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1# Question 4.2: Iris clustering with k-means23data(iris)45dim(iris)6names(iris)7head(iris)8table(iris$Species)910# Step 2: I will Keep only the four predictors for k-means11# Species is not included.1213iris_predictors <- iris[, 1:4]1415head(iris_predictors)16summary(iris_predictors)1718# Step 3: Test possible numbers of clusters19# Elbow Method2021set.seed(6501)2223k_values <- 2:624within_ss <- numeric(length(k_values))2526for (i in seq_along(k_values)) {27  28  model <- kmeans(29    iris_predictors,30    centers = k_values[i],31    nstart = 5032  )33  34  within_ss[i] <- model$tot.withinss35}3637data.frame(38  k = k_values,39  total_within_cluster_sum_of_squares = within_ss40)4142plot(43  k_values,44  within_ss,45  type = "b",46  xlab = "Number of clusters (k)",47  ylab = "Total within-cluster sum of squares",48  main = "Elbow Method for Iris Data"49)5051# Step 4: Run k-means with k = 3 using all four predictors5253set.seed(6501)5455iris_kmeans_all <- kmeans(56  iris_predictors,57  centers = 3,58  nstart = 5059)6061cluster_table_all <- table(62  Cluster = iris_kmeans_all$cluster,63  Species = iris$Species64)6566cluster_table_all676869# Step 5: Compare all predictor combinations with k = 37071cluster_accuracy <- function(selected_predictors, actual_species) {72  73  set.seed(6501)74  75  model <- kmeans(76    selected_predictors,77    centers = 3,78    nstart = 5079  )80  81  comparison_table <- table(82    Cluster = model$cluster,83    Species = actual_species84  )85  86  sum(apply(comparison_table, 1, max)) / length(actual_species)87}8889predictor_names <- names(iris)[1:4]9091combination_results <- data.frame(92  predictors = character(),93  accuracy = numeric()94)9596for (size in seq_along(predictor_names)) {97  98  combinations <- combn(99    predictor_names,100    size,101    simplify = FALSE102  )103  104  for (variables in combinations) {105    106    current_accuracy <- cluster_accuracy(107      iris[, variables, drop = FALSE],108      iris$Species109    )110    111    combination_results <- rbind(112      combination_results,113      data.frame(114        predictors = paste(variables, collapse = " + "),115        accuracy = current_accuracy116      )117    )118  }119}120121combination_results <- combination_results[122  order(-combination_results$accuracy),123]124125combination_results126127128# Step 6: Final best k-means model129130best_predictors <- c(131  "Petal.Length",132  "Petal.Width"133)134135set.seed(6501)136137best_iris_model <- kmeans(138  iris[, best_predictors],139  centers = 3,140  nstart = 50141)142143best_cluster_table <- table(144  Cluster = best_iris_model$cluster,145  Species = iris$Species146)147148best_accuracy <- sum(149  apply(best_cluster_table, 1, max)150) / nrow(iris)151152best_cluster_table153best_accuracy

1# Excerpt: data is loaded by the full script.2model <- ksvm(3  as.matrix(data[, 1:10]),4  as.factor(data[, 11]),5  type = "C-svc",6  kernel = "vanilladot",7  C = 0.01,8  scaled = TRUE9)