Caret Cancer de Mama

Teoría

La función caret (Clasification And Regression Training) es un paquete integral con una amplia variedad de algoritmos para el aprendizaje automático.

Instalar paquetes y llamar librerías

#install.packages("caret") # Algoritmos de aprendizaje automático
#install.packages("ggplot2") # Gráficas con mejor diseño
library(ggplot2)
#install.packages("lattice") # Crear gráficos
library(lattice)
#install.packages("datasets") # Usar la base de datos "BreastCancer"
library(datasets)
library(DataExplorer)
library(caret)
library(MASS)
library(mlbench)
library(dplyr)

## 
## Attaching package: 'dplyr'

## The following object is masked from 'package:MASS':
## 
##     select

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

Crear base de datos

data("BreastCancer")
bc <- BreastCancer

Incluir funciones para evaluacion y comparacion de modelos

Análisis exploratorio

summary(bc)

##       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(bc)

## '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 ...

plot_missing(bc)

plot_correlation(bc)

sum(is.na(bc))

## [1] 16

bc <- na.omit(bc)
sum(is.na(bc))

## [1] 0

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

bc <- bc %>%
  mutate(Class = ifelse(Class == "benign", 0, 
                        ifelse(Class == "malignant", 1, Class))) %>% select(-Id)

bc$Cl.thickness  <- as.factor(as.character(bc$Cl.thickness))
bc$Cell.size  <- as.factor(as.character(bc$Cell.size))
bc$Cell.shape  <- as.factor(as.character(bc$Cell.shape))
bc$Marg.adhesion  <- as.factor(as.character(bc$Marg.adhesion))
bc$Epith.c.size  <- as.factor(as.character(bc$Epith.c.size))
bc$Class <- as.factor(bc$Class)

str(bc)

## 'data.frame':    683 obs. of  10 variables:
##  $ Cl.thickness   : Factor w/ 10 levels "1","10","2","3",..: 6 6 4 7 5 9 1 3 3 5 ...
##  $ Cell.size      : Factor w/ 10 levels "1","10","2","3",..: 1 5 1 9 1 2 1 1 1 3 ...
##  $ Cell.shape     : Factor w/ 10 levels "1","10","2","3",..: 1 5 1 9 1 2 1 3 1 1 ...
##  $ Marg.adhesion  : Factor w/ 10 levels "1","10","2","3",..: 1 6 1 1 4 9 1 1 1 1 ...
##  $ Epith.c.size   : Factor w/ 10 levels "1","10","2","3",..: 3 8 3 4 3 8 3 3 3 3 ...
##  $ 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 "0","1": 1 1 1 1 1 2 1 1 1 1 ...
##  - attr(*, "na.action")= 'omit' Named int [1:16] 24 41 140 146 159 165 236 250 276 293 ...
##   ..- attr(*, "names")= chr [1:16] "24" "41" "140" "146" ...

Partir datos 80-20

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

Distintos tipos de Métodos para Modelar

Los métodos más utilizados para moelar aprendizaje automático son:

• SVM: Support Vector Machine o Máquina de Vectores de Soporte. Hay varios subtipos: Linea (svmLineal)m Radial (svmRadial), Polinómico (svmPoly), etc.

• Árbol de Decisión: rpart

• Redes Neuronales: nnet

• Random Forest o Bosques Aleatorios: rf

1. Modelo con el método svmLineal

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

# Predicción en datos de entrenamiento y prueba
resultado_entrenamiento <- predict(modelo, entrenamiento)
resultado_prueba <- predict(modelo, prueba)

# Matriz de Confusión
mcre <- confusionMatrix(resultado_entrenamiento, entrenamiento$Class)
mcre

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction   0   1
##          0 356   0
##          1   0 192
##                                      
##                Accuracy : 1          
##                  95% CI : (0.9933, 1)
##     No Information Rate : 0.6496     
##     P-Value [Acc > NIR] : < 2.2e-16  
##                                      
##                   Kappa : 1          
##                                      
##  Mcnemar's Test P-Value : NA         
##                                      
##             Sensitivity : 1.0000     
##             Specificity : 1.0000     
##          Pos Pred Value : 1.0000     
##          Neg Pred Value : 1.0000     
##              Prevalence : 0.6496     
##          Detection Rate : 0.6496     
##    Detection Prevalence : 0.6496     
##       Balanced Accuracy : 1.0000     
##                                      
##        'Positive' Class : 0          
## 

mcrp <- confusionMatrix(resultado_prueba, prueba$Class)
mcrp

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction  0  1
##          0 82  6
##          1  6 41
##                                           
##                Accuracy : 0.9111          
##                  95% CI : (0.8499, 0.9532)
##     No Information Rate : 0.6519          
##     P-Value [Acc > NIR] : 2.463e-12       
##                                           
##                   Kappa : 0.8042          
##                                           
##  Mcnemar's Test P-Value : 1               
##                                           
##             Sensitivity : 0.9318          
##             Specificity : 0.8723          
##          Pos Pred Value : 0.9318          
##          Neg Pred Value : 0.8723          
##              Prevalence : 0.6519          
##          Detection Rate : 0.6074          
##    Detection Prevalence : 0.6519          
##       Balanced Accuracy : 0.9021          
##                                           
##        'Positive' Class : 0               
## 

2. Modelo con el método svmRadial

# Entrenamiento del modelo
model2_bc <- train(Class ~ ., 
                data = entrenamiento,
                method = "svmRadial", 
                preProcess = c("scale", "center"),
                trControl = trainControl(method = "cv", number = 10),
                tuneGrid = data.frame(sigma = 1, C = 1)
)

# Predicción en datos de entrenamiento y prueba
resultado_entrenamiento2 <- predict(model2_bc, entrenamiento)
resultado_prueba2 <- predict(model2_bc, prueba)

# Matriz de Confusión
mcre2 <- confusionMatrix(resultado_entrenamiento2, entrenamiento$Class) # matriz de confusion del resultado del entrenamiento
mcre2

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction   0   1
##          0 356   0
##          1   0 192
##                                      
##                Accuracy : 1          
##                  95% CI : (0.9933, 1)
##     No Information Rate : 0.6496     
##     P-Value [Acc > NIR] : < 2.2e-16  
##                                      
##                   Kappa : 1          
##                                      
##  Mcnemar's Test P-Value : NA         
##                                      
##             Sensitivity : 1.0000     
##             Specificity : 1.0000     
##          Pos Pred Value : 1.0000     
##          Neg Pred Value : 1.0000     
##              Prevalence : 0.6496     
##          Detection Rate : 0.6496     
##    Detection Prevalence : 0.6496     
##       Balanced Accuracy : 1.0000     
##                                      
##        'Positive' Class : 0          
## 

mcrp2 <- confusionMatrix(resultado_prueba2, prueba$Class) # matriz de confusion del resultado de la prueba
mcrp2

