosa
## 12           4.8         3.4          1.6         0.2     setosa
## 13           4.8         3.0          1.4         0.1     setosa
## 14           4.3         3.0          1.1         0.1     setosa
## 15           5.8         4.0          1.2         0.2     setosa
## 16           5.7         4.4          1.5         0.4     setosa
## 17           5.4         3.9          1.3         0.4     setosa
## 18           5.1         3.5          1.4         0.3     setosa
## 19           5.7         3.8          1.7         0.3     setosa
## 20           5.1         3.8          1.5         0.3     setosa
## 21           5.4         3.4          1.7         0.2     setosa
## 22           5.1         3.7          1.5         0.4     setosa
## 23           4.6         3.6          1.0         0.2     setosa
## 24           5.1         3.3          1.7         0.5     setosa
## 25           4.8         3.4          1.9         0.2     setosa
## 26           5.0         3.0          1.6         0.2     setosa
## 27           5.0         3.4          1.6         0.4     setosa
## 28           5.2         3.5          1.5         0.2     setosa
## 29           5.2         3.4          1.4         0.2     setosa
## 30           4.7         3.2          1.6         0.2     setosa
## 31           4.8         3.1          1.6         0.2     setosa
## 32           5.4         3.4          1.5         0.4     setosa
## 33           5.2         4.1          1.5         0.1     setosa
## 34           5.5         4.2          1.4         0.2     setosa
## 35           4.9         3.1          1.5         0.2     setosa
## 36           5.0         3.2          1.2         0.2     setosa
## 37           5.5         3.5          1.3         0.2     setosa
## 38           4.9         3.6          1.4         0.1     setosa
## 39           4.4         3.0          1.3         0.2     setosa
## 40           5.1         3.4          1.5         0.2     setosa
## 41           5.0         3.5          1.3         0.3     setosa
## 42           4.5         2.3          1.3         0.3     setosa
## 43           4.4         3.2          1.3         0.2     setosa
## 44           5.0         3.5          1.6         0.6     setosa
## 45           5.1         3.8          1.9         0.4     setosa
## 46           4.8         3.0          1.4         0.3     setosa
## 47           5.1         3.8          1.6         0.2     setosa
## 48           4.6         3.2          1.4         0.2     setosa
## 49           5.3         3.7          1.5         0.2     setosa
## 50           5.0         3.3          1.4         0.2     setosa
## 51           7.0         3.2          4.7         1.4 versicolor
## 52           6.4         3.2          4.5         1.5 versicolor
## 53           6.9         3.1          4.9         1.5 versicolor
## 54           5.5         2.3          4.0         1.3 versicolor
## 55           6.5         2.8          4.6         1.5 versicolor
## 56           5.7         2.8          4.5         1.3 versicolor
## 57           6.3         3.3          4.7         1.6 versicolor
## 58           4.9         2.4          3.3         1.0 versicolor
## 59           6.6         2.9          4.6         1.3 versicolor
## 60           5.2         2.7          3.9         1.4 versicolor
## 61           5.0         2.0          3.5         1.0 versicolor
## 62           5.9         3.0          4.2         1.5 versicolor
## 63           6.0         2.2          4.0         1.0 versicolor
## 64           6.1         2.9          4.7         1.4 versicolor
## 65           5.6         2.9          3.6         1.3 versicolor
## 66           6.7         3.1          4.4         1.4 versicolor
## 67           5.6         3.0          4.5         1.5 versicolor
## 68           5.8         2.7          4.1         1.0 versicolor
## 69           6.2         2.2          4.5         1.5 versicolor
## 70           5.6         2.5          3.9         1.1 versicolor
## 71           5.9         3.2          4.8         1.8 versicolor
## 72           6.1         2.8          4.0         1.3 versicolor
## 73           6.3         2.5          4.9         1.5 versicolor
## 74           6.1         2.8          4.7         1.2 versicolor
## 75           6.4         2.9          4.3         1.3 versicolor
## 76           6.6         3.0          4.4         1.4 versicolor
## 77           6.8         2.8          4.8         1.4 versicolor
## 78           6.7         3.0          5.0         1.7 versicolor
## 79           6.0         2.9          4.5         1.5 versicolor
## 80           5.7         2.6          3.5         1.0 versicolor
## 81           5.5         