Machine Learning

leg.ufpr.br/~walmes/ensino/ML

1 Classificação de cultivares de uva de vinho

Os dados são medidas de comprimento feitos em 100 folhas de 3 variedades de uva: malbec, marlot e souvignon blanc. Os dados foram fornecidos pelo pesquisador João Peterson Pereira Gardin. Os valores de área das folhas foram determinados por análise de imagem das folhas digitalizadas por scanner usando o pacote EBImage.

#-----------------------------------------------------------------------
# Pacotes.

library(lattice)
library(latticeExtra)

#-----------------------------------------------------------------------
# Dados hospedados na web.

url <- "http://www.leg.ufpr.br/~walmes/data/areafoliarUva.txt"
uva <- read.table(url, header = TRUE, sep = "\t",
                  stringsAsFactors = FALSE)
uva$cult <- factor(uva$cult)
uva$id <- NULL

# Comprimento da nervura lateral: média dos lados direito e esquerdo.
uva$nl <- with(uva, apply(cbind(nld, nle), 1, mean))
uva <- subset(uva, select = -c(nld, nle))
str(uva)
## 'data.frame':    300 obs. of  7 variables:
##  $ cult: Factor w/ 3 levels "malbec","merlot",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ area: num  100.8 85.8 119.5 137 84.7 ...
##  $ mc  : num  12 11.5 12.5 15.5 10 12 15.5 17.5 13.5 13.3 ...
##  $ nc  : num  7.5 9 8.5 10 7 8.5 11 13 10 9.5 ...
##  $ ml  : num  12.8 10.5 13 14.4 11 12 14 14 12 15 ...
##  $ cll : num  9.5 9.5 10.2 12 7.5 8.9 13.5 10.8 9.7 10.3 ...
##  $ nl  : num  6.95 7.75 8.8 9.5 6.75 ...
splom(uva[-(1:2)],
      groups = uva$cult,
      auto.key = TRUE,
      as.matrix = TRUE,
      cex = 0.2)

# IMPORTANT: padronizar as variáveis para reduzir problemas de escala.
str(uva)
## 'data.frame':    300 obs. of  7 variables:
##  $ cult: Factor w/ 3 levels "malbec","merlot",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ area: num  100.8 85.8 119.5 137 84.7 ...
##  $ mc  : num  12 11.5 12.5 15.5 10 12 15.5 17.5 13.5 13.3 ...
##  $ nc  : num  7.5 9 8.5 10 7 8.5 11 13 10 9.5 ...
##  $ ml  : num  12.8 10.5 13 14.4 11 12 14 14 12 15 ...
##  $ cll : num  9.5 9.5 10.2 12 7.5 8.9 13.5 10.8 9.7 10.3 ...
##  $ nl  : num  6.95 7.75 8.8 9.5 6.75 ...
uva$larea <- log10(uva$area)
uva$area <- NULL

uva[, -1] <- sapply(uva[, -1], FUN = scale)
str(uva)
## 'data.frame':    300 obs. of  7 variables:
##  $ cult : Factor w/ 3 levels "malbec","merlot",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ mc   : num  -0.377 -0.519 -0.235 0.617 -0.945 ...
##  $ nc   : num  -0.765 -0.191 -0.382 0.192 -0.956 ...
##  $ ml   : num  0.0462 -0.7287 0.1135 0.5852 -0.5603 ...
##  $ cll  : num  -0.391 -0.391 -0.139 0.511 -1.113 ...
##  $ nl   : num  -0.699 -0.3 0.225 0.574 -0.799 ...
##  $ larea: num  -0.109 -0.4 0.2 0.448 -0.425 ...
# Verifica se a média 0 e variância 1.
# apply(uva[, -1], 2, mean, na.rm = TRUE)
# apply(uva[, -1], 2, sd, na.rm = TRUE)

2 Explorando utilidades no pacote kernlab

library(kernlab)