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction  0  1
##          0 47  0
##          1 41 47
##                                           
##                Accuracy : 0.6963          
##                  95% CI : (0.6113, 0.7724)
##     No Information Rate : 0.6519          
##     P-Value [Acc > NIR] : 0.1602          
##                                           
##                   Kappa : 0.4439          
##                                           
##  Mcnemar's Test P-Value : 4.185e-10       
##                                           
##             Sensitivity : 0.5341          
##             Specificity : 1.0000          
##          Pos Pred Value : 1.0000          
##          Neg Pred Value : 0.5341          
##              Prevalence : 0.6519          
##          Detection Rate : 0.3481          
##    Detection Prevalence : 0.3481          
##       Balanced Accuracy : 0.7670          
##                                           
##        'Positive' Class : 0               
## 

3. Modelo con el método svmPoly

# Entrenamiento del modelo
model3 <- 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)
)
# Define la cuadrícula de sintonización para los parámetros sigma y C


# Predicción en datos de entrenamiento y prueba
resultado_entrenamiento3 <- predict(model3, entrenamiento)
resultado_prueba3 <- predict(model3, prueba)

# Matriz de Confusión
mcre3 <- confusionMatrix(resultado_entrenamiento3, entrenamiento$Class) # matriz de confusion del resultado del entrenamiento
mcre3

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction   0   1
##          0 356   0
##          1   0 192
##                                      
##                Accuracy : 1          
##                  95% CI : (0.9933, 1)
##     No Information Rate : 0.6496     
##     P-Value [Acc > NIR] : < 2.2e-16  
##                                      
##                   Kappa : 1          
##                                      
##  Mcnemar's Test P-Value : NA         
##                                      
##             Sensitivity : 1.0000     
##             Specificity : 1.0000     
##          Pos Pred Value : 1.0000     
##          Neg Pred Value : 1.0000     
##              Prevalence : 0.6496     
##          Detection Rate : 0.6496     
##    Detection Prevalence : 0.6496     
##       Balanced Accuracy : 1.0000     
##                                      
##        'Positive' Class : 0          
## 

mcrp3 <- confusionMatrix(resultado_prueba3, prueba$Class) # matriz de confusion del resultado de la prueba
mcrp3

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction  0  1
##          0 82  6
##          1  6 41
##                                           
##                Accuracy : 0.9111          
##                  95% CI : (0.8499, 0.9532)
##     No Information Rate : 0.6519          
##     P-Value [Acc > NIR] : 2.463e-12       
##                                           
##                   Kappa : 0.8042          
##                                           
##  Mcnemar's Test P-Value : 1               
##                                           
##             Sensitivity : 0.9318          
##             Specificity : 0.8723          
##          Pos Pred Value : 0.9318          
##          Neg Pred Value : 0.8723          
##              Prevalence : 0.6519          
##          Detection Rate : 0.6074          
##    Detection Prevalence : 0.6519          
##       Balanced Accuracy : 0.9021          
##                                           
##        'Positive' Class : 0               
## 

4. Modelo con el método rpart

# Entrenamiento del modelo
model4 <- train(Class ~ ., 
                data = entrenamiento,
                method = "rpart", 
                preProcess = c("scale", "center"),
                trControl = trainControl(method = "cv", number = 10),
                tuneLength = 10 # numero de divisiones del árbol
                )

# Predicción en datos de entrenamiento y prueba
resultado_entrenamiento4 <- predict(model4, entrenamiento)
resultado_prueba4 <- predict(model4, prueba)

# Matriz de Confusión
mcre4 <- confusionMatrix(resultado_entrenamiento4, entrenamiento$Class) # matriz de confusion del resultado del entrenamiento
mcre4

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction   0   1
##          0 346  17
##          1  10 175
##                                           
##                Accuracy : 0.9507          
##                  95% CI : (0.9291, 0.9673)
##     No Information Rate : 0.6496          
##     P-Value [Acc > NIR] : <2e-16          
##                                           
##                   Kappa : 0.8908          
##                                           
##  Mcnemar's Test P-Value : 0.2482          
##                                           
##             Sensitivity : 0.9719          
##             Specificity : 0.9115          
##          Pos Pred Value : 0.9532          
##          Neg Pred Value : 0.9459          
##              Prevalence : 0.6496          
##          Detection Rate : 0.6314          
##    Detection Prevalence : 0.6624          
##       Balanced Accuracy : 0.9417          
##                                           
##        'Positive' Class : 0               
## 

mcrp4 <- confusionMatrix(resultado_prueba4, prueba$Class) # matriz de confusion del resultado de la prueba
mcrp4

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction  0  1
##          0 88  8
##          1  0 39
##                                           
##                Accuracy : 0.9407          
##                  95% CI : (0.8866, 0.9741)
##     No Information Rate : 0.6519          
##     P-Value [Acc > NIR] : 1.347e-15       
##                                           
##                   Kappa : 0.864           
##                                           
##  Mcnemar's Test P-Value : 0.01333         
##                                           
##             Sensitivity : 1.0000          
##             Specificity : 0.8298          
##          Pos Pred Value : 0.9167          
##          Neg Pred Value : 1.0000          
##              Prevalence : 0.6519          
##          Detection Rate : 0.6519          
##    Detection Prevalence : 0.7111          
##       Balanced Accuracy : 0.9149          
##                                           
##        'Positive' Class : 0               
## 

5. Modelo con el método redes neuronales

# Entrenamiento del modelo
model5 <- train(Class ~ ., 
                data = entrenamiento,
                method = "nnet", 
                preProcess = c("scale", "center"),
                trControl = trainControl(method = "cv", number = 10)
                )