2.4          3.8         1.1 versicolor
## 82           5.5         2.4          3.7         1.0 versicolor
## 83           5.8         2.7          3.9         1.2 versicolor
## 84           6.0         2.7          5.1         1.6 versicolor
## 85           5.4         3.0          4.5         1.5 versicolor
## 86           6.0         3.4          4.5         1.6 versicolor
## 87           6.7         3.1          4.7         1.5 versicolor
## 88           6.3         2.3          4.4         1.3 versicolor
## 89           5.6         3.0          4.1         1.3 versicolor
## 90           5.5         2.5          4.0         1.3 versicolor
## 91           5.5         2.6          4.4         1.2 versicolor
## 92           6.1         3.0          4.6         1.4 versicolor
## 93           5.8         2.6          4.0         1.2 versicolor
## 94           5.0         2.3          3.3         1.0 versicolor
## 95           5.6         2.7          4.2         1.3 versicolor
## 96           5.7         3.0          4.2         1.2 versicolor
## 97           5.7         2.9          4.2         1.3 versicolor
## 98           6.2         2.9          4.3         1.3 versicolor
## 99           5.1         2.5          3.0         1.1 versicolor
## 100          5.7         2.8          4.1         1.3 versicolor
## 101          6.3         3.3          6.0         2.5  virginica
## 102          5.8         2.7          5.1         1.9  virginica
## 103          7.1         3.0          5.9         2.1  virginica
## 104          6.3         2.9          5.6         1.8  virginica
## 105          6.5         3.0          5.8         2.2  virginica
## 106          7.6         3.0          6.6         2.1  virginica
## 107          4.9         2.5          4.5         1.7  virginica
## 108          7.3         2.9          6.3         1.8  virginica
## 109          6.7         2.5          5.8         1.8  virginica
## 110          7.2         3.6          6.1         2.5  virginica
## 111          6.5         3.2          5.1         2.0  virginica
## 112          6.4         2.7          5.3         1.9  virginica
## 113          6.8         3.0          5.5         2.1  virginica
## 114          5.7         2.5          5.0         2.0  virginica
## 115          5.8         2.8          5.1         2.4  virginica
## 116          6.4         3.2          5.3         2.3  virginica
## 117          6.5         3.0          5.5         1.8  virginica
## 118          7.7         3.8          6.7         2.2  virginica
## 119          7.7         2.6          6.9         2.3  virginica
## 120          6.0         2.2          5.0         1.5  virginica
## 121          6.9         3.2          5.7         2.3  virginica
## 122          5.6         2.8          4.9         2.0  virginica
## 123          7.7         2.8          6.7         2.0  virginica
## 124          6.3         2.7          4.9         1.8  virginica
## 125          6.7         3.3          5.7         2.1  virginica
## 126          7.2         3.2          6.0         1.8  virginica
## 127          6.2         2.8          4.8         1.8  virginica
## 128          6.1         3.0          4.9         1.8  virginica
## 129          6.4         2.8          5.6         2.1  virginica
## 130          7.2         3.0          5.8         1.6  virginica
## 131          7.4         2.8          6.1         1.9  virginica
## 132          7.9         3.8          6.4         2.0  virginica
## 133          6.4         2.8          5.6         2.2  virginica
## 134          6.3         2.8          5.1         1.5  virginica
## 135          6.1         2.6          5.6         1.4  virginica
## 136          7.7         3.0          6.1         2.3  virginica
## 137          6.3         3.4          5.6         2.4  virginica
## 138          6.4         3.1          5.5         1.8  virginica
## 139          6.0         3.0          4.8         1.8  virginica
## 140          6.9         3.1          5.4         2.1  virginica
## 141          6.7         3.1          5.6         2.4  virginica
## 142          6.9         3.1          5.1         2.3  virginica
## 143          5.8         2.7          5.1         1.9  virginica
## 144          6.8         3.2          5.9         2.3  virginica
## 145          6.7         3.3          5.7         2.5  virginica
## 146          6.7         3.0          5.2         2.3  virginica
## 147          6.3         2.5          5.0         1.9  virginica
## 148          6.5         3.0          5.2         2.0  virginica
## 149          6.2         3.4          5.4         2.3  virginica
## 150          5.9         3.0          5.1         1.8  virginica