# Chamada com apenas duas classes. Simplificar para aprender.
da <- uva
levels(da$cult) <- c("malbec-merlot", "malbec-merlot", "sauvignonblanc")
table(da$cult)
## 
##  malbec-merlot sauvignonblanc 
##            200            100
m0 <- ksvm(cult ~ ., data = da)
m0
## Support Vector Machine object of class "ksvm" 
## 
## SV type: C-svc  (classification) 
##  parameter : cost C = 1 
## 
## Gaussian Radial Basis kernel function. 
##  Hyperparameter : sigma =  0.374508321409246 
## 
## Number of Support Vectors : 209 
## 
## Objective Function Value : -175.957 
## Training error : 0.253333
# Classe e funções disponíveis.
class(m0)
## [1] "ksvm"
## attr(,"package")
## [1] "kernlab"
isS4(m0)
## [1] TRUE
methods(class = class(m0))
##  [1] alphaindex alpha      b          coef       cross      error     
##  [7] fitted     kcall      kernelf    kpar       lev        nSV       
## [13] obj        param      plot       predict    prior      prob.model
## [19] scaling    show       SVindex    type       xmatrix    ymatrix   
## see '?methods' for accessing help and source code
# Número de vetores de suporte.
nSV(m0)
## [1] 209
# Classficação nas observações de treino.
table(fitted(m0))
## 
##  malbec-merlot sauvignonblanc 
##            240             60
# Desempenho na classificação.
abs(c("Acerto" = 1, "Erro" = 0) - error(m0))
##    Acerto      Erro 
## 0.7466667 0.2533333
# ATTENTION: Cuidado que o modelo ingênuo irá acertar 1/2.

# Parâmetros do SVM.
param(m0)
## $C
## [1] 1
# Só funciona para classificações binárias com duas preditoras.
# plot(m0)

splom(~da[, -1] | da$cult,
      groups = fitted(m0),
      auto.key = list(title = "Classificação"))

# Matriz de confusão.
ct <- table(fitted(m0), da$cult)
prop.table(ct)
##                 
##                  malbec-merlot sauvignonblanc
##   malbec-merlot      0.6066667      0.1933333
##   sauvignonblanc     0.0600000      0.1400000
# Percentual de acerto na classificação (já visto antes).
100 * sum(diag(ct))/sum(ct)
## [1] 74.66667
#-----------------------------------------------------------------------
# Usando funções kernel e fazendo tunnings arbitrários.

# Agora é a classificação das 3 espécies de uva.
m0 <- ksvm(cult ~ .,
           data = uva,
           scaled = TRUE,  # Padronizar com média 0 e variância 1.
           type = "C-svc", # Emprego: classificação/regressão, etc.
           C = 50,         # Parâmetro de penalização.
           kernel = "rbfdot",        # Função kernel.
           kpar = list(sigma = 0.1), # Parâmetros da função kernel.
           cross = 1)      # Quantidade de folds para validação cruzada.
## 
##  cross should be >1 no cross-validation done! 
## 
m0
## Support Vector Machine object of class "ksvm" 
## 
## SV type: C-svc  (classification) 
##  parameter : cost C = 50 
## 
## Gaussian Radial Basis kernel function. 
##  Hyperparameter : sigma =  0.1 
## 
## Number of Support Vectors : 230 
## 
## Objective Function Value : -4267.729 -5455.378 -3393.475 
## Training error : 0.303333
# ATTENTION

# Matriz de confusão.
ct <- table(uva$cult, fitted(m0))
prop.table(ct)
##                 
##                      malbec     merlot sauvignonblanc
##   malbec         0.19666667 0.05333333     0.08333333
##   merlot         0.04666667 0.24666667     0.04000000
##   sauvignonblanc 0.06666667 0.01333333     0.25333333
# Gráfico de mosaico da matriz de confusão.
mosaicplot(ct,
           color = brewer.pal(n = nlevels(uva$cult),
                              name = "Spectral"))

# Percentual de acerto na classificação.
100 * sum(diag(ct))/sum(ct)
## [1] 69.66667
1 - error(m0)
## [1] 0.6966667
#-----------------------------------------------------------------------
# Mais variações.