## # weights:  83
## initial  value 373.635149 
## iter  10 value 50.010671
## iter  20 value 25.241095
## iter  30 value 21.925308
## iter  40 value 21.587540
## iter  50 value 21.561887
## iter  60 value 17.027619
## iter  70 value 17.025370
## iter  80 value 17.024262
## iter  90 value 17.023785
## iter 100 value 17.023409
## final  value 17.023409 
## stopped after 100 iterations
## # weights:  247
## initial  value 324.935863 
## iter  10 value 24.197369
## iter  20 value 13.270270
## iter  30 value 11.090580
## iter  40 value 10.919035
## iter  50 value 9.535371
## iter  60 value 9.386065
## iter  70 value 9.371595
## iter  80 value 9.315208
## iter  90 value 9.240369
## iter 100 value 9.085473
## final  value 9.085473 
## stopped after 100 iterations
## # weights:  411
## initial  value 329.413639 
## iter  10 value 18.363156
## iter  20 value 4.104714
## iter  30 value 0.313717
## iter  40 value 0.037740
## iter  50 value 0.013030
## iter  60 value 0.002195
## iter  70 value 0.000359
## iter  80 value 0.000193
## final  value 0.000091 
## converged
## # weights:  83
## initial  value 318.958373 
## iter  10 value 57.637764
## iter  20 value 33.652471
## iter  30 value 26.386981
## iter  40 value 19.289464
## iter  50 value 18.320550
## iter  60 value 18.174575
## iter  70 value 18.129560
## iter  80 value 18.126970
## final  value 18.126968 
## converged
## # weights:  247
## initial  value 396.840774 
## iter  10 value 60.301000
## iter  20 value 30.285635
## iter  30 value 18.109551
## iter  40 value 11.365297
## iter  50 value 10.437392
## iter  60 value 10.281993
## iter  70 value 10.213385
## iter  80 value 10.213031
## iter  80 value 10.213031
## iter  80 value 10.213031
## final  value 10.213031 
## converged
## # weights:  411
## initial  value 403.742728 
## iter  10 value 42.745688
## iter  20 value 23.969799
## iter  30 value 10.812540
## iter  40 value 8.884698
## iter  50 value 8.695950
## iter  60 value 8.518855
## iter  70 value 8.469847
## iter  80 value 8.464782
## iter  90 value 8.460793
## iter 100 value 8.460143
## final  value 8.460143 
## stopped after 100 iterations
## # weights:  83
## initial  value 307.501897 
## iter  10 value 53.323549
## iter  20 value 43.553017
## iter  30 value 39.751860
## iter  40 value 39.734468
## iter  50 value 39.730037
## iter  60 value 39.726097
## iter  70 value 39.723878
## iter  80 value 39.717712
## iter  90 value 39.714081
## iter 100 value 36.159141
## final  value 36.159141 
## stopped after 100 iterations
## # weights:  247
## initial  value 320.984086 
## iter  10 value 37.588695
## iter  20 value 25.922245
## iter  30 value 25.830445
## iter  40 value 25.693199
## iter  50 value 25.635604
## iter  60 value 25.591611
## iter  70 value 25.410406
## iter  80 value 24.618588
## iter  90 value 18.563094
## iter 100 value 6.738598
## final  value 6.738598 
## stopped after 100 iterations
## # weights:  411
## initial  value 319.401333 
## iter  10 value 30.716565
## iter  20 value 6.430031
## iter  30 value 1.796554
## iter  40 value 0.225601
## iter  50 value 0.131631
## iter  60 value 0.114607
## iter  70 value 0.103543
## iter  80 value 0.094038
## iter  90 value 0.086110
## iter 100 value 0.079612
## final  value 0.079612 
## stopped after 100 iterations
## # weights:  83
## initial  value 399.275854 
## iter  10 value 147.256303
## iter  20 value 58.230939
## iter  30 value 30.096555
## iter  40 value 29.630330
## iter  50 value 29.597795
## iter  60 value 29.592758
## iter  70 value 29.591759
## iter  80 value 29.591598
## iter  90 value 29.591514
## iter 100 value 29.591455
## final  value 29.591455 
## stopped after 100 iterations
## # weights:  247
## initial  value 318.996893 
## iter  10 value 37.506485
## iter  20 value 21.935282
## iter  30 value 20.343560
## iter  40 value 19.104752
## iter  50 value 17.100408
## iter  60 value 16.299547
## iter  70 value 15.400348
## iter  80 value 15.395893
## iter  90 value 15.378299
## iter 100 value 10.155206
## final  value 10.155206 
## stopped after 100 iterations
## # weights:  411
## initial  value 351.316133 
## iter  10 value 20.691403
## iter  20 value 8.754505
## iter  30 value 8.163574
## iter  40 value 7.745295
## iter  50 value 7.719769
## iter  60 value 7.220389
## iter  70 value 7.208166
## iter  80 value 7.203428
## iter  90 value 7.029015
## iter 100 value 7.001851
## final  value 7.001851 
## stopped after 100 iterations
## # weights:  83
## initial  value 410.719376 
## iter  10 value 121.894143
## iter  20 value 79.143390
## iter  30 value 56.729354
## iter  40 value 45.456008
## iter  50 value 32.850148
## iter  60 value 28.792197
## iter  70 value 25.194005
## iter  80 value 22.021304
## iter  90 value 21.619492
## iter 100 value 21.604683
## final  value 21.604683 
## stopped after 100 iterations
## # weights:  247
## initial  value 353.788416 
## iter  10 value 51.867085
## iter  20 value 29.505012
## iter  30 value 19.478593
## iter  40 value 16.876406
## iter  50 value 13.295657
## iter  60 value 12.069946
## iter  70 value 12.019379
## iter  80 value 12.017621
## iter  90 value 12.014693
## iter 100 value 12.009964
## final  value 12.009964 
## stopped after 100 iterations
## # weights:  411
## initial  value 375.590053 
## iter  10 value 39.047954
## iter  20 value 13.891850
## iter  30 value 11.530722
## iter  40 value 11.090873
## iter  50 value 10.208973
## iter  60 value 9.600850
## iter  70 value 9.407459
## iter  80 value 9.395895
## iter  90 value 9.391065
## iter 100 value 9.388096
## final  value 9.388096 
## stopped after 100 iterations
## # weights:  83
## initial  value 317.324835 
## iter  10 value 47.946792
## iter  20 value 42.634575
## iter  30 value 39.581261
## iter  40 value 39.561390
## iter  50 value 39.554272
## iter  60 value 39.531222
## iter  70 value 36.356421
## iter  80 value 36.351714
## iter  90 value 36.342081
## iter 100 value 29.832717
## final  value 29.832717 
## stopped after 100 iterations
## # weights:  247
## initial  value 336.154420 
## iter  10 value 39.725801
## iter  20 value 23.047981
## iter  30 value 18.171629
## iter  40 value 13.227256
## iter  50 value 8.818794
## iter  60 value 8.700327
## iter  70 value 8.675930
## iter  80 value 8.666686
## iter  90 value 8.646051
## iter 100 value 8.365185
## final  value 8.365185 
## stopped after 100 iterations
## # weights:  411
## initial  value 355.907547 
## iter  10 value 7.607314
## iter  20 value 2.842838
## iter  30 value 2.404559
## iter  40 value 2.056356
## iter  50 value 2.039687
## iter  60 value 1.500617
## iter  70 value 0.173945
## iter  80 value 0.134923
