Практическая работа №5: Кластерный и регрессионный анализ

data(iris)

iris_normalized <- as.data.frame(scale(iris[, -5]))
iris_normalized$Species <- iris$Species

set.seed(42)
train_index <- sample(1:nrow(iris), size = 0.7 * nrow(iris))
train_data <- iris_normalized[train_index, ]
test_data <- iris_normalized[-train_index, ]

train_features <- train_data[, -5]
test_features <- test_data[, -5]
train_labels <- train_data[, 5]
test_labels <- test_data[, 5]

k_value <- 11
predicted_classes <- knn(train = train_features, test = test_features, cl = train_labels, k = k_value)

cat("Матрица ошибок и статистика для KNN (k=", k_value, "):\n")

## Матрица ошибок и статистика для KNN (k= 11 ):

CrossTable(x = test_labels, y = predicted_classes, prop.chisq = FALSE, prop.c = FALSE, prop.r = FALSE, dnn = c("Actual Class", "Predicted Class"))

## 
##  
##    Cell Contents
## |-------------------------|
## |                       N |
## |         N / Table Total |
## |-------------------------|
## 
##  
## Total Observations in Table:  45 
## 
##  
##              | Predicted Class 
## Actual Class |     setosa | versicolor |  virginica |  Row Total | 
## -------------|------------|------------|------------|------------|
##       setosa |         12 |          0 |          0 |         12 | 
##              |      0.267 |      0.000 |      0.000 |            | 
## -------------|------------|------------|------------|------------|
##   versicolor |          0 |         14 |          1 |         15 | 
##              |      0.000 |      0.311 |      0.022 |            | 
## -------------|------------|------------|------------|------------|
##    virginica |          0 |          1 |         17 |         18 | 
##              |      0.000 |      0.022 |      0.378 |            | 
## -------------|------------|------------|------------|------------|
## Column Total |         12 |         15 |         18 |         45 | 
## -------------|------------|------------|------------|------------|
## 
## 

accuracy <- sum(test_labels == predicted_classes) / length(test_labels)
cat("\nДоля правильных прогнозов (Accuracy):", round(accuracy, 4), "\n")

## 
## Доля правильных прогнозов (Accuracy): 0.9556

iris_svm <- iris
iris_svm$Species <- as.factor(iris_svm$Species)

model_svm <- svm(Species ~ ., data = iris_svm, kernel = "linear", cross = 10, scale = TRUE)

print(model_svm)

## 
## Call:
## svm(formula = Species ~ ., data = iris_svm, kernel = "linear", cross = 10, 
##     scale = TRUE)
## 
## 
## Parameters:
##    SVM-Type:  C-classification 
##  SVM-Kernel:  linear 
##        cost:  1 
## 
## Number of Support Vectors:  29

svm_predictions <- predict(model_svm, iris_svm)

cat("\nМатрица ошибок для SVM (Linear Kernel):\n")

## 
## Матрица ошибок для SVM (Linear Kernel):

table_svm <- table(Predicted = svm_predictions, Actual = iris_svm$Species)
print(table_svm)

##             Actual
## Predicted    setosa versicolor virginica
##   setosa         50          0         0
##   versicolor      0         46         1
##   virginica       0          4        49

svm_accuracy <- sum(diag(table_svm)) / sum(table_svm)
cat("\nДоля правильных прогнозов (SVM Accuracy):", round(svm_accuracy, 4), "\n")

## 
## Доля правильных прогнозов (SVM Accuracy): 0.9667

iris_numeric <- iris[, 1:4]

pca_result <- rda(iris_numeric, scale = TRUE)

summary(pca_result)

## 
## Call:
## rda(X = iris_numeric, scale = TRUE) 
## 
## Partitioning of correlations:
##               Inertia Proportion
## Total               4          1
## Unconstrained       4          1
## 
## Eigenvalues, and their contribution to the correlations 
## 
## Importance of components:
##                          PC1    PC2     PC3      PC4
## Eigenvalue            2.9185 0.9140 0.14676 0.020715
## Proportion Explained  0.7296 0.2285 0.03669 0.005179
## Cumulative Proportion 0.7296 0.9581 0.99482 1.000000

eigenvalues <- pca_result$CA$eig
variance_explained <- eigenvalues / sum(eigenvalues)
cumulative_variance <- cumsum(variance_explained)

cat("\nОбъясненная дисперсия по компонентам:\n")

## 
## Объясненная дисперсия по компонентам:

print(round(data.frame(PC = 1:4, Variance = variance_explained, Cumulative = cumulative_variance), 4))

##     PC Variance Cumulative
## PC1  1   0.7296     0.7296
## PC2  2   0.2285     0.9581
## PC3  3   0.0367     0.9948
## PC4  4   0.0052     1.0000

par(mar = c(5, 4, 4, 2) + 0.1)
plot(pca_result, scaling = 2, main = "PCA Biplot (vegan::rda)", xlab = "PC1", ylab = "PC2")

points(pca_result, display = "sites", col = as.numeric(iris$Species), pch = 19, cex = 0.8)
legend("topright", legend = levels(iris$Species), col = 1:3, pch = 19, title = "Species")

scores_sites <- scores(pca_result, display = "sites", scaling = 2)
scores_species <- scores(pca_result, display = "species", scaling = 2)

df_sites <- as.data.frame(scores_sites)
df_sites$Species <- iris$Species

df_species <- as.data.frame(scores_species)
df_species$Variable <- rownames(df_species)

ggplot() +
  geom_point(data = df_sites, aes(x = PC1, y = PC2, color = Species), alpha = 0.7, size = 3) +
  geom_segment(data = df_species, aes(x = 0, y = 0, xend = PC1, yend = PC2),
               arrow = arrow(length = unit(0.2, "cm")), color = "black") + 
  geom_text(data = df_species, aes(x = PC1, y = PC2, label = Variable),
            vjust = 1.5, hjust = 0.5, color = "black", size = 4) +
  theme_minimal() +
  labs(title = "Ординационная диаграмма PCA (vegan::rda)",
       x = paste0("PC1 (", round(variance_explained[1]*100, 1), "%)"),
       y = paste0("PC2 (", round(variance_explained[2]*100, 1), "%)")) +
  theme(legend.title = element_blank())