# Para diminuir o número de vetores de suporte.
m0 <- ksvm(cult ~ .,
           data = uva,
           scaled = TRUE,
           type = "C-svc",
           kernel = "rbfdot",
           kpar = list(sigma = 0.01),
           C = 1e5,
           cross = 1)
## 
##  cross should be >1 no cross-validation done! 
## 
m0
## Support Vector Machine object of class "ksvm" 
## 
## SV type: C-svc  (classification) 
##  parameter : cost C = 1e+05 
## 
## Gaussian Radial Basis kernel function. 
##  Hyperparameter : sigma =  0.01 
## 
## Number of Support Vectors : 198 
## 
## Objective Function Value : -7051232 -8357558 -4886157 
## Training error : 0.23
1 - error(m0)
## [1] 0.77
# Kernel linear (baunilha).
m0 <- ksvm(cult ~ .,
           data = uva,
           scaled = TRUE,
           type = "nu-svc",
           kernel = "vanilladot",
           nu = 0.5,
           cross = 1)
##  Setting default kernel parameters  
## 
##  cross should be >1 no cross-validation done! 
## 
m0
## Support Vector Machine object of class "ksvm" 
## 
## SV type: nu-svc  (classification) 
##  parameter : nu = 0.5 
## 
## Linear (vanilla) kernel function. 
## 
## Number of Support Vectors : 225 
## 
## Objective Function Value : 42.5648 320.9918 16.3111 
## Training error : 0.42
1 - error(m0)
## [1] 0.58

3 Explorando utilidades no pacote e1071

library(e1071)

# Especificação com fórmula.
m1 <- svm(cult ~ .,
          data = uva)
summary(m1)
## 
## Call:
## svm(formula = cult ~ ., data = uva)
## 
## 
## Parameters:
##    SVM-Type:  C-classification 
##  SVM-Kernel:  radial 
##        cost:  1 
##       gamma:  0.1666667 
## 
## Number of Support Vectors:  263
## 
##  ( 98 77 88 )
## 
## 
## Number of Classes:  3 
## 
## Levels: 
##  malbec merlot sauvignonblanc
# str(m1)

# Quantidade e coordenadas dos pontos de suporte.
m1$tot.nSV
## [1] 263
m1$nSV
## [1] 98 77 88
head(m1$SV)
##           mc         nc          ml        cll         nl       larea
## 1 -0.3771832 -0.7647780  0.04615744 -0.3910711 -0.6988537 -0.10946742
## 2 -0.5191593 -0.1908119 -0.72874853 -0.3910711 -0.2995563 -0.39990852
## 3 -0.2352071 -0.3821339  0.11354057 -0.1385344  0.2245216  0.20007331
## 4  0.6166496  0.1918322  0.58522247  0.5108456  0.5739069  0.44769609
## 5 -0.9450877 -0.9561001 -0.56029071 -1.1126045 -0.7986780 -0.42505850
## 6 -0.3771832 -0.3821339 -0.22337507 -0.6075311  0.1246973  0.03131424
#-----------------------------------------------------------------------
# Fazendo a tunagem com a grid search.

# tune() é uma função do e1071 que permite avaliar o modelo em vários
# valores para os hiperparâmetros.
# help(tune, h = "html")

# Configura.
x <- as.matrix(subset(uva, select = -cult))
y <- uva$cult
tune <- tune(method = svm,
             train.x = x,
             train.y = y,
             kernel = "radial",
             ranges = list(cost = 10^seq(-2, 5, l = 8),
                           gamma = 2^seq(-3, 3, l = 8)),
             tunecontrol = tune.control(cross = 5))
print(tune)
## 
## Parameter tuning of 'svm':
## 
## - sampling method: 5-fold cross validation 
## 
## - best parameters:
##  cost gamma
##  1000 0.125
## 
## - best performance: 0.4033333
# ATTENTION: o acerto do modelo ingênuo é 1/3.