## iter  90 value 0.126418
## iter 100 value 0.117700
## final  value 0.117700 
## stopped after 100 iterations
## # weights:  83
## initial  value 304.878892 
## iter  10 value 53.658023
## iter  20 value 45.483812
## iter  30 value 42.526718
## iter  40 value 42.525605
## iter  50 value 42.525438
## iter  60 value 42.525323
## final  value 42.525309 
## converged
## # weights:  247
## initial  value 321.339700 
## iter  10 value 41.898623
## iter  20 value 17.062164
## iter  30 value 9.929280
## iter  40 value 7.774503
## iter  50 value 6.212717
## iter  60 value 6.191650
## iter  70 value 6.187855
## iter  80 value 5.550241
## iter  90 value 4.832015
## iter 100 value 4.782757
## final  value 4.782757 
## stopped after 100 iterations
## # weights:  411
## initial  value 442.755632 
## iter  10 value 36.594432
## iter  20 value 11.008288
## iter  30 value 8.521503
## iter  40 value 7.913952
## iter  50 value 7.856826
## iter  60 value 7.748840
## iter  70 value 7.697261
## iter  80 value 6.135351
## iter  90 value 6.083494
## iter 100 value 6.063149
## final  value 6.063149 
## stopped after 100 iterations
## # weights:  83
## initial  value 362.653174 
## iter  10 value 78.227678
## iter  20 value 54.789295
## iter  30 value 40.834704
## iter  40 value 31.723420
## iter  50 value 23.153795
## iter  60 value 22.044195
## iter  70 value 21.867575
## iter  80 value 21.647002
## iter  90 value 21.632273
## iter 100 value 21.619513
## final  value 21.619513 
## stopped after 100 iterations
## # weights:  247
## initial  value 408.594347 
## iter  10 value 112.221292
## iter  20 value 44.094922
## iter  30 value 25.987559
## iter  40 value 16.034581
## iter  50 value 12.492871
## iter  60 value 12.114491
## iter  70 value 12.072795
## iter  80 value 12.071994
## final  value 12.071991 
## converged
## # weights:  411
## initial  value 418.370721 
## iter  10 value 68.428554
## iter  20 value 27.912396
## iter  30 value 13.504148
## iter  40 value 10.967551
## iter  50 value 10.258892
## iter  60 value 9.891453
## iter  70 value 9.740163
## iter  80 value 9.702950
## iter  90 value 9.681110
## iter 100 value 9.677718
## final  value 9.677718 
## stopped after 100 iterations
## # weights:  83
## initial  value 322.165018 
## iter  10 value 132.531064
## iter  20 value 109.912008
## iter  30 value 105.725503
## iter  40 value 105.689596
## iter  50 value 97.285659
## iter  60 value 91.729992
## iter  70 value 86.641050
## iter  80 value 86.282199
## iter  90 value 83.404959
## iter 100 value 80.454198
## final  value 80.454198 
## stopped after 100 iterations
## # weights:  247
## initial  value 429.601322 
## iter  10 value 37.348912
## iter  20 value 21.826465
## iter  30 value 15.622029
## iter  40 value 13.684480
## iter  50 value 12.489567
## iter  60 value 11.064243
## iter  70 value 10.732953
## iter  80 value 10.400882
## iter  90 value 9.638218
## iter 100 value 9.215717
## final  value 9.215717 
## stopped after 100 iterations
## # weights:  411
## initial  value 322.717597 
## iter  10 value 23.498085
## iter  20 value 11.876630
## iter  30 value 7.558572
## iter  40 value 6.872976
## iter  50 value 6.373976
## iter  60 value 5.788632
## iter  70 value 4.910256
## iter  80 value 4.384007
## iter  90 value 1.618620
## iter 100 value 0.201096
## final  value 0.201096 
## stopped after 100 iterations
## # weights:  83
## initial  value 423.189085 
## iter  10 value 98.568316
## iter  20 value 55.902316
## iter  30 value 43.666625
## iter  40 value 33.067515
## iter  50 value 32.965397
## iter  60 value 22.814943
## iter  70 value 22.764657
## iter  80 value 22.763024
## iter  90 value 22.762328
## iter  90 value 22.762328
## iter  90 value 22.762327
## final  value 22.762327 
## converged
## # weights:  247
## initial  value 416.671102 
## iter  10 value 32.351600
## iter  20 value 26.033187
## iter  30 value 22.007964
## iter  40 value 20.856000
## iter  50 value 20.715288
## iter  60 value 19.868537
## iter  70 value 15.977669
## iter  80 value 14.734450
## iter  90 value 14.591448
## iter 100 value 14.051185
## final  value 14.051185 
## stopped after 100 iterations
## # weights:  411
## initial  value 348.181757 
## iter  10 value 20.296521
## iter  20 value 6.160163
## iter  30 value 3.016387
## iter  40 value 2.743314
## iter  50 value 0.121064
## iter  60 value 0.069201
## iter  70 value 0.025341
## iter  80 value 0.010843
## iter  90 value 0.001997
## iter 100 value 0.000465
## final  value 0.000465 
## stopped after 100 iterations
## # weights:  83
## initial  value 345.838875 
## iter  10 value 125.484239
## iter  20 value 77.767736
## iter  30 value 29.835119
## iter  40 value 26.443435
## iter  50 value 22.149082
## iter  60 value 22.075985
## iter  70 value 22.075624
## iter  70 value 22.075623
## iter  70 value 22.075623
## final  value 22.075623 
## converged
## # weights:  247
## initial  value 338.774453 
## iter  10 value 62.726504
## iter  20 value 38.356677
## iter  30 value 20.660954
## iter  40 value 12.552314
## iter  50 value 11.435050
## iter  60 value 10.883996
## iter  70 value 10.791865
## iter  80 value 10.783840
## iter  90 value 10.758564
## iter 100 value 10.758187
## final  value 10.758187 
## stopped after 100 iterations
## # weights:  411
## initial  value 479.706024 
## iter  10 value 40.346499
## iter  20 value 19.458565
## iter  30 value 12.385741
## iter  40 value 9.989186
## iter  50 value 9.016262
## iter  60 value 8.827129
## iter  70 value 8.775357
## iter  80 value 8.764210
## iter  90 value 8.762907
## iter 100 value 8.762802
## final  value 8.762802 
## stopped after 100 iterations
## # weights:  83
## initial  value 331.563494 
## iter  10 value 39.578829
## iter  20 value 36.410202
## iter  30 value 36.317587
## iter  40 value 36.303196
## iter  50 value 36.238962
## iter  60 value 32.991043
## iter  70 value 32.987250
## iter  80 value 32.983318
## iter  90 value 23.381541
## iter 100 value 17.713663
## final  value 17.713663 
## stopped after 100 iterations
## # weights:  247
## initial  value 472.807591 
## iter  10 value 37.491348
## iter  20 value 11.590607
## iter  30 value 8.101483
## iter  40 value 7.667777
## iter  50 value 6.340593
## iter  60 value 6.314589
## iter  70 value 6.307880
## iter  80 value 6.299962
## iter  90 value 6.296085
## iter 100 value 6.290074
## final  value 6.290074 
## stopped after 100 iterations
## # weights:  411
## initial  value 352.606924 
## iter  10 value 31.497198
## iter  20 value 19.093436
## iter  30 value 15.001494
## iter  40 value 13.818165
## iter  50 value 12.534943
## iter  60 value 7.728711
## iter  