
train_qda <- train(y ~., method = "qda", data = train_set)
train_qda$finalModel

Call:
qda(x, grouping = y)

Prior probabilities of groups:
        1         2         7 
0.3641474 0.3123048 0.3235478 

Group means:
         x_1       x_2
1 0.07506762 0.2345093
2 0.12928502 0.2801805
7 0.24040191 0.2956395


y_hat_qda <- predict(train_qda, test_set)
confusionMatrix(data = y_hat_qda, reference = test_set$y)

Confusion Matrix and Statistics

          Reference
Prediction   1   2   7
         1 107  15   6
         2   8 102  17
         7  14  24 106

Overall Statistics
                                          
               Accuracy : 0.7895          
                 95% CI : (0.7461, 0.8285)
    No Information Rate : 0.3534          
    P-Value [Acc > NIR] : < 2e-16         
                                          
                  Kappa : 0.6844          
                                          
 Mcnemar's Test P-Value : 0.08866         

Statistics by Class:

                     Class: 1 Class: 2 Class: 7
Sensitivity            0.8295   0.7234   0.8217
Specificity            0.9222   0.9031   0.8593
Pos Pred Value         0.8359   0.8031   0.7361
Neg Pred Value         0.9188   0.8566   0.9098
Prevalence             0.3233   0.3534   0.3233
Detection Rate         0.2682   0.2556   0.2657
Detection Prevalence   0.3208   0.3183   0.3609
Balanced Accuracy      0.8758   0.8133   0.8405


confusionMatrix(data = y_hat_qda, reference = test_set$y)$overall["Accuracy"]


y_hat_qda <- predict(train_qda, mnist_27$true_p)
y_hat_qda <- as.numeric(levels(y_hat_qda))[y_hat_qda]

options(repr.plot.width=7, repr.plot.height=7)
mnist_27$true_p %>%
  mutate(y_hat = factor(y_hat_qda)) %>%
  ggplot(aes(x_1, x_2,  z=y_hat, fill=y_hat)) +
  geom_raster()


train_lda <- train(y ~., method = "lda", data = train_set)
train_lda$finalModel

Call:
lda(x, grouping = y)

Prior probabilities of groups:
        1         2         7 
0.3641474 0.3123048 0.3235478 

Group means:
         x_1       x_2
1 0.07506762 0.2345093
2 0.12928502 0.2801805
7 0.24040191 0.2956395

Coefficients of linear discriminants:
          LD1       LD2
x_1 12.790861  3.054090
x_2 -2.955191 -9.101932

Proportion of trace:
   LD1    LD2 
0.9832 0.0168


y_hat_lda <- predict(train_lda, test_set)
confusionMatrix(data = y_hat_lda, reference = test_set$y)

Confusion Matrix and Statistics

          Reference
Prediction   1   2   7
         1 100  70   8
         2  14  43  17
         7  15  28 104

Overall Statistics
                                          
               Accuracy : 0.619           
                 95% CI : (0.5694, 0.6669)
    No Information Rate : 0.3534          
    P-Value [Acc > NIR] : < 2.2e-16       
                                          
                  Kappa : 0.4324          
                                          
 Mcnemar's Test P-Value : 3.724e-09       

Statistics by Class:

                     Class: 1 Class: 2 Class: 7
Sensitivity            0.7752   0.3050   0.8062
Specificity            0.7111   0.8798   0.8407
Pos Pred Value         0.5618   0.5811   0.7075
Neg Pred Value         0.8688   0.6985   0.9008
Prevalence             0.3233   0.3534   0.3233
Detection Rate         0.2506   0.1078   0.2607
Detection Prevalence   0.4461   0.1855   0.3684
Balanced Accuracy      0.7432   0.5924   0.8235


confusionMatrix(data = y_hat_lda, reference = test_set$y)$overall["Accuracy"]


y_hat_lda <- predict(train_lda, mnist_27$true_p)
y_hat_lda <- as.numeric(levels(y_hat_lda))[y_hat_lda]
mnist_27$true_p %>%
  mutate(y_hat = factor(y_hat_lda)) %>%
  ggplot(aes(x_1, x_2,  z=y_hat, fill=y_hat)) +
  geom_raster()

QDA¶

LDA¶