# A superfície do erro.
levelplot(error ~ log10(cost) + log2(gamma),
          data = tune$performances,
          contour = TRUE) +
    layer(panel.abline(v = log10(cost), h = log2(gamma), lty = 2),
          data = tune$best.model)

# Usando os valores otimizados na validação cruzada.
m2 <- svm(cult ~ .,
          data = uva,
          kernel = "radial",
          cost = tune$best.model$cost,
          gamma = tune$best.model$gamma)
summary(m2)
## 
## Call:
## svm(formula = cult ~ ., data = uva, kernel = "radial", cost = tune$best.model$cost, 
##     gamma = tune$best.model$gamma)
## 
## 
## Parameters:
##    SVM-Type:  C-classification 
##  SVM-Kernel:  radial 
##        cost:  1000 
##       gamma:  0.125 
## 
## Number of Support Vectors:  201
## 
##  ( 73 59 69 )
## 
## 
## Number of Classes:  3 
## 
## Levels: 
##  malbec merlot sauvignonblanc
yfit <- predict(m2)
ct <- table(yfit, y)
ct
##                 y
## yfit             malbec merlot sauvignonblanc
##   malbec             80      9              8
##   merlot              8     86              3
##   sauvignonblanc     12      5             89
sum(diag(ct))/sum(ct)
## [1] 0.85

O código abaixo foi aperfeiçoado do material http://rischanlab.github.io/SVM.html e trabalha os dados de especies de iris em iris.

#-----------------------------------------------------------------------
# Usando com todas as variáveis e 3 classes de espécie e avaliando
# diferentes funções kernel.

# Nomes das funções kernel.
ker <- c("linear", "polynomial", "radial", "sigmoid")

# Ajusta com cada opção de kernel.
svm0 <- sapply(ker,
               simplify = FALSE,
               FUN = function(k) {
                   svm(Species ~ Petal.Length + Sepal.Length,
                       data = iris,
                       kernel = k)
               })
# lapply(svm0, summary)

# Número de pontos de suporte.
colSums(sapply(svm0, getElement, "nSV"))
##     linear polynomial     radial    sigmoid 
##         49         60         57         64
# Tabelas de confusão.
lapply(svm0,
       FUN = function(model) {
           ct <- table(iris$Species, predict(model))
           cat("Acertos:", 100 * sum(diag(ct))/sum(ct), "\n")
           return(ct)
       })
## Acertos: 97.33333 
## Acertos: 90 
## Acertos: 96 
## Acertos: 72.66667
## $linear
##             
##              setosa versicolor virginica
##   setosa         50          0         0
##   versicolor      0         47         3
##   virginica       0          1        49
## 
## $polynomial
##             
##              setosa versicolor virginica
##   setosa         50          0         0
##   versicolor      0         50         0
##   virginica       0         15        35
## 
## $radial
##             
##              setosa versicolor virginica
##   setosa         50          0         0
##   versicolor      0         48         2
##   virginica       0          4        46
## 
## $sigmoid
##             
##              setosa versicolor virginica
##   setosa         50          0         0
##   versicolor      4         23        23
##   virginica       0         14        36
# Gerando um grid no retângulo que contém os pontos.
grid <- with(iris,
             expand.grid(Sepal.Length = seq(min(Sepal.Length),
                                            max(Sepal.Length),
                                            l = 51),
                         Petal.Length = seq(min(Petal.Length),
                                            max(Petal.Length),
                                            l = 51)))

y <- lapply(svm0, FUN = predict, newdata = grid)
y <- lapply(y, as.data.frame)
names(y) <- ker
y <- plyr::ldply(y)
names(y) <- c("kernel", "y")

grid <- cbind(grid, y)
# str(grid)

# Exibindo a fronteira de classificação.
xyplot(Petal.Length ~ Sepal.Length | kernel,
       data = grid,
       groups = y,
       pch = 3,
       as.table = TRUE,
       aspect = 1,
       auto.key = list(columns = 3)) +
    as.layer(xyplot(Petal.Length ~ Sepal.Length,
                    data = iris,
                    pch = 19,
                    groups = Species))

4 Tunning de hiperparâmentros com o caret

Adaptação feita baseada no material http://dataaspirant.com/2017/01/19/support-vector-machine-classifier-implementation-r-caret-package/.

Modelos disponíveis no caret: https://rdrr.io/cran/caret/man/models.html.