70 value 5.089390
## iter  80 value 5.017709
## iter  90 value 5.007984
## iter 100 value 4.382313
## final  value 4.382313 
## stopped after 100 iterations
## # weights:  83
## initial  value 363.395485 
## iter  10 value 42.710982
## iter  20 value 36.273921
## iter  30 value 36.259569
## iter  40 value 36.259475
## iter  50 value 36.259436
## iter  50 value 36.259436
## final  value 36.259436 
## converged
## # weights:  247
## initial  value 318.389292 
## iter  10 value 30.075533
## iter  20 value 20.630980
## iter  30 value 16.614563
## iter  40 value 15.217691
## iter  50 value 13.926245
## iter  60 value 13.163435
## iter  70 value 11.524621
## iter  80 value 9.267836
## iter  90 value 9.041419
## iter 100 value 9.033010
## final  value 9.033010 
## stopped after 100 iterations
## # weights:  411
## initial  value 376.840066 
## iter  10 value 48.716139
## iter  20 value 27.402176
## iter  30 value 7.823619
## iter  40 value 0.339544
## iter  50 value 0.020036
## iter  60 value 0.006464
## iter  70 value 0.002406
## iter  80 value 0.000676
## iter  90 value 0.000270
## final  value 0.000092 
## converged
## # weights:  83
## initial  value 321.355181 
## iter  10 value 60.191634
## iter  20 value 42.134754
## iter  30 value 30.946083
## iter  40 value 24.295596
## iter  50 value 22.561110
## iter  60 value 22.411909
## iter  70 value 22.407399
## final  value 22.407384 
## converged
## # weights:  247
## initial  value 475.306726 
## iter  10 value 145.391333
## iter  20 value 74.213763
## iter  30 value 35.863610
## iter  40 value 23.997682
## iter  50 value 14.446250
## iter  60 value 11.353779
## iter  70 value 11.081877
## iter  80 value 10.929958
## iter  90 value 10.911007
## iter 100 value 10.909130
## final  value 10.909130 
## stopped after 100 iterations
## # weights:  411
## initial  value 352.784287 
## iter  10 value 39.757791
## iter  20 value 22.887694
## iter  30 value 14.294650
## iter  40 value 11.918362
## iter  50 value 10.536873
## iter  60 value 9.365154
## iter  70 value 9.144375
## iter  80 value 9.138044
## iter  90 value 9.137862
## final  value 9.137856 
## converged
## # weights:  83
## initial  value 414.434442 
## iter  10 value 53.272377
## iter  20 value 33.405426
## iter  30 value 29.534825
## iter  40 value 22.057561
## iter  50 value 21.948962
## iter  60 value 17.706869
## iter  70 value 17.702747
## iter  80 value 17.702167
## iter  90 value 17.701397
## iter 100 value 17.700844
## final  value 17.700844 
## stopped after 100 iterations
## # weights:  247
## initial  value 305.757140 
## iter  10 value 35.820849
## iter  20 value 14.635996
## iter  30 value 9.976552
## iter  40 value 7.831708
## iter  50 value 6.606666
## iter  60 value 6.580143
## iter  70 value 6.551154
## iter  80 value 6.226117
## iter  90 value 6.204714
## iter 100 value 6.197260
## final  value 6.197260 
## stopped after 100 iterations
## # weights:  411
## initial  value 305.436786 
## iter  10 value 28.273847
## iter  20 value 16.579537
## iter  30 value 13.341741
## iter  40 value 11.148623
## iter  50 value 9.994417
## iter  60 value 8.984229
## iter  70 value 8.368035
## iter  80 value 8.012897
## iter  90 value 6.098687
## iter 100 value 4.925818
## final  value 4.925818 
## stopped after 100 iterations
## # weights:  83
## initial  value 324.476204 
## iter  10 value 36.615518
## iter  20 value 29.615467
## iter  30 value 29.592020
## iter  40 value 29.591457
## final  value 29.591454 
## converged
## # weights:  247
## initial  value 446.088008 
## iter  10 value 24.570634
## iter  20 value 9.854754
## iter  30 value 4.520976
## iter  40 value 4.417626
## iter  50 value 4.166881
## iter  60 value 4.162604
## iter  70 value 4.160414
## iter  80 value 4.159764
## iter  90 value 4.159488
## iter 100 value 4.159013
## final  value 4.159013 
## stopped after 100 iterations
## # weights:  411
## initial  value 323.836817 
## iter  10 value 17.271652
## iter  20 value 5.922613
## iter  30 value 0.641732
## iter  40 value 0.072225
## iter  50 value 0.009256
## iter  60 value 0.002760
## iter  70 value 0.000827
## iter  80 value 0.000307
## iter  90 value 0.000206
## iter 100 value 0.000146
## final  value 0.000146 
## stopped after 100 iterations
## # weights:  83
## initial  value 384.525267 
## iter  10 value 54.441366
## iter  20 value 39.969248
## iter  30 value 33.957643
## iter  40 value 30.552212
## iter  50 value 26.358328
## iter  60 value 21.940774
## iter  70 value 21.862617
## iter  80 value 21.860287
## final  value 21.860281 
## converged
## # weights:  247
## initial  value 395.127787 
## iter  10 value 77.670501
## iter  20 value 46.107871
## iter  30 value 37.412720
## iter  40 value 32.364264
## iter  50 value 25.040275
## iter  60 value 19.860236
## iter  70 value 15.488320
## iter  80 value 13.287123
## iter  90 value 12.752815
## iter 100 value 12.714153
## final  value 12.714153 
## stopped after 100 iterations
## # weights:  411
## initial  value 347.534493 
## iter  10 value 34.592515
## iter  20 value 16.578743
## iter  30 value 10.844778
## iter  40 value 9.629021
## iter  50 value 8.792030
## iter  60 value 8.428157
## iter  70 value 8.385866
## iter  80 value 8.362507
## iter  90 value 8.361327
## iter 100 value 8.361138
## final  value 8.361138 
## stopped after 100 iterations
## # weights:  83
## initial  value 325.078075 
## iter  10 value 39.207835
## iter  20 value 33.044497
## iter  30 value 22.915520
## iter  40 value 22.854877
## iter  50 value 22.853160
## iter  60 value 19.565324
## iter  70 value 19.169659
## iter  80 value 19.166065
## iter  90 value 19.164044
## iter 100 value 19.162303
## final  value 19.162303 
## stopped after 100 iterations
## # weights:  247
## initial  value 381.280502 
## iter  10 value 26.582402
## iter  20 value 21.426055
## iter  30 value 21.227402
## iter  40 value 19.241281
## iter  50 value 15.286576
## iter  60 value 15.267535
## iter  70 value 15.257189
## iter  80 value 15.252443
## iter  90 value 15.245505
## iter 100 value 15.241917
## final  value 15.241917 
## stopped after 100 iterations
## # weights:  411
## initial  value 385.211649 
## iter  10 value 18.277608
## iter  20 value 7.177657
## iter  30 value 1.681694
## iter  40 value 1.556520
## iter  50 value 1.529355
## iter  60 value 1.502919
## iter  70 value 1.440263
## iter  80 value 0.110011
## iter  90 value 0.093966
## iter 100 value 0.088360
## final  value 0.088360 
## stopped after 100 iterations
## # weights:  83
## initial  value 347.208663 
## iter  10 value 186.365060
## iter  20 value 67.729968
## iter  30 value 58.257140
## iter  40 