EDA

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)
plot_missing(df)

plot_boxplot(df, by = "Species")

plot_histogram(df)

plot_bar(df)

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

#Partir la base de 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 Metodos para Modelar Los metodos mas utilizados para modelar aprendizaje automatico son:

  • SVM: Support Vector Machine o Maquina de Vectores de soporte. Hay varios subtipos: Lineal (svmLineal), Radial(svmRadial), Polinomico(svmPoly), etc.
  • Arboles de Decision: rpart
  • Redes Neuronales: nnet
  • Random Forest o Bosque Aleatorios: rf

1.Modelo con svmLineal

modelo <- 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_entrenamiento <- predict(modelo,entrenamiento)
resultado_prueba <- predict(modelo,prueba)

#Matriz de Confusion

mcre <- confusionMatrix(resultado_entrenamiento, entrenamiento$Species)
mcre
## Confusion Matrix and Statistics
## 
##             Reference
## Prediction   setosa versicolor virginica
##   setosa         40          0         0
##   versicolor      0         39         0
##   virginica       0          1        40
## 
## Overall Statistics
##                                           
##                Accuracy : 0.9917          
##                  95% CI : (0.9544, 0.9998)
##     No Information Rate : 0.3333          
##     P-Value [Acc > NIR] : < 2.2e-16       
##                                           
##                   Kappa : 0.9875          
##                                           
##  Mcnemar's Test P-Value : NA              
## 
## Statistics by Class:
## 
##                      Class: setosa Class: versicolor Class: virginica
## Sensitivity                 1.0000            0.9750           1.0000
## Specificity                 1.0000            1.0000           0.9875
## Pos Pred Value              1.0000            1.0000           0.9756
## Neg Pred Value              1.0000            0.9877           1.0000
## Prevalence                  0.3333            0.3333           0.3333
## Detection Rate              0.3333            0.3250           0.3333
## Detection Prevalence        0.3333            0.3250           0.3417
## Balanced Accuracy           1.0000            0.9875           0.9938
mcrp <- confusionMatrix(resultado_prueba, prueba$Species) #matriz de confusión del resultado de la prueba
mcrp
## 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

2.Modelo con 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) #Cuando es svmRadial
                )

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

#Matriz de Confusion

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) #matriz de confusión del resultado de la prueba
mcrp2
## 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

3.Modelo con 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) #Cuando es svmPoly
                )

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

#Matriz de Confusion

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) #matriz de confusión del resultado de la prueba
mcrp3
## 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

4.Modelo con metodo rpart

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

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

Matriz de Confusion

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) #matriz de confusión del resultado de la prueba
mcrp4
## 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

5.Modelo con metodo nnet

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 Confusion

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) #matriz de confusión del resultado de la prueba
mcrp5
## 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

6.Modelo con rf

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)) #Cuando es rf
                )
## 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 Confusion

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) #matriz de confusión del resultado de la prueba
mcrp6
## 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

Resumen de Resultados

resultados <- data.frame(
  "1. svmLinear" = c(mcre$overall["Accuracy"], mcrp$overall["Accuracy"]),
  "2. svmRadial" = c(mcre2$overall["Accuracy"], mcrp2$overall["Accuracy"]),
  "3. svmPoly" = c(mcre3$overall["Accuracy"], mcrp3$overall["Accuracy"]),
  "4. rpart" = c(mcre4$overall["Accuracy"], mcrp4$overall["Accuracy"]),
  "5. nnet" = c(mcre5$overall["Accuracy"], mcrp5$overall["Accuracy"]),
  "6. rf" = c(mcre6$overall["Accuracy"], mcrp6$overall["Accuracy"])
)
rownames(resultados) <- c("Presicion de entrenamiento", "Presicion de prueba")
resultados
##                            X1..svmLinear X2..svmRadial X3..svmPoly X4..rpart
## Presicion de entrenamiento     0.9916667     0.9916667   0.9916667 0.9666667
## Presicion de prueba            0.9916667     0.9916667   0.9916667 0.9666667
##                             X5..nnet X6..rf
## Presicion de entrenamiento 0.9666667      1
## Presicion de prueba        0.9666667      1

Conclusiones

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

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

---
title: "Machine learning"
author: "Luis Mendoza - A00829099"
date: "2024-02-26"
output: 
  html_document:
    toc: TRUE
    toc_float: TRUE
    code_download: TRUE
---

![](C:\\Users\\Luis Rodriguez\\Downloads\\Flores_de_Íris.png)

# Teoria 
El paquete *caret (Clasification and Regression Training)* es un paquete integral con una amplia variedad de algoritmos para el aprendizaje automatico.

# Instalar paquetes y librerias
```{r}
#install.packages("ggplot2") #Graficas con mejor diseno
library(ggplot2)
#install.packages("lattice") #Usar la base de datos de iris
library(lattice)
#install.packages("caret") #Algoritmos de aprendizajea automatico
library(caret)
#install.packages("datasets") #Usar la base de datos de iris
library(datasets)
#install.packages("DataExplorer") #Usar la base de datos de iris
library(DataExplorer)
```

# Crear base de datos
```{r}
df <- data.frame(iris)
df
```

# EDA 
```{r}
summary(df)
str(df)
#create_report(df)
plot_missing(df)
plot_boxplot(df, by = "Species")
plot_histogram(df)
plot_bar(df)
```
** Nota: La variable que queremos predecir debe tener formato de FACTOR**

#Partir la base de datos 80-20
```{r}
set.seed(123)
renglones_entrenamiento <- createDataPartition(df$Species, p=0.8, list=FALSE)
entrenamiento <- iris[renglones_entrenamiento, ]
prueba <- iris[renglones_entrenamiento, ]
```