Modelos de máquinas de vetores de suporte: https://topepo.github.io/caret/train-models-by-tag.html#support-vector-machines.

library(caret)
packageVersion("caret")
## [1] '6.0.77'
# Modelos de SVM.
names(getModelInfo(model = "^svm"))
##  [1] "svmBoundrangeString" "svmExpoString"       "svmLinear"          
##  [4] "svmLinear2"          "svmLinear3"          "svmLinearWeights"   
##  [7] "svmLinearWeights2"   "svmPoly"             "svmRadial"          
## [10] "svmRadialCost"       "svmRadialSigma"      "svmRadialWeights"   
## [13] "svmSpectrumString"
# Definir a semente para haver reprodutibilidade.
set.seed(1234)

# Especificação da validação cruzada.
trctrl <- trainControl(method = "repeatedcv",
                       number = 5,
                       repeats = 3,
                       returnResamp = "all",
                       savePredictions = "all")

# Ajuste.
svm_Linear <- train(cult ~ .,
                    data = uva,
                    method = "svmLinear",
                    trControl = trctrl)

# Resultado do ajuste.
svm_Linear
## Support Vector Machines with Linear Kernel 
## 
## 300 samples
##   6 predictors
##   3 classes: 'malbec', 'merlot', 'sauvignonblanc' 
## 
## No pre-processing
## Resampling: Cross-Validated (5 fold, repeated 3 times) 
## Summary of sample sizes: 240, 240, 240, 240, 240, 240, ... 
## Resampling results:
## 
##   Accuracy  Kappa
##   0.55      0.325
## 
## Tuning parameter 'C' was held constant at a value of 1
# Estrutura.
# str(svm_Linear)
names(svm_Linear)
##  [1] "method"       "modelInfo"    "modelType"    "results"     
##  [5] "pred"         "bestTune"     "call"         "dots"        
##  [9] "metric"       "control"      "finalModel"   "preProcess"  
## [13] "trainingData" "resample"     "resampledCM"  "perfNames"   
## [17] "maximize"     "yLimits"      "times"        "levels"      
## [21] "terms"        "coefnames"    "xlevels"
# Mostra que foi feito a chamada da kernlab::ksvm().
svm_Linear$finalModel
## Support Vector Machine object of class "ksvm" 
## 
## SV type: C-svc  (classification) 
##  parameter : cost C = 1 
## 
## Linear (vanilla) kernel function. 
## 
## Number of Support Vectors : 253 
## 
## Objective Function Value : -133.5853 -139.6498 -105.8677 
## Training error : 0.406667
# Matriz de confusão.
confusionMatrix(svm_Linear$trainingData$.outcome,
                predict(svm_Linear))
## Confusion Matrix and Statistics
## 
##                 Reference
## Prediction       malbec merlot sauvignonblanc
##   malbec             47     24             29
##   merlot             20     64             16
##   sauvignonblanc     20     13             67
## 
## Overall Statistics
##                                           
##                Accuracy : 0.5933          
##                  95% CI : (0.5354, 0.6494)
##     No Information Rate : 0.3733          
##     P-Value [Acc > NIR] : 9.81e-15        
##                                           
##                   Kappa : 0.39            
##  Mcnemar's Test P-Value : 0.5074          
## 
## Statistics by Class:
## 
##                      Class: malbec Class: merlot Class: sauvignonblanc
## Sensitivity                 0.5402        0.6337                0.5982
## Specificity                 0.7512        0.8191                0.8245
## Pos Pred Value              0.4700        0.6400                0.6700
## Neg Pred Value              0.8000        0.8150                0.7750
## Prevalence                  0.2900        0.3367                0.3733
## Detection Rate              0.1567        0.2133                0.2233
## Detection Prevalence        0.3333        0.3333                0.3333
## Balanced Accuracy           0.6457        0.7264                0.7113
svm_Linear$results
##   C Accuracy Kappa AccuracySD    KappaSD
## 1 1     0.55 0.325 0.06009252 0.09013878
str(svm_Linear$pred)
## 'data.frame':    900 obs. of  5 variables:
##  $ pred    : Factor w/ 3 levels "malbec","merlot",..: 3 1 2 3 1 1 3 3 2 2 ...
##  $ obs     : Factor w/ 3 levels "malbec","merlot",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ rowIndex: int  1 2 4 10 21 24 26 41 46 47 ...
##  $ C       : num  1 1 1 1 1 1 1 1 1 1 ...
##  $ Resample: chr  "Fold1.Rep1" "Fold1.Rep1" "Fold1.Rep1" "Fold1.Rep1" ...
# Desempenho em cada partição.
aggregate(cbind(acc = pred == obs) ~ Resample,
          data = svm_Linear$pred,
          FUN = mean)
##      Resample       acc
## 1  Fold1.Rep1 0.5666667
## 2  Fold1.Rep2 0.6000000
## 3  Fold1.Rep3 0.4666667
## 4  Fold2.Rep1 0.5833333
## 5  Fold2.Rep2 0.5166667
## 6  Fold2.Rep3 0.6333333
## 7  Fold3.Rep1 0.5666667
## 8  Fold3.Rep2 0.6000000
## 9  Fold3.Rep3 0.4833333
## 10 Fold4.Rep1 0.5000000
## 11 Fold4.Rep2 0.5666667
## 12 Fold4.Rep3 0.5166667
## 13 Fold5.Rep1 0.6166667
## 14 Fold5.Rep2 0.4333333
## 15 Fold5.Rep3 0.6000000
#-----------------------------------------------------------------------
# Tunando.