value 58.252905
## iter  50 value 54.045032
## iter  60 value 54.042663
## iter  70 value 54.042461
## final  value 54.042459 
## converged
## # weights:  247
## initial  value 312.113077 
## iter  10 value 46.493217
## iter  20 value 39.873209
## iter  30 value 39.644910
## iter  40 value 39.306371
## iter  50 value 39.251848
## iter  60 value 38.852498
## iter  70 value 38.840106
## iter  80 value 38.839901
## iter  90 value 38.677097
## iter 100 value 38.617816
## final  value 38.617816 
## stopped after 100 iterations
## # weights:  411
## initial  value 300.552579 
## iter  10 value 15.585435
## iter  20 value 9.514834
## iter  30 value 7.716820
## iter  40 value 7.188319
## iter  50 value 7.139834
## iter  60 value 7.127998
## iter  70 value 4.771481
## iter  80 value 4.620824
## iter  90 value 4.615926
## iter 100 value 4.597679
## final  value 4.597679 
## stopped after 100 iterations
## # weights:  83
## initial  value 322.607546 
## iter  10 value 120.020873
## iter  20 value 68.151574
## iter  30 value 42.828788
## iter  40 value 30.232388
## iter  50 value 23.823618
## iter  60 value 22.654288
## iter  70 value 22.397084
## iter  80 value 22.334864
## iter  90 value 22.325904
## iter 100 value 22.321285
## final  value 22.321285 
## stopped after 100 iterations
## # weights:  247
## initial  value 420.254648 
## iter  10 value 59.013405
## iter  20 value 26.311798
## iter  30 value 16.355978
## iter  40 value 14.973845
## iter  50 value 14.428144
## iter  60 value 14.143222
## iter  70 value 14.036036
## iter  80 value 13.943858
## iter  90 value 13.902017
## iter 100 value 13.866617
## final  value 13.866617 
## stopped after 100 iterations
## # weights:  411
## initial  value 381.988851 
## iter  10 value 44.236412
## iter  20 value 24.776275
## iter  30 value 17.192349
## iter  40 value 15.277607
## iter  50 value 13.284299
## iter  60 value 10.918848
## iter  70 value 9.496306
## iter  80 value 9.073378
## iter  90 value 8.999449
## iter 100 value 8.984649
## final  value 8.984649 
## stopped after 100 iterations
## # weights:  83
## initial  value 401.070059 
## iter  10 value 43.098192
## iter  20 value 33.058078
## iter  30 value 26.353500
## iter  40 value 22.839703
## iter  50 value 22.836439
## iter  60 value 22.835277
## iter  70 value 18.697529
## iter  80 value 15.234638
## iter  90 value 15.233030
## iter 100 value 15.232286
## final  value 15.232286 
## stopped after 100 iterations
## # weights:  247
## initial  value 313.002738 
## iter  10 value 42.572011
## iter  20 value 42.464848
## iter  30 value 41.934093
## iter  40 value 41.457126
## iter  50 value 41.067206
## iter  60 value 40.913579
## iter  70 value 40.865055
## iter  80 value 37.946890
## iter  90 value 34.965295
## iter 100 value 34.864997
## final  value 34.864997 
## stopped after 100 iterations
## # weights:  411
## initial  value 323.458812 
## iter  10 value 7.017947
## iter  20 value 1.781510
## iter  30 value 0.800011
## iter  40 value 0.178438
## iter  50 value 0.166575
## iter  60 value 0.153104
## iter  70 value 0.138888
## iter  80 value 0.124647
## iter  90 value 0.114195
## iter 100 value 0.107296
## final  value 0.107296 
## stopped after 100 iterations
## # weights:  83
## initial  value 372.186377 
## iter  10 value 35.516922
## iter  20 value 30.190891
## iter  30 value 29.543063
## iter  40 value 29.527497
## iter  50 value 29.525078
## iter  60 value 29.521076
## iter  70 value 29.520121
## iter  80 value 29.519868
## iter  90 value 29.519830
## iter 100 value 29.519723
## final  value 29.519723 
## stopped after 100 iterations
## # weights:  247
## initial  value 348.196422 
## iter  10 value 67.209271
## iter  20 value 48.731305
## iter  30 value 45.163292
## iter  40 value 43.901667
## iter  50 value 41.782432
## iter  60 value 41.196818
## iter  70 value 41.179131
## iter  80 value 40.604475
## iter  90 value 39.100728
## iter 100 value 38.933283
## final  value 38.933283 
## stopped after 100 iterations
## # weights:  411
## initial  value 375.440700 
## iter  10 value 24.999531
## iter  20 value 10.975472
## iter  30 value 3.681002
## iter  40 value 2.362900
## iter  50 value 0.464151
## iter  60 value 0.023842
## iter  70 value 0.003190
## iter  80 value 0.001639
## iter  90 value 0.000465
## iter 100 value 0.000188
## final  value 0.000188 
## stopped after 100 iterations
## # weights:  83
## initial  value 355.343494 
## iter  10 value 65.142462
## iter  20 value 47.372080
## iter  30 value 37.574348
## iter  40 value 26.884776
## iter  50 value 24.944949
## iter  60 value 21.922548
## iter  70 value 21.279979
## iter  80 value 21.261494
## iter  90 value 21.259775
## final  value 21.259772 
## converged
## # weights:  247
## initial  value 346.808588 
## iter  10 value 49.181931
## iter  20 value 23.923815
## iter  30 value 16.285646
## iter  40 value 14.987987
## iter  50 value 14.626359
## iter  60 value 14.595872
## iter  70 value 14.592341
## iter  80 value 14.592292
## iter  80 value 14.592292
## iter  80 value 14.592292
## final  value 14.592292 
## converged
## # weights:  411
## initial  value 301.257159 
## iter  10 value 48.410296
## iter  20 value 25.041698
## iter  30 value 13.157589
## iter  40 value 10.408976
## iter  50 value 9.661210
## iter  60 value 9.434577
## iter  70 value 9.269354
## iter  80 value 9.258845
## iter  90 value 9.216337
## iter 100 value 9.214935
## final  value 9.214935 
## stopped after 100 iterations
## # weights:  83
## initial  value 329.936083 
## iter  10 value 38.035236
## iter  20 value 29.569921
## iter  30 value 29.554229
## iter  40 value 29.550593
## iter  50 value 29.548561
## iter  60 value 29.544628
## iter  70 value 22.892755
## iter  80 value 22.832907
## iter  90 value 22.831293
## iter 100 value 22.830199
## final  value 22.830199 
## stopped after 100 iterations
## # weights:  247
## initial  value 379.062874 
## iter  10 value 39.162589
## iter  20 value 26.606671
## iter  30 value 26.527781
## iter  40 value 26.443090
## iter  50 value 26.351086
## iter  60 value 26.300281
## iter  70 value 22.962106
## iter  80 value 22.813156
## iter  90 value 22.782400
## iter 100 value 19.354953
## final  value 19.354953 
## stopped after 100 iterations
## # weights:  411
## initial  value 358.276627 
## iter  10 value 24.866177
## iter  20 value 20.469382
## iter  30 value 20.147295
## iter  40 value 19.837837
## iter  50 value 19.724894
## iter  60 value 15.856196
## iter  70 value 6.844589
## iter  80 value 3.170871
## iter  90 value 2.206285
## iter 100 value 2.124214
## final  value 2.124214 
## stopped after 100 iterations
## # weights:  