#Distintos tipos de Metodos para Modelar
Los metodos mas utilizados para modelar aprendizaje automatico son:

* **SVM**: *Support Vector Machine* o Maquina de Vectores de soporte. Hay varios subtipos: Lineal (svmLineal), Radial(svmRadial), Polinomico(svmPoly), etc.  
* **Arboles de Decision**: rpart  
* **Redes Neuronales**: nnet
* **Random Forest** o Bosque Aleatorios: rf

# 1.Modelo con svmLineal
```{r}
modelo <- 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_entrenamiento <- predict(modelo,entrenamiento)
resultado_prueba <- predict(modelo,prueba)
```

#Matriz de Confusion
```{r}
mcre <- confusionMatrix(resultado_entrenamiento, entrenamiento$Species)
mcre
mcrp <- confusionMatrix(resultado_prueba, prueba$Species) #matriz de confusión del resultado de la prueba
mcrp
```

# 2.Modelo con svmRadial
```{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) #Cuando es svmRadial
                )

resultado_entrenamiento2 <- predict(modelo2,entrenamiento)
resultado_prueba2 <- predict(modelo2,prueba)
```
#Matriz de Confusion
```{r}
mcre2 <- confusionMatrix(resultado_entrenamiento2, entrenamiento$Species)
mcre2
mcrp2 <- confusionMatrix(resultado_prueba2, prueba$Species) #matriz de confusión del resultado de la prueba
mcrp2
```

# 3.Modelo con svmPoly
```{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) #Cuando es svmPoly
                )

resultado_entrenamiento3 <- predict(modelo3,entrenamiento)
resultado_prueba3 <- predict(modelo3,prueba)
```
#Matriz de Confusion
```{r}
mcre3 <- confusionMatrix(resultado_entrenamiento3, entrenamiento$Species)
mcre3
mcrp3 <- confusionMatrix(resultado_prueba3, prueba$Species) #matriz de confusión del resultado de la prueba
mcrp3
```

# 4.Modelo con metodo rpart
```{r}
modelo4 <- train(Species ~ .,data = entrenamiento, method = "rpart",preProcess=c("scale","center"), trControl = trainControl(method="cv",number=10),
                tuneLength = 10 #Cuando es metodo rpart
                )

resultado_entrenamiento4 <- predict(modelo4,entrenamiento)
resultado_prueba4 <- predict(modelo4,prueba)
```
# Matriz de Confusion
```{r}
mcre4 <- confusionMatrix(resultado_entrenamiento4, entrenamiento$Species)
mcre4
mcrp4 <- confusionMatrix(resultado_prueba4, prueba$Species) #matriz de confusión del resultado de la prueba
mcrp4
```
# 5.Modelo con metodo nnet
```{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)
```
#Matriz de Confusion
```{r}
mcre5 <- confusionMatrix(resultado_entrenamiento5, entrenamiento$Species)
mcre5
mcrp5 <- confusionMatrix(resultado_prueba5, prueba$Species) #matriz de confusión del resultado de la prueba
mcrp5
```

# 6.Modelo con rf
```{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)) #Cuando es rf
                )

resultado_entrenamiento6 <- predict(modelo6,entrenamiento)
resultado_prueba6 <- predict(modelo6,prueba)
```
#Matriz de Confusion
```{r}
mcre6 <- confusionMatrix(resultado_entrenamiento6, entrenamiento$Species)
mcre6
mcrp6 <- confusionMatrix(resultado_prueba6, prueba$Species) #matriz de confusión del resultado de la prueba
mcrp6
```
 
# Resumen de Resultados
```{r}
resultados <- data.frame(
  "1. svmLinear" = c(mcre$overall["Accuracy"], mcrp$overall["Accuracy"]),
  "2. svmRadial" = c(mcre2$overall["Accuracy"], mcrp2$overall["Accuracy"]),
  "3. svmPoly" = c(mcre3$overall["Accuracy"], mcrp3$overall["Accuracy"]),
  "4. rpart" = c(mcre4$overall["Accuracy"], mcrp4$overall["Accuracy"]),
  "5. nnet" = c(mcre5$overall["Accuracy"], mcrp5$overall["Accuracy"]),
  "6. rf" = c(mcre6$overall["Accuracy"], mcrp6$overall["Accuracy"])
)
rownames(resultados) <- c("Presicion de entrenamiento", "Presicion de prueba")
resultados
```

# Conclusiones

El modelo con el metodo de bosques aleatorios presenta sobreajuste, ya que tiene una alta presicion en entrenamiento, pero baja en prueba.  

Acorde al resumen de resultados, el mejor modelo es el de **Maquina de Vectores de Soporte Lineal**