# Parâmetro de penalidade.
grid <- expand.grid(C = c(0.01, 0.05, 0.1, 0.25, 0.5, 0.75,
                          1, 1.25, 1.5, 1.75, 2, 5, 10, 20))

svm_Linear_Grid <- train(cult ~ .,
                         data = uva,
                         method = "svmLinear",
                         trControl = trctrl,
                         tuneGrid = grid)

svm_Linear_Grid
## Support Vector Machines with Linear Kernel 
## 
## 300 samples
##   6 predictors
##   3 classes: 'malbec', 'merlot', 'sauvignonblanc' 
## 
## No pre-processing
## Resampling: Cross-Validated (5 fold, repeated 3 times) 
## Summary of sample sizes: 240, 240, 240, 240, 240, 240, ... 
## Resampling results across tuning parameters:
## 
##   C      Accuracy   Kappa    
##    0.01  0.4677778  0.2016667
##    0.05  0.4911111  0.2366667
##    0.10  0.5111111  0.2666667
##    0.25  0.5522222  0.3283333
##    0.50  0.5477778  0.3216667
##    0.75  0.5566667  0.3350000
##    1.00  0.5588889  0.3383333
##    1.25  0.5533333  0.3300000
##    1.50  0.5555556  0.3333333
##    1.75  0.5544444  0.3316667
##    2.00  0.5555556  0.3333333
##    5.00  0.5744444  0.3616667
##   10.00  0.5788889  0.3683333
##   20.00  0.5811111  0.3716667
## 
## Accuracy was used to select the optimal model using  the largest value.
## The final value used for the model was C = 20.
sc <- list(x = list(log = 2))
c("Performance média" =
      plot(svm_Linear_Grid, scales = sc),
  "Performances por partição" =
      xyplot(svm_Linear_Grid, scales = sc) +
      as.layer(plot(svm_Linear_Grid, scales = sc)))

#-----------------------------------------------------------------------
# Usando kernel radial.

# O parâmetro C já é avaliado em grid.
svm_Radial <- train(cult ~ .,
                    data = uva,
                    method = "svmRadial",
                    trControl = trctrl,
                    tuneLength = 10)
svm_Radial
## Support Vector Machines with Radial Basis Function Kernel 
## 
## 300 samples
##   6 predictors
##   3 classes: 'malbec', 'merlot', 'sauvignonblanc' 
## 
## No pre-processing
## Resampling: Cross-Validated (5 fold, repeated 3 times) 
## Summary of sample sizes: 240, 240, 240, 240, 240, 240, ... 
## Resampling results across tuning parameters:
## 
##   C       Accuracy   Kappa    
##     0.25  0.5577778  0.3366667
##     0.50  0.5644444  0.3466667
##     1.00  0.5611111  0.3416667
##     2.00  0.5700000  0.3550000
##     4.00  0.5688889  0.3533333
##     8.00  0.5577778  0.3366667
##    16.00  0.5500000  0.3250000
##    32.00  0.5411111  0.3116667
##    64.00  0.5311111  0.2966667
##   128.00  0.5255556  0.2883333
## 
## Tuning parameter 'sigma' was held constant at a value of 0.6060484
## Accuracy was used to select the optimal model using  the largest value.
## The final values used for the model were sigma = 0.6060484 and C = 2.
sc <- list(x = list(log = 2))
c("Performance média" =
      plot(svm_Radial, scales = sc),
  "Performances por partição" =
      xyplot(svm_Radial, scales = sc) +
      as.layer(plot(svm_Radial, scales = sc)))