83
## initial  value 317.440169 
## iter  10 value 54.923071
## iter  20 value 51.172372
## iter  30 value 51.091985
## final  value 51.091979 
## converged
## # weights:  247
## initial  value 439.239795 
## iter  10 value 46.652621
## iter  20 value 20.691344
## iter  30 value 11.781652
## iter  40 value 7.180477
## iter  50 value 6.207021
## iter  60 value 4.364374
## iter  70 value 4.210725
## iter  80 value 4.191674
## iter  90 value 4.189105
## iter 100 value 3.833204
## final  value 3.833204 
## stopped after 100 iterations
## # weights:  411
## initial  value 377.678789 
## iter  10 value 11.081353
## iter  20 value 3.150839
## iter  30 value 0.165932
## iter  40 value 0.007874
## iter  50 value 0.001463
## iter  60 value 0.000247
## iter  70 value 0.000130
## final  value 0.000098 
## converged
## # weights:  83
## initial  value 365.641033 
## iter  10 value 54.592180
## iter  20 value 34.661442
## iter  30 value 24.123223
## iter  40 value 22.201034
## iter  50 value 21.821299
## iter  60 value 21.782052
## iter  70 value 21.779687
## iter  80 value 21.779588
## final  value 21.779585 
## converged
## # weights:  247
## initial  value 350.780477 
## iter  10 value 58.820904
## iter  20 value 34.178461
## iter  30 value 17.584910
## iter  40 value 12.569362
## iter  50 value 12.052357
## iter  60 value 11.783290
## iter  70 value 11.751100
## iter  80 value 11.750788
## iter  90 value 11.750450
## iter 100 value 11.677639
## final  value 11.677639 
## stopped after 100 iterations
## # weights:  411
## initial  value 359.433557 
## iter  10 value 50.985670
## iter  20 value 21.654904
## iter  30 value 13.173778
## iter  40 value 10.345448
## iter  50 value 9.947984
## iter  60 value 9.894558
## iter  70 value 9.877974
## iter  80 value 9.829511
## iter  90 value 9.594694
## iter 100 value 9.583042
## final  value 9.583042 
## stopped after 100 iterations
## # weights:  83
## initial  value 353.694281 
## iter  10 value 49.536295
## iter  20 value 42.838397
## iter  30 value 42.577492
## iter  40 value 42.571522
## iter  50 value 42.562278
## iter  60 value 42.555152
## iter  70 value 36.331011
## iter  80 value 29.762819
## iter  90 value 29.640346
## iter 100 value 29.637627
## final  value 29.637627 
## stopped after 100 iterations
## # weights:  247
## initial  value 349.495677 
## iter  10 value 27.229579
## iter  20 value 12.230997
## iter  30 value 6.135160
## iter  40 value 5.699552
## iter  50 value 5.688158
## iter  60 value 5.660438
## iter  70 value 4.865054
## iter  80 value 4.273040
## iter  90 value 3.961903
## iter 100 value 2.664277
## final  value 2.664277 
## stopped after 100 iterations
## # weights:  411
## initial  value 325.244422 
## iter  10 value 13.994065
## iter  20 value 5.371401
## iter  30 value 1.946264
## iter  40 value 1.621766
## iter  50 value 0.340361
## iter  60 value 0.250310
## iter  70 value 0.227572
## iter  80 value 0.215527
## iter  90 value 0.168118
## iter 100 value 0.152238
## final  value 0.152238 
## stopped after 100 iterations
## # weights:  83
## initial  value 318.790750 
## iter  10 value 52.858689
## iter  20 value 38.330165
## iter  30 value 32.994238
## iter  40 value 32.989829
## iter  50 value 32.989373
## iter  60 value 32.988995
## iter  70 value 32.988890
## final  value 32.988876 
## converged
## # weights:  247
## initial  value 378.740142 
## iter  10 value 31.265542
## iter  20 value 14.143921
## iter  30 value 4.457114
## iter  40 value 2.402665
## iter  50 value 1.976904
## iter  60 value 1.942636
## iter  70 value 1.929772
## iter  80 value 1.922414
## iter  90 value 1.915049
## iter 100 value 1.912571
## final  value 1.912571 
## stopped after 100 iterations
## # weights:  411
## initial  value 339.631589 
## iter  10 value 9.798732
## iter  20 value 2.502565
## iter  30 value 1.950346
## iter  40 value 1.924779
## iter  50 value 1.919301
## iter  60 value 1.916556
## iter  70 value 1.914399
## iter  80 value 1.912137
## iter  90 value 1.910643
## iter 100 value 1.910323
## final  value 1.910323 
## stopped after 100 iterations
## # weights:  83
## initial  value 375.793406 
## iter  10 value 86.144534
## iter  20 value 51.300483
## iter  30 value 38.700038
## iter  40 value 30.193609
## iter  50 value 26.470177
## iter  60 value 22.800404
## iter  70 value 21.794936
## iter  80 value 21.767107
## iter  90 value 21.766941
## final  value 21.766940 
## converged
## # weights:  247
## initial  value 324.225056 
## iter  10 value 35.990308
## iter  20 value 20.838116
## iter  30 value 16.763917
## iter  40 value 16.174224
## iter  50 value 16.075592
## iter  60 value 16.058033
## iter  70 value 16.057466
## final  value 16.057452 
## converged
## # weights:  411
## initial  value 330.800904 
## iter  10 value 26.244831
## iter  20 value 15.196122
## iter  30 value 10.803513
## iter  40 value 9.972055
## iter  50 value 9.829904
## iter  60 value 9.779015
## iter  70 value 9.718205
## iter  80 value 9.701157
## iter  90 value 9.700747
## iter 100 value 9.700669
## final  value 9.700669 
## stopped after 100 iterations
## # weights:  83
## initial  value 328.406826 
## iter  10 value 65.376300
## iter  20 value 48.068151
## iter  30 value 47.901025
## iter  40 value 47.887847
## iter  50 value 47.832617
## iter  60 value 44.835700
## iter  70 value 44.831758
## iter  80 value 41.766685
## iter  90 value 41.664104
## iter 100 value 41.659349
## final  value 41.659349 
## stopped after 100 iterations
## # weights:  247
## initial  value 447.269008 
## iter  10 value 29.244654
## iter  20 value 10.517168
## iter  30 value 3.692586
## iter  40 value 2.807922
## iter  50 value 2.794028
## iter  60 value 2.789609
## iter  70 value 2.773421
## iter  80 value 2.578589
## iter  90 value 2.575291
## iter 100 value 2.572542
## final  value 2.572542 
## stopped after 100 iterations
## # weights:  411
## initial  value 336.546343 
## iter  10 value 42.561447
## iter  20 value 23.083490
## iter  30 value 21.011181
## iter  40 value 20.951251
## iter  50 value 19.839178
## iter  60 value 15.075206
## iter  70 value 14.759495
## iter  80 value 14.247192
## iter  90 value 11.879146
## iter 100 value 7.796720
## final  value 7.796720 
## stopped after 100 iterations
## # weights:  247
## initial  value 377.554459 
## iter  10 value 36.236384
## iter  20 value 20.791838
## iter  30 value 20.221999
## iter  40 value 17.801853
## iter  50 value 14.888808
## iter  60 value 10.276462
## iter  70 value 7.372925
## iter  80 value 7.338279
## iter  90 value 7.201956
## iter 100 value 7.124445
## final  value 7.124445 
## stopped after 100 iterations