svm_Radial$finalModel
## Support Vector Machine object of class "ksvm" 
## 
## SV type: C-svc  (classification) 
##  parameter : cost C = 2 
## 
## Gaussian Radial Basis kernel function. 
##  Hyperparameter : sigma =  1 
## 
## Number of Support Vectors : 263 
## 
## Objective Function Value : -182.9919 -215.1982 -148.8929 
## Training error : 0.253333
# Número de pontos de suporte.
svm_Radial$finalModel@nSV
## [1] 263
# Acurácia.
1 - error(svm_Radial$finalModel)
## [1] 0.7466667
# str(svm_Radial$finalModel)

#-----------------------------------------------------------------------
# Usando kernel polinomial.

# Gride de configurações para tunning.
grid <- expand.grid(C = 2^seq(-2, 5),
                    degree = c(2, 3),
                    scale = 1,
                    KEEP.OUT.ATTRS = FALSE)
dim(grid)
## [1] 16  3
trctrl <- trainControl(method = "cv",
                       number = 5,
                       returnResamp = "all",
                       savePredictions = "all")

# O parâmetro C já é avaliado em grid.
svm_Poly <- train(cult ~ .,
                  data = uva,
                  method = "svmPoly",
                  trControl = trctrl,
                  tuneGrid = grid)
svm_Poly
## Support Vector Machines with Polynomial Kernel 
## 
## 300 samples
##   6 predictors
##   3 classes: 'malbec', 'merlot', 'sauvignonblanc' 
## 
## No pre-processing
## Resampling: Cross-Validated (5 fold) 
## Summary of sample sizes: 240, 240, 240, 240, 240 
## Resampling results across tuning parameters:
## 
##   C      degree  Accuracy   Kappa
##    0.25  2       0.6066667  0.410
##    0.25  3       0.5900000  0.385
##    0.50  2       0.6133333  0.420
##    0.50  3       0.5833333  0.375
##    1.00  2       0.6266667  0.440
##    1.00  3       0.5866667  0.380
##    2.00  2       0.6333333  0.450
##    2.00  3       0.5733333  0.360
##    4.00  2       0.6366667  0.455
##    4.00  3       0.5966667  0.395
##    8.00  2       0.6266667  0.440
##    8.00  3       0.6166667  0.425
##   16.00  2       0.6200000  0.430
##   16.00  3       0.6033333  0.405
##   32.00  2       0.6266667  0.440
##   32.00  3       0.6066667  0.410
## 
## Tuning parameter 'scale' was held constant at a value of 1
## Accuracy was used to select the optimal model using  the largest value.
## The final values used for the model were degree = 2, scale = 1 and C = 4.
sc <- list(x = list(log = 2))
plot(svm_Poly, scales = sc)

xyplot(svm_Poly,
       scales = sc,
       type = c("p", "a"))

svm_Poly$finalModel
## Support Vector Machine object of class "ksvm" 
## 
## SV type: C-svc  (classification) 
##  parameter : cost C = 4 
## 
## Polynomial kernel function. 
##  Hyperparameters : degree =  2  scale =  1  offset =  1 
## 
## Number of Support Vectors : 208 
## 
## Objective Function Value : -335.2436 -410.6984 -263.2073 
## Training error : 0.3
# Número de pontos de suporte.
svm_Poly$finalModel@nSV
## [1] 208
# Acurácia.
1 - error(svm_Poly$finalModel)
## [1] 0.7
Machine Learning Prof. Eduardo V. Ferreira & Prof. Walmes M. Zeviani
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