# Predicción en datos de entrenamiento y prueba
resultado_entrenamiento5 <- predict(model5, entrenamiento)
resultado_prueba5 <- predict(model5, prueba)

# Matriz de Confusión
mcre5 <- confusionMatrix(resultado_entrenamiento5, entrenamiento$Class) # matriz de confusion del resultado del entrenamiento
mcre5

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction   0   1
##          0 354   1
##          1   2 191
##                                           
##                Accuracy : 0.9945          
##                  95% CI : (0.9841, 0.9989)
##     No Information Rate : 0.6496          
##     P-Value [Acc > NIR] : <2e-16          
##                                           
##                   Kappa : 0.988           
##                                           
##  Mcnemar's Test P-Value : 1               
##                                           
##             Sensitivity : 0.9944          
##             Specificity : 0.9948          
##          Pos Pred Value : 0.9972          
##          Neg Pred Value : 0.9896          
##              Prevalence : 0.6496          
##          Detection Rate : 0.6460          
##    Detection Prevalence : 0.6478          
##       Balanced Accuracy : 0.9946          
##                                           
##        'Positive' Class : 0               
## 

mcrp5 <- confusionMatrix(resultado_prueba5, prueba$Class) # matriz de confusion del resultado de la prueba
mcrp5

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction  0  1
##          0 86  4
##          1  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 : 0               
## 

6. Modelo con el método rf

# Entrenamiento del modelo
model6 <- train(Class ~ ., 
                data = entrenamiento,
                method = "rf", 
                preProcess = c("scale", "center"),
                trControl = trainControl(method = "cv", number = 10),
                tuneGrid = expand.grid(mtry=c(2,4,6))
                )

# Predicción en datos de entrenamiento y prueba
resultado_entrenamiento6 <- predict(model6, entrenamiento)
resultado_prueba6 <- predict(model6, prueba)

# Matriz de Confusión
mcre6 <- confusionMatrix(resultado_entrenamiento6, entrenamiento$Class) # matriz de confusion del resultado del entrenamiento
mcre6

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction   0   1
##          0 356   1
##          1   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 : 0          
## 

mcrp6 <- confusionMatrix(resultado_prueba6, prueba$Class) # matriz de confusion del resultado de la prueba
mcrp6

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction  0  1
##          0 86  3
##          1  2 44
##                                           
##                Accuracy : 0.963           
##                  95% CI : (0.9157, 0.9879)
##     No Information Rate : 0.6519          
##     P-Value [Acc > NIR] : <2e-16          
##                                           
##                   Kappa : 0.918           
##                                           
##  Mcnemar's Test P-Value : 1               
##                                           
##             Sensitivity : 0.9773          
##             Specificity : 0.9362          
##          Pos Pred Value : 0.9663          
##          Neg Pred Value : 0.9565          
##              Prevalence : 0.6519          
##          Detection Rate : 0.6370          
##    Detection Prevalence : 0.6593          
##       Balanced Accuracy : 0.9567          
##                                           
##        'Positive' Class : 0               
## 

Resumen de Resultados

resultados <- data.frame(
  "svmLinear" = c(mcre$overall["Accuracy"], mcrp$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"]),
  "nnet" = c(mcre5$overall["Accuracy"], mcrp5$overall["Accuracy"]),
  "rf" = c(mcre6$overall["Accuracy"], mcrp6$overall["Accuracy"])
)

rownames(resultados) <- c("Precisión de entrenamiento", "Precisión de prueba")
resultados

##                            svmLinear svmRadial   svmPoly     rpart      nnet
## Precisión de entrenamiento 1.0000000 1.0000000 1.0000000 0.9507299 0.9945255
## Precisión de prueba        0.9111111 0.6962963 0.9111111 0.9407407 0.9555556
##                                   rf
## Precisión de entrenamiento 0.9981752
## Precisión de prueba        0.9629630

Conclusiones

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

Acorde al resumen de resultados, el mejor modelo es el de Arboles